CN113917835B - Temperature control method of free piston Stirling refrigerator based on model prediction algorithm - Google Patents
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Abstract
The invention discloses a temperature control method of a free piston Stirling refrigerator based on a model prediction algorithm. The temperature ring is used as an outermost ring, and is suitable for the characteristics of large inertia and long delay of temperature response, the method adopts model predictive control, a control objective function of the temperature ring is designed according to the dynamic response performance index of the temperature, and the uncertainty problem caused by time lag, model mismatch and the like can be corrected in time by using a repeated optimization process; the middle loop is a speed loop, the innermost loop is a current loop, and a P I control algorithm is adopted. Compared with the traditional PID control, the method effectively solves the problem of poor control effect caused by time lag and model mismatch of the refrigeration system, and improves the dynamic response quality of the refrigeration process.
Description
Technical Field
The invention relates to the technical field of Stirling refrigerator drive control, in particular to a temperature control method of a free piston Stirling refrigerator based on a model prediction algorithm.
Background
Stirling refrigerators are widely used in the fields of military, civil and commercial refrigeration requiring low-temperature refrigeration technologies such as infrared, aerospace and superconducting due to the characteristics of compact structure, wide refrigeration temperature range, high reliability and the like. The Stirling refