A reagent-centred thermal control system driven by a cascade temperature control algorithm for high-speed PCR

Abstract

Accelerating quantitative polymerase chain reaction (qPCR) without compromising analytical fidelity remains a significant challenge in molecular diagnostics, primarily due to the thermal lag between heating elements and reagents. Here, we report a high-speed qPCR platform that overcomes this limitation using a reagent-centric cascade control strategy. The system employs a planar PCB-based copper heater that functions as both a heating element and a temperature sensor, ensuring low-latency, sensor-efficient thermal feedback. To overcome this thermal delay, a virtual temperature sensor—derived from system identification—is used to estimate the real-time reagent temperature, which drives an outer-loop fuzzy PID controller with feedforward compensation. Inner cascaded loops stabilize the heater current and surface temperature. The system achieves reagent-phase average heating and cooling rates of 24.1 °C s⁻¹ and 19 °C s⁻¹, respectively. Furthermore, the reagent temperature is controlled with an accuracy of ±0.2 °C and an overshoot of less than 0.2 °C. A complete 45-cycle amplification is achieved in as little as 4.4 minutes. Crucially, this speed is attained without analytical compromise, demonstrating excellent quantitative accuracy (R² = 0.9965) and amplification efficiency (109.8%). The proposed reagent-centred control framework offers a scalable pathway for developing high-throughput PCR and molecular diagnostic instruments, supporting fast, accurate, and scalable nucleic acid testing.

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Introduction

The polymerase chain reaction (PCR), developed in 1983 by Dr Kary Mullis, has become a well-known method for the specific amplification of nucleic acid fragments in vitro.^1,2 By increasing the number of copies of targeted double-stranded DNA to detectable levels, PCR plays a pivotal role in various fields of experimental research and clinical diagnostics,^3–6 including DNA sequencing,^7–9 forensic identification,^10–13 and paternity testing.^14,15 The recent global outbreak of COVID-19 has further underscored the essential role of PCR in public health, highlighting the urgent need for diagnostic platforms that are not only accurate but also capable of delivering results rapidly.^16–19 Although PCR remains the gold standard for nucleic acid detection due to its high specificity and sensitivity, the conventionally slow thermal cycling process has become a major bottleneck in time-sensitive clinical scenarios. Therefore, accelerating PCR while maintaining analytical fidelity has emerged as a critical challenge in the advancement of molecular diagnostic technologies.

A standard PCR cycle involves three key temperature stages: denaturation (94–98 °C), annealing (40–60 °C), and extension (70–75 °C).^20,21 Denaturation separates the double-stranded DNA, allowing primers to bind during the annealing phase. In the subsequent extension step, a thermostable DNA polymerase synthesizes the complementary strand. In many fast PCR protocols, the annealing and extension stages are merged into a single intermediate-temperature step (typically ∼60 °C).^19,22 This simplification is supported by the overlapping optimal temperature ranges for primer hybridization and polymerase activity, enabling time reduction without sacrificing amplification fidelity. Despite such protocol-level optimizations, standard PCR assays typically require 1–2 hours to yield results.¹⁹

Each cycle involves rapid transitions between precise temperature setpoints, and even slight deviations can compromise amplification efficiency and specificity. Among the factors influencing total assay time, the rate of temperature change is particularly critical. Faster thermal ramping directly reduces the cycle duration, making it a key determinant of overall speed. Consequently, achieving rapid yet accurate temperature control imposes stringent demands on the system design and control algorithm.

In response to these challenges, extensive research efforts have been devoted to improving the design of PCR systems and developing temperature control strategies that enhance thermal responsiveness and precision. Song et al. developed a portable rotary PCR device employing spatial-domain thermocycling, where capillary tubes are mechanically moved between preheated zones to achieve time-efficient amplification with minimal power usage.²³ Ling et al. introduced a serpentine microchannel design incorporating gradient thermal conductivity materials, enabling heating and cooling rates of 7.2 °C s⁻¹ and 6.1 °C s⁻¹, respectively, significantly outperforming conventional fan-based systems.²⁴ Similar improvements were achieved by Nouwairi et al. using dual Peltier modules and chip-level geometric optimization, reaching ramp rates of 12 °C s⁻¹ (heating) and 10 °C s⁻¹ (cooling) while maintaining reliable fluorescence readout.²⁵ Plasmonic photothermal strategies, such as those employed by Cheong et al., reached heating rates over 12 °C s⁻¹, though passive cooling and spatial non-uniformity posed challenges for precise control.²⁶ Leveraging near-instantaneous light-to-heat conversion in nanomaterials, this approach has enabled exceptional heating rates, with some systems reporting over 18 °C s⁻¹. However, as highlighted in recent reviews,²⁷ this method often presents a critical trade-off. While heating is rapid, cooling is frequently limited by slower passive heat dissipation, with reported rates often below 9 °C s⁻¹, and achieving precise, uniform temperature distribution across the reaction volume remains a significant challenge. This leaves a clear need for systems that can provide a more balanced performance profile, combining rapid bidirectional ramping with the high-precision control necessary for quantitative analysis. Beyond the limitations of the heating modality itself, a more fundamental challenge to achieving high-precision control lies in the typical feedback strategy. Most of these systems, from conventional Peltier modules to advanced photothermal designs, control temperature based on the heater or block feedback—rather than directly sensing the reagent temperature—resulting in a persistent thermal lag between the heating interface and the actual reaction zone. This lag should be prevented under rapid cycling protocols, where precise timing and thermal uniformity are essential.

To address this issue, several compensation strategies have been proposed. Amasia et al. introduced temperature overshoot control, allowing the reagent temperature to catch up with the heater temperature through delayed heat transfer.²⁸ Park et al. adopted a fixed offset calibration to align heater and reagent temperatures through empirical zone tuning.²⁹ Wang et al. built a steady-state temperature mapping between a heater and fluid, achieving improved final accuracy (±0.2 °C), but lacked dynamic correction during cycling transitions.³⁰ Huang et al. proposed a spatial-domain PCR system consisting of five independent temperature zones and optimized via thermal simulation and reagent experiments. To mitigate the thermal lag, they manually tuned the temperature overshoot amplitude for a specific reagent setup. While this approach ensured acceptable amplification performance, the actual reagent temperature was neither measured nor estimated.³¹ Shoaee et al. proposed an inverse heat transfer problem (IHTP) approach combining CFD and PSO algorithms to reconstruct boundary conditions that delivered accurate internal reagent temperatures. The method achieved high precision (error <0.1 °C) and shortened cycle times by up to 46%. However, this strategy relied entirely on simulated assumptions without directly measuring the reagent-phase temperature.³²

Even recent advances in integrated “sample-to-answer” microfluidic platforms, which successfully combine upstream nucleic acid extraction with downstream digital PCR, still rely on external, conventional thermal cyclers for amplification and thus do not address the fundamental limitations imposed by the thermal lag.³³ In summary, despite these promising efforts, a persistent gap remains: few systems integrate real-time sensing, dynamic thermal modelling and intelligent control into a deployable platform that addresses the temperature lag of reagents in fast PCR applications.

In this work, we introduce a real-time controllable PCR system that enables ultra-fast thermal cycling through integrated hardware design and intelligent control. The system incorporates a planar copper-based resistive heater, fabricated via PCB technology, which functions as both a heating element and a temperature sensor. This cost-effective, expandable configuration facilitates rapid thermal responsiveness with negligible spatial latency. In order to address the unmeasurable nature of reagent temperature, a virtual sensing model has been developed based on system identification. Utilising M-sequence excitation and least-squares fitting, a dynamic mapping is established from heater to reagent temperature, thereby enabling real-time, sensor-free estimation for reagent-centric control. A three-layer cascade control architecture is implemented: an outer fuzzy PID loop regulates the estimated reagent temperature, while middle and inner discrete-time PI loops stabilize the heater temperature and power, respectively. Multi-rate sampling (10 ms for reagent, 5 ms for heater, and 1 ms for power) ensures synchronisation and stability across thermal domains. All control functions are executed on a Speedgoat real-time platform, which facilitates high-speed actuation, fluorescence signal acquisition, and closed-loop execution. The experimental results obtained demonstrate a temperature precision of ±0.2 °C, thermal ramp rates in excess of 24.1 °C s⁻¹, and the completion of 45 qPCR cycles in less than 8 minutes. Compared to the commercial Thermo Fisher QuantStudio 6 Pro system, our platform achieves comparable amplification accuracy with an over eightfold reduction in assay time. The virtual sensing framework and control strategy proposed here provide a practical path toward embedding high-speed PCR into compact, low-power devices for point-of-care and field diagnostics.

Experimental

Overview and composition of the PCR system

The developed ultra-fast PCR system integrates compact thermal management, fluorescence detection, mechanical actuation, and real-time control into a modular benchtop platform (Fig. 1). Designed for rapid thermal cycling with sub-second responsiveness, the system serves as a flexible platform for control algorithm prototyping and performance benchmarking.

Fig. 1 Photograph of the real-time PCR test platform. Key functional modules, including the thermal module, optical module, and real-time control system, are highlighted with descriptive call-outs.

The thermal module features a planar copper thin-film heater fabricated on a double-layer PCB (Shenzhen Jieduobang Technology Co., Ltd, China), functioning simultaneously as a heating element and temperature sensor. A precision-machined chip slot ensures appropriate alignment with the heater surface. To maintain consistent thermal contact between the chip and the heater, a TST28-31R stepper motor (Yingpeng Aircraft Electromechanical Co., Ltd, Shenzhen, China) applies a vertical compressive force of approximately 50 N during operation.

Joule heating is driven by a voltage-controlled constant-current source (Model BB4808G4, Liuzhou Qiming Electric Technology Co., Ltd, China), which delivers regulated current to the heater. This module is powered by a 24 V switching power supply (Model NDR-240-24, MEAN WELL Enterprises Co., Ltd, Taiwan), providing high-current stability for dynamic thermal control. Active liquid cooling is achieved through a water channel integrated beneath the heater block, enabling rapid bidirectional temperature transitions.

Fluorescence excitation and detection are implemented via a 4-channel optical module (Model GS-PCR-4CH-S5, Shanghai Gous Optics Co., Ltd, China), which integrates multi-wavelength LEDs, bandpass filters, and photodiode sensors. Real-time signal acquisition is conducted during the annealing phase for quantitative monitoring.

All control tasks are deployed on a Speedgoat Performance real-time target (Speedgoat GmbH, Switzerland), programmed via Simulink Real-Time. Multi-rate control loops (1 ms, 5 ms, and 10 ms) govern power regulation, heater surface temperature, and estimated reagent-phase temperature, respectively. Sensor acquisition and actuator output are synchronized through analog and digital I/O channels, enabling closed-loop control, fluorescence triggering, and motor actuation. Although Speedgoat is employed in this study for rapid prototyping, the control architecture is inherently portable to embedded microcontroller platforms such as STM32 or TI C2000. This design flexibility supports future deployment in compact, energy-efficient, and cost-effective hardware suited for point-of-care diagnostics.

The seamless integration of thermal, optical, and control subsystems into a unified framework allows the system to achieve ultra-fast and highly sensitive PCR amplification. The architecture ensures high accuracy and reproducibility, making it particularly suitable for point-of-care diagnostics and high-throughput testing scenarios.

Design and manufacture of microfluidic chips

The overall structure and key dimensions of the fabricated microfluidic chip are illustrated in Fig. 2. The chip has an approximate footprint of 50 mm × 18 mm. It comprises a 500 µm-thick polycarbonate (PC) substrate, which is precision CNC milled to define a reagent inlet and a reaction chamber with a depth of 30 µm. The chamber is sealed with a 65 µm-thick aluminum/polycarbonate (Al/PC) composite film, consisting of a 50 µm-thick aluminum layer bonded to a 15 µm-thick PC backing. The upper surface of this composite film is designed to interface directly with the planar heating element through a defined heater contact surface.

Fig. 2 Schematic of the microfluidic chip.

The substrate, 500 μm in thickness, is fabricated by precision CNC milling to define the microfluidic pathway and chamber geometry. Polycarbonate was selected for its high thermal stability, excellent mechanical strength, and intrinsic optical transparency, which enable real-time fluorescence detection through the body of the framework—eliminating the need for a discrete optical window. Additionally, the structure is compatible with injection molding, facilitating cost-effective transition from laboratory-scale prototyping to large-volume manufacturing using thermoplastic processes.

The cover layer consists of a 50 μm-thick aluminum layer bonded to a 15 μm-thick PC backing. The outward-facing aluminum layer provides high thermal conductivity to facilitate efficient heat transfer from the underlying heater, while the inward-facing PC layer prevents direct contact between aluminum and reagents, maintaining biocompatibility and avoiding undesirable reactions.

Heater design and temperature calibration

The heating and sensing unit of the system is a planar PCB-based copper resistive element fabricated by Shenzhen Jieduobang Technology Co., Ltd. Leveraging mass-produced PCBs as functional components is an emerging and powerful strategy for creating low-cost, scalable point-of-care diagnostic platforms, with applications ranging from electrochemical sensors to integrated thermal systems.³⁴ The detailed conceptual structure and assembly of this thermal module are provided in the SI (see Appendix A, Fig. S1). This structure features patterned copper traces on an FR-4 substrate, which simultaneously serve as both the Joule heating source and resistance temperature detector (RTD). This dual-function configuration enables accurate and low-latency thermal feedback without additional sensors, thanks to the minimal spatial offset between actuation and sensing.

PCB-based copper heaters offer multiple advantages, including low material cost, compatibility with standard PCB manufacturing workflows, and seamless integration into automated production lines. These features make the design suitable for scalable, low-cost, and disposable PCR platforms.

Temperature sensing is based on the well-known linear dependence of copper's electrical resistance on temperature. The resistance–temperature (R–T) behavior follows the expression:

R(T) = R₀[1 + TCR(T − T₀)] (1)

where R₀ is the resistance at reference temperature T₀, and α = 0.00386 °C⁻¹ is the temperature coefficient of resistance (TCR) for copper.

The R–T relationship was calibrated in situ after full system assembly using a self-heating procedure. A PT100 sensor was attached to the heater surface using thermally conductive silicone grease to ensure optimal thermal contact. Input power was gradually increased to raise the surface temperature from 35 °C to 95 °C, allowing thermal equilibrium at each step. The reference temperature was measured using a FLUKE 1586A precision scanner, while the copper resistance was calculated from concurrent voltage and current measurements. This method captures the thermal behavior under actual operation. The resulting calibration curve (Fig. 3) demonstrated excellent linearity (R² = 0.9998), validating the copper trace as a reliable embedded temperature sensor for real-time control. Error bars, representing the standard deviation of n = 3 measurements at each point, are included in the figure. The small size of these error bars, which are in some cases smaller than the data markers, reflects the high precision and stability of the temperature calibration setup.

Fig. 3 Calibration curve of the copper heater's resistance–temperature relationship.

The calibrated resistance–temperature (R–T) relationship of the integrated copper heater enables both direct surface temperature monitoring and reagent-layer estimation. The heater's copper traces serve dually as heating elements and co-located resistive sensors, providing low-latency feedback essential for rapid thermal cycling. The same R–T data were used to train a virtual sensing model that captures the thermal lag between the heater and the reaction fluid, enabling reagent-centric control without additional embedded sensors.

Crucially, this multifunctional device is fabricated on a standard FR-4 substrate using established PCB workflows, making it fully compatible with low-cost, large-scale production. Its integration into automated assembly lines and suitability for disposable use support practical translation to scalable, point-of-care PCR applications.

Real-time control platform

The PCR system was implemented using a rapid control prototyping (RCP) framework based on a Speedgoat Baseline Performance real-time target. This RCP configuration allowed for the direct, real-time control of the physical hardware to validate the proposed algorithm, distinguishing it from a purely simulation-based study. As shown in Fig. 4, the architecture comprises a virtual host interface, a real-time simulation core, modular I/O layers, and physical hardware modules including the heater, fluorescence detection unit, and microfluidic chip.

Fig. 4 Real-time control architecture of the integrated PCR platform.

All control logic—including virtual temperature estimation, fuzzy-tuned PID regulation, and multi-loop cascade control—was developed in MATLAB/Simulink and deployed to the real-time target via Simulink Real-Time. Control tasks were executed deterministically with a synchronized schedule to evaluate the system, and sampling intervals were matched to the physical time constants of each subsystem. The outer-loop fuzzy PID controller, responsible for reagent-phase temperature regulation, was updated every 10 ms. The heater surface temperature loop and power delivery loop were updated at 5 ms and 1 ms, respectively, to accommodate faster thermal and electrical dynamics.

Three Speedgoat I/O modules interfaced with the physical system. The IO171 module acquired thermocouple signals from within the reaction chamber, used for offline validation and dynamic model training. The IO132 module captured the heater voltage and current in real time for resistance-based temperature inference, and simultaneously issued analog output signals to control a voltage-controlled current source (VCCS) that drove the copper heating resistance. The IO503 serial interface managed bidirectional RS-485 communication: at the start of each run, it activated a stepper motor to apply force on the microfluidic chip, ensuring robust thermal contact with the heater; during cycling, it triggered and retrieved real-time fluorescence data from the optical detection module.

The system's layered communication architecture also enabled Ethernet-based real-time interaction with the host computer for status monitoring, parameter tuning, and performance logging. All modules were abstracted as reusable function blocks, facilitating streamlined algorithm development and hardware integration.

Importantly, although Speedgoat served as the prototyping backbone, all control algorithms were designed for embedded deployment. The code structure, computational load, and I/O dependencies were optimized to support direct migration to low-power microcontroller platforms (e.g., STM32 or TI C2000). This ensures future scalability for point-of-care applications, enabling compact, low-cost, and field-deployable PCR instrumentation without compromising control performance.

Materials and reagents

To evaluate the system's potential for clinical application, nucleic acid amplification was performed using a synthetic plasmid containing a 190 bp target fragment from Mycoplasma pneumoniae (MP). The plasmid was cloned into the pUC-GW-Kan vector and synthesized by Azenta Life Sciences (GENEWIZ, China), delivered lyophilized and reconstituted in 1× TE buffer (low EDTA, pH 8.0; Sangon Biotech, Shanghai, China). The plasmid solution was stored at −20 °C until analysis. Prior to testing, the stock solution was diluted with 1× TE buffer to appropriate concentrations depending on experimental requirements.

All PCR reactions were conducted using a commercial one-step real-time PCR kit (CK-3, Vazyme Biotech, China), comprising a 5× One Step U + Mix and a One Step U + Enzyme Mix. The assay targets Mycoplasma pneumoniae using specific primers and dual-labeled hydrolysis probes. Each 50 μL reaction contained 10 μL of 5× One Step U + Mix, 5 μL of Enzyme Mix, 4 μL of MP primer–probe mix (final concentrations: 0.6 μM primers and 0.3 μM probes for each target), and 31 μL of plasmid DNA template. The detailed formulation is listed in Table 1.

Table 1 Composition of the reaction mixture for one-step real-time PCR (50 μL)

Component	Volume (per 50 μL reaction)
5× one step U + mix	10 μL
One step U + enzyme mix	5 μL
MP primer–probe mix	4 μL
Template DNA	31 μL
Total	50 μL

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Thermal cycling was performed as follows: 95 °C for 30 s (initial denaturation), followed by 45 cycles of 95 °C for 10 s and 60 °C for 30 s with fluorescence acquisition.

To ensure consistency and reproducibility, all reactions—including serial dilutions for standard curve generation and sensitivity testing—were conducted using this fixed reagent composition from a commercial kit. Reagents were stored at −20 °C and thawed on ice before use. Reaction mixtures (50 μL per chamber) were manually introduced into the microfluidic chip using a micropipette, and each chamber was sealed with a silicone plug to prevent evaporation and contamination. Fluorescence signals were acquired in real time through a transparent polycarbonate detection window that was optically aligned with the fluorescence detection module.

Control algorithm

Overview of the cascade control strategy

To address the thermal lag and spatial offset between the heater and the reagent during rapid PCR thermal cycling, a multi-layer cascade control architecture was developed (Fig. 5). This architecture integrates three hierarchically coordinated feedback loops, each operating at different physical levels and sampling rates, to regulate output power, heater surface temperature, and reagent-phase temperature, respectively.

Fig. 5 Schematic of the multi-loop cascade temperature control architecture.

At the outermost layer, the unobservable reagent temperature is dynamically estimated using a virtual sensor model trained on resistance–temperature calibration data. This model captures the thermal delay and spatial gradient between the heater and the fluid, enabling indirect reagent-centric feedback control without requiring embedded sensors.

The estimated reagent temperature is compared with a predefined thermal cycling profile. The resulting error signal is processed using a fuzzy-PID controller, which adaptively adjusts the PID gains based on the error magnitude and rate of change. In parallel, a feedforward controller anticipates temperature transitions and supplements the control output to improve response speed and tracking accuracy. These combined signals form the reference input for the next control layer.

The middle layer controls the heater surface temperature using a PI controller, based on real-time resistance feedback from the integrated copper heater, which also serves as a resistance temperature detector (RTD). The controller operates with a sampling period of 5 ms, enabling responsive and stable temperature regulation at the heater level.

At the innermost layer, a second PI controller regulates power delivery with a 1 ms update interval. The heater is driven by a voltage-controlled current source (VCCS), which ensures consistent thermal output based on continuously measured voltage and current.

The three control loops operate at 1 ms, 5 ms, and 10 ms intervals, respectively, selected to match the dynamic response characteristics of each layer. This ensures that each loop updates at an appropriate rate to maintain stability and responsiveness without excessive computational load.

This cascade structure allows each layer to focus on a well-defined, directly measurable quantity while jointly contributing to overall thermal regulation. The multi-rate design improves robustness, minimizes overshoot, and enhances temperature tracking accuracy under high-speed cycling conditions. The entire control framework is deployed on a Speedgoat real-time platform using Simulink Real-Time, supporting future adaptation to embedded or miniaturized PCR devices.

Virtual temperature estimation via system identification

Real-time measurement of reagent-phase temperature is impractical in microfluidic PCR platforms due to spatial constraints and the requirements for disposable, sensor-free chip formats. To address this, a virtual temperature sensing model was developed to estimate reagent temperature from heater-side resistance measurements, enabling closed-loop thermal regulation without embedding temperature sensors inside the chip.

We used system identification to characterize the dynamic thermal transfer between the heater surface and the reagent chamber. For this, the heater was excited with a pseudo-random binary signal (M-sequence) delivered by a voltage-controlled current source. This broadband signal is ideal for system identification due to its excellent autocorrelation properties, which enable full-spectrum thermal excitation while simultaneously suppressing high-frequency noise artifacts.

The excitation protocol used a shift period of 5 s and a total duration of 155 s. Temperature data were sampled at 0.1 s intervals. The heater surface temperature was derived from resistance readings via the pre-calibrated R–T curve. Meanwhile, reagent temperature was recorded using an ultra-thin T-type thermocouple (50 μm diameter, manufactured by Kaipusen, Xinghua Sutai Electric Instrument Co., Ltd, China), inserted into the fluidic chamber with minimal thermal intrusion. The thermocouple output was logged using a high-precision temperature scanner (FLUKE 1586A), ensuring reliable reference data for model training and validation (Fig. 6).

Fig. 6 Self-heating excitation input and temperature response curves used for virtual sensor identification.

The thermal transfer relationship from heater temperature T(z) to reagent temperature T_l(z) was modelled as a second-order discrete-time system using the Tustin transform:

Model parameters were identified via least-squares fitting, achieving 95.6% accuracy across a full thermal cycle. Higher-order models provided negligible improvement and were not adopted. The trained model captured key thermal delays and spatial gradients, supporting accurate virtual temperature prediction under dynamic conditions.

This virtual sensor was implemented in the outer control loop, enabling real-time estimation of reagent temperature using only surface-level resistance readings. This sensorless strategy significantly simplifies chip design, reduces cost, and maintains compatibility with mass-producible PCR formats. It also provides the foundational structure for the fuzzy adaptive control scheme discussed in the next section.

Fuzzy PID control with feedforward compensation for reagent-phase temperature

To regulate reagent-phase temperature during high-speed PCR cycling, the outer control loop adopts a composite strategy that integrates direct reference propagation with a fuzzy-tuned incremental PID controller. The control objective is to generate a heater temperature reference T_{set_heater}(k) such that the inner loops can track the desired reagent temperature trajectory T_liquid(k), estimated via the virtual sensor.

The overall control signal is computed as the sum of a feedforward term and a feedback correction:

T_{set\_heater}(k) = T^ff(k) + T^fb(k) (3)

The feedforward path passes the outer-loop reference directly to the heater domain with unit gain, assuming that the desired reagent temperature already reflects the target heater trajectory due to the unidirectional nature of thermal conduction. The feedback controller compensates for unmodeled dynamics such as delays, thermal lags, or overshoot effects, enhancing convergence speed and control precision.

The feedback term T^fb(k) is computed using an incremental fuzzy PID algorithm that updates the control increment based on:

where the error signal is defined as e(k) = T_ref(k) − T_liquid(k). The PID gains K_p(k), K_i(k), and K_d(k) are dynamically adjusted via fuzzy inference rules based on e(k) and Δe(k), enhancing robustness under varying thermal conditions. The rule base and membership functions are detailed in Appendix B.

As illustrated in Fig. 5, this fuzzy-PID controller operates within the outermost control loop, which is updated every 10 ms to match the slower dynamics of reagent temperature. Its composite output T_{set_heater}(k) is forwarded to the intermediate loop, where saturation constraints are applied to ensure safe operation. This layered architecture enables fast reference propagation, suppresses transient errors, and ensures robust temperature tracking throughout rapid thermal transitions.

Inner-loop PI cascade for heater and power regulation

To physically realize the outer-loop reference temperature T_{set_heater}(k) the inner control layers translate this command into accurate and stable power delivery via resistive Joule heating. This is accomplished through a two-stage cascade strategy involving a heater-surface temperature PI loop and a power-stabilization PI loop, each addressing different dynamic characteristics of the system.

Heater temperature control via PI regulation

The heating element comprises a planar copper thin-film structure that concurrently functions as both a heater and a temperature sensor. The surface temperature T_heater(k) is continuously monitored through resistance feedback, based on the calibrated R–T relationship in the previous section. To track the desired reference temperature T_{set_heater}(k), an incremental discrete-time PI controller computes the target electrical power P_ref(k) as:

This incremental PI structure improves numerical stability, mitigates integral windup, and is well-suited for real-time embedded implementation on constrained hardware platforms.

Power stabilization control

To ensure that the delivered power matches the computed reference P_ref(k), a second-stage PI controller regulates the heating current. The actual power P_meas(k) is calculated from real-time measurements of voltage and current:

P_meas(k) = V(k)I(k) (7)

Here, u(k) denotes the digital control command to a voltage-controlled current source (VCCS), which drives the heater with precise power and minimal delay.

This cascaded PI structure enhances thermal tracking performance and suppresses power-induced overshoot, while preserving system modularity and stability under the fast-changing thermal loads characteristic of ultrafast PCR.

All inner-loop controllers are deployed synchronously on the Speedgoat real-time platform. The power control loop operates at a 1 ms sampling interval to capture rapid electrical dynamics, while the heater temperature control loop runs at 5 ms to match the slower thermal response. This asynchronous scheduling ensures fast convergence of electrical control while maintaining temperature stability.

Real-time control implementation and deployment

The complete multi-loop control architecture—including the virtual temperature sensor, outer-loop fuzzy-PID controller, and cascaded inner-loop PI regulators—was deployed on a Speedgoat Baseline Performance real-time platform using Simulink Real-Time. All control modules operated under deterministic scheduling with synchronized analog I/O.

The outer-loop fuzzy-PID controller, executing at a 10 ms rate, regulated the reagent-phase temperature based on virtual temperature feedback. Controller gains were adaptively updated in real time via fuzzy inference. The virtual sensor was realized as a discrete-time transfer function model identified through system response data and operated at the same rate.

Two cascaded inner-loop PI controllers managed the heater-side dynamics. The power regulation loop operated at 1 ms to stabilize current delivery, while the heater temperature loop ran at 5 ms to match the thermal time constant of the system. All controllers were implemented using incremental discrete-time structures and synchronized via a global clock to ensure temporal consistency.

Voltage, current, and resistance measurements were performed through Speedgoat's analog interfaces. Internal variables—including the estimated reagent temperature, control references, and error signals—were continuously logged and streamed to a host PC via Ethernet for online monitoring, debugging, and performance validation.

To support future deployment, all control modules were developed with automatic C-code generation enabled. This ensures direct portability to embedded targets such as STM32, TI C2000, or NXP MCUs, supporting downstream integration into low-cost, miniaturized PCR platforms for point-of-care applications.

Results and discussion

Assessment of temperature control

Precise regulation of reagent-phase temperature is essential for achieving reliable and accelerated PCR amplification. Due to spatial constraints and microfluidic integration, direct temperature sensing inside the reaction chamber is impractical. To address this limitation, a virtual sensor model was established to estimate the reagent temperature based on heater resistance and electrical power measurements.

For model identification and validation, a fine-diameter T-type thermocouple (50 μm, KAIPUSEN Instrument Co., China) was temporarily inserted into the reaction chamber during system characterization. The thermocouple was connected to a FLUKE 1586A precision scanner, providing reference measurements for training the virtual sensor. After model calibration, the thermocouple was removed to avoid interference with optical detection and sample sealing.

The virtual sensor was implemented as a second-order discrete-time transfer function, derived via system identification using a pseudo-random excitation sequence:

The model achieved a fitting accuracy of 95.93% over a complete thermal cycle using least-squares estimation. Higher-order models were evaluated but did not yield meaningful performance improvements.

Based on the virtual sensor model, the outer-loop fuzzy PID controller was applied to track a typical two-step reagent temperature program (from 60 °C to 95 °C, and back to 60 °C). Fig. 7a and b compare the temperature responses of the proposed cascade controller and a conventional fixed-gain PID controller, respectively. The cascade approach regulates heater power indirectly through estimated reagent temperature, compensating for the thermal lag between the heater and fluid. In contrast, the conventional controller directly regulates heater temperature without accounting for this lag.

Fig. 7 Control performance in rapid thermal cycling. (a) Control response under the cascade strategy; the inset highlights overshoot behavior. (b) Control response under the conventional method. (c) Evaluation of heating and cooling rates under cascade control. (d) Temperature deviation at target points (60 °C, 72 °C, and 95 °C) under cascade control.

Under cascade control (Fig. 7a), the system exhibits a rapid temperature transition with an average ramp rate of 24.1 °C s⁻¹ during heating and 19.0 °C s⁻¹ during cooling, while maintaining small overshoots of 0.14 °C and 0.2 °C, respectively. The rise time T_r, defined as the time required for the reagent temperature to rise from 10% to 90% of its final value, is reduced to 1.16 s in the heating phase and 1.47 s in the cooling phase, as summarized in Table 2. In contrast, the conventional method (Fig. 7b) exhibits a significantly slower response due to unaddressed thermal separation, with prolonged rise times of 3.9 s and 3.85 s, and average ramp rates below 7.5 °C s⁻¹.

Table 2 The dynamic performance indexes

Controllers	Phase	Overshoot (°C)	T r (s)	Average ramp rate (°C s^−1)
Cascade control	Heating	0.14	1.16	24.1
	Cooling	0.2	1.47	19.0
Conventional control	Heating	0	3.9	7.2
	Cooling	0	3.85	7.3

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Fig. 7c further illustrates the instantaneous ramp rate dT/dt extracted from the fluid temperature signal. Under cascade control, the peak heating and cooling rates reached 31 °C s⁻¹ and −25 °C s⁻¹, respectively, highlighting the system's ability to support sub-second thermal transitions with high repeatability.

Temperature control accuracy is statistically analyzed in Fig. 7d. Across 60 °C, 72 °C, and 95 °C targets, the steady-state deviations are centered around 0 °C with narrow interquartile ranges (<±0.2 °C), confirming the precision of the proposed method. These results demonstrate that the cascade architecture achieves both fast and accurate reagent temperature regulation, outperforming conventional heater-focused control approaches in dynamic performance.

Optimization of thermal cycling parameters for rapid PCR

As demonstrated in the preceding analysis, the established system achieved average heating and cooling ramp rates of 24.1 °C s⁻¹ and 19.0 °C s⁻¹, respectively, thereby demonstrating superior performance in comparison with those of the majority of commercially available PCR instruments. While such thermal responsiveness significantly reduces ramping durations, the fixed dwell times at key thermal stages—pre-denaturation, denaturation, and annealing—remain a bottleneck in reducing total cycle time. Consequently, we conducted further research to ascertain whether these isothermal stages could be compressed without compromising amplification fidelity.

Using the standard protocol specified in the reagent datasheet as the baseline, we systematically halved the dwell time at each stage and monitored the cycle threshold (Ct) values as the primary performance metric. Each condition was tested in triplicate (n = 3), and differences were statistically evaluated using one-way ANOVA.

As demonstrated in Fig. 8a, the impact of different pre-treatment durations on qPCR amplification efficiency was evaluated by comparing the cycle threshold (Ct) values under four conditions: 60 s (manufacturer-recommended), 30 s, 10 s, and 5 s, with each condition being tested in triplicate. The one-way analysis of variance (ANOVA) confirmed a statistically significant effect of the pre-treatment duration on Ct values (α = 0.05 and p = 0.0026). In comparison with the 60 s control, the Ct increased by 0.047, 0.110, and 0.187 cycles for 30 s, 10 s, and 5 s, respectively. Despite the significance, all Ct shifts remained below 0.5 cycles,^35,36 a widely accepted threshold for technical variability in qPCR. All tested durations maintained reproducibility within this limit, suggesting that the observed Ct variations are methodologically acceptable. Notably, the 5 s condition, which introduced the largest shift, still fell within the acceptable range. Given the minimal Ct increase and the substantial reduction in processing time, 5 s is identified as the optimal pre-treatment duration for balancing assay speed and amplification fidelity in this system.

Fig. 8 Effect of reducing dwell times on qPCR amplification efficiency. (a) Pre-denaturation stage. (b) Denaturation stage. (c) Annealing stage.

Fig. 8b shows that the denaturation step could also be safely reduced. The Ct values remained highly consistent across 10 s, 5 s, 3 s, and 1 s dwell conditions, with no perceptible change in amplification efficiency. One-way ANOVA again confirmed no statistically significant difference between these groups (α = 0.05 and p-value = 0.3062). This result indicates that under the current thermal regime, even a 1s dwell at denaturation temperature ensures sufficient strand separation. This outcome is not unexpected, given that the denaturation of polynucleic acids occurs within a remarkably brief timeframe (in milliseconds).

To determine the minimal annealing time required for effective amplification, qPCR was performed with annealing durations ranging from 30 s to 2 s. As shown in Fig. 8c, Ct values remained relatively stable between 30 s and 5 s, followed by a pronounced increase at 2 s. One-way ANOVA confirmed the effect of annealing time to be statistically significant (α = 0.05, p = 4.89 × 10⁻⁹), with Ct increments of +0.10, +0.21, +0.39, and +2.06 cycles at 15 s, 8 s, 5 s, and 2 s, respectively, compared to the 30 s reference. Despite this statistical significance, all conditions down to 5 s exhibited Ct shifts within 0.5 cycles, a threshold commonly accepted for qPCR technical reproducibility. As indicated in Fig. 8c, these differences remain below the resolution limit for distinguishing two-fold expression differences at 95% confidence. Only the 2 s condition exceeded this limit, suggesting insufficient template annealing and reduced reaction efficiency. The 5 s annealing step thus offers a robust and reproducible alternative, achieving an 83% reduction in annealing time with only a +0.39 cycle increase in Ct and minimal standard deviation. This finding highlights the feasibility of aggressive cycle compression in high-speed qPCR protocols without compromising assay performance.

Taken together, these results indicate that both the pre-denaturation and denaturation stages can be substantially shortened without any negative impact on performance. However, the annealing step must be retained at 5 s to ensure robust amplification. It was determined that an optimised protocol comprising 1 s of denaturation and 5 s of annealing per cycle would be the most appropriate. This protocol facilitates rapid PCR while maintaining minimal compromise to quantification accuracy.

To explicitly characterize the trade-off between assay speed and analytical fidelity in our high-performance system, we defined and tested three distinct thermal cycling protocols under identical conditions: a “reference” protocol based on manufacturer guidelines, an “optimal” protocol informed by system-level thermal dynamics in the previous section, and an “ultrafast” protocol configured with the shortest stable dwell durations supported by the controller (Fig. 9a).

Fig. 9 Testing results under each amplification protocol. (a) Summary of thermal cycling parameters across three protocols: reference (long dwell), optimal (moderate dwell), and ultrafast (minimal dwell). (b) Reagent-phase temperature profiles recorded during cycling. (c) Corresponding fluorescence amplification curves and Ct values for each condition (n = 3).

The reagent-phase temperature trajectories across 45 cycles are shown in Fig. 9b. The reference, optimized, and ultrafast protocols were completed in 33.6, 7.1, and 4.4 minutes, respectively—representing a 4.9-fold reduction in assay time. Notably, temperature profiles under the ultrafast condition remained highly repeatable across all cycles, with no observable overshoot, drift, or waveform distortion, demonstrating the system's ability to maintain thermal stability even under sub-second hold periods.

Fluorescence amplification results (Fig. 9c) confirmed functional consistency across protocols. Despite increasingly compressed dwell durations, all three configurations yielded clear exponential amplification curves. The average Ct values were 24.25 ± 0.10, 24.80 ± 0.05, and 27.71 ± 0.10, respectively. Although the ultrafast protocol exhibited a slight increase in Ct, reflecting reduced enzymatic dwell time, amplification remained reproducible, with low variability across replicates (n = 3). This suggests that thermal limitations—not system instability—were the primary contributors to performance differences.

Despite the significantly compressed thermal dwell durations in the ultrafast protocol, robust and reproducible amplification curves were still obtained. Compared to the reference and optimized protocols, a slight delay in the Ct value (Fig. 9c) was observed under ultrafast cycling conditions. This shift is attributable primarily to the reduced enzymatic reaction time per cycle, as both the denaturation and annealing phases were limited to sub-second durations. Correspondingly, a decrease in the slope and plateau of the exponential amplification phase was evident, indicating a moderate reduction in amplification efficiency—an expected outcome in the context of ultrafast PCR. Nevertheless, such trade-offs are commonly accepted in time-critical diagnostic applications, where qualitative detection is often prioritized over absolute quantification. Notably, the optimized protocol achieved full amplification within 15 minutes with minimal loss of efficiency, while the ultrafast mode further reduced the total runtime to 4.4 minutes. These results highlight the value of integrating system-level thermal optimization with adaptive control strategies to enable rapid nucleic acid testing, especially in point-of-care scenarios. Future improvements in reagent formulation—such as increasing primer or enzyme concentrations—may further compensate for reduced reaction time without compromising fidelity.

In summary, the combination of rapid thermal responsiveness and high control fidelity enabled robust amplification even with extreme time compression. The ability to achieve full 45-cycle amplification in under 7 minutes without significant loss of fidelity highlights the platform's promise for rapid diagnostics and time-sensitive molecular assays.

Amplification performance and comparison with that of a commercial PCR system

To benchmark the amplification performance of the proposed system, a comparative study was conducted against a commercial real-time thermal cycler (Thermo Fisher QuantStudio 6 Pro, referred to as Q6 Pro). Identical reagents, probe-based chemistry, and a five-point serial dilution of the DNA template (ranging from 100 to 100 000 copies per μL) were applied on both platforms. Each reaction was performed in triplicate using a standard two-step amplification protocol.

As shown in Fig. 10a, the total time required to complete 45 PCR cycles on the custom platform was approximately 7.1 minutes—substantially shorter than the 62 minutes required by the Q6 Pro under its default cycling program. The substantial enhancement in efficiency, evidenced by a more than eightfold reduction in processing time, can be attributed to two primary factors. Firstly, the system's dual-loop real-time control architecture facilitated high heating and cooling rates of 24.1 °C s⁻¹ and 19.0 °C s⁻¹, respectively. Secondly, the optimised steady-state dwell durations at the denaturation and annealing stages played a crucial role in achieving these results.

Fig. 10 Comparison of amplification performance between the custom-developed PCR system and a commercial instrument. (a) Total time required to complete 45 PCR cycles on each system. (b) Average Ct values across a five-point serial dilution (10 to 100 000 copies per μL, n = 3). (c) Standard curve analysis showing Ct vs. log₁₀(template copies), annotated with linear fit equations, R² values, and calculated amplification efficiencies.

Despite this significant reduction in thermal cycling time, the custom system demonstrated comparable amplification performance. As illustrated in Fig. 10b, the mean Ct values were obtained across all concentrations of the template. At elevated template inputs (i.e. ≥1000 copies per μL), Ct values exhibited a high degree of similarity between platforms. For lower concentrations (10–1000 copies per μL), the custom system exhibited slightly elevated Ct values, with an average deviation of less than 0.5 cycles. This is likely attributable to reduced annealing efficiency under shortened dwell conditions. It is noteworthy that the standard deviations across all replicates remained below 0.3 cycles, even at the lowest template input, indicating high intra-run consistency.

The quantitative accuracy of the assay was further validated by standard curve analysis (Fig. 10c). The amplification efficiency (E) was calculated from the slope of the standard curve according to the equation: E = (10^−1/slope − 1) × 100%. The custom platform achieved an R² of 0.9965 and an amplification efficiency of 109.8%, closely matching those of the commercial system (R² = 0.9971 and efficiency = 109.4%). The regression slopes (−3.1072 vs. −3.1146) were found to be almost identical, indicating that neither the accelerated cycling nor the real-time control system compromised amplification kinetics or fluorescence signal detection.

It is widely accepted in qPCR analysis that amplification efficiencies in the range of 90–110% indicate a robust and reliable assay. The observation of an efficiency slightly above 100% is a known phenomenon that can be attributed to factors such as minor pipetting inaccuracies during serial dilution, the specific kinetics of the reagent chemistry, or the presence of inhibitors at high template concentrations that are diluted out in subsequent steps. Since our system and the gold-standard commercial instrument produced nearly identical efficiencies (109.8% vs. 109.4%) using the same reagents, it can be concluded that this value is a characteristic of the assay itself rather than an artifact of our instrument's thermal control.

Collectively, these results demonstrate that the proposed PCR system delivers rapid amplification without compromising analytical accuracy. The platform has been demonstrated to achieve comparable performance to a state-of-the-art commercial instrument, despite significantly reducing the total assay time. This is enabled by real-time closed-loop temperature control and virtual sensing. This capability is especially advantageous for time-critical molecular diagnostics and point-of-care applications.

Conclusions

This work demonstrates a high-speed, high-precision PCR system driven by a reagent-centric cascade control architecture. By shifting the control focus from the heating element to the reagent-phase temperature, the architecture addresses the intrinsic thermal lag and spatial decoupling that limit the accuracy of conventional heater-centric feedback systems. A virtual sensing model, calibrated from heater resistance–temperature characteristics, enables real-time estimation of reagent temperature without embedding sensors inside the disposable chip.

The control architecture integrates a fuzzy PID feedforward–feedback controller with nested regulation loops operating at distinct multi-rate sampling intervals (1 ms for power, 5 ms for the heater, and 10 ms for the reagent). This multi-scale strategy allows the system to adapt dynamically to thermal demands, achieving experimental heating and cooling rates of 24.1 °C s⁻¹ and 19.0 °C s⁻¹, respectively. The reagent-phase control maintains a steady-state error below 0.2 °C and an overshoot of less than 0.2 °C.

Our system demonstrated remarkable versatility by successfully executing multiple protocols: a high-fidelity ‘optimal’ protocol was completed in 7.1 minutes, while an ‘ultrafast’ protocol pushed the total time down to just 4.4 minutes. In a direct comparison with the commercial Thermo Fisher QuantStudio 6 Pro platform, our system reduces the total reaction time by over eightfold while maintaining comparable amplification efficiency (109.8%), quantification accuracy (R² = 0.9965), and reproducibility (SD < 0.3 cycles). We further demonstrated the potential for acceleration by optimizing thermal dwell times, highlighting the trade-off between time-to-result and amplification fidelity.

The hardware design is centered on a PCB-based copper resistive heater that provides both heating and sensing in a single, co-located structure. This integrated approach minimizes feedback latency and simplifies the system architecture. The device's compatibility with mature, low-cost PCB manufacturing processes facilitates mass production and integration into compact diagnostic platforms.

Regarding scalability, the inherent planarity of the PCB-based heater design facilitates straightforward expansion into multi-well arrays on a single substrate, a concept not easily achievable with bulkier thermal blocks. Furthermore, our modular cascade control architecture is designed to be extensible; the control loops for power, heater temperature, and reagent temperature can be replicated for each thermal zone and managed in parallel by a single, capable embedded microcontroller. This combination of scalable hardware and software provides a clear pathway toward true high-throughput implementation.

Finally, the control algorithm was deployed on a Speedgoat real-time platform using automatic code generation, which demonstrates a clear pathway for rapid prototyping and seamless transfer to embedded microcontrollers. Overall, the system offers a portable, low-cost, and high-performance framework for time-critical nucleic acid testing applications, paving the way for next-generation point-of-care and high-throughput PCR diagnostics.

Author contributions

Yuheng Luo: conceptualization, methodology, software, validation, formal analysis, investigation, and writing – original draft. Wangyang Hu: software, validation, and investigation. Jiajia Wu: investigation and visualization. Baoce Sun: resources and writing – review & editing. Gang Jin: methodology, supervision, project administration, and writing – review & editing. Qiang Xu: conceptualization, methodology, supervision, project administration, funding acquisition, and writing – review & editing.

Conflicts of interest

There are no conflicts to declare.

Data availability

All data supporting the findings of this study are available within the article and its supplementary information (SI). Supplementary data associated with this article can be found in the online version. Supplementary information is available. See DOI: https://doi.org/10.1039/d5an00965k.

The source data for thermal control performance and fluorescence amplification, along with the algorithmic framework for real-time control, are available from the corresponding authors upon reasonable request.

Acknowledgements

This study was funded by the Guangzhou National Laboratory under the project Ultra-Fast Integrated Nucleic Acid Detection System (Grant No. GZNL2024A01029) and Flexible Manufacturing Technology for Respiratory Infectious Disease Diagnostic Devices.

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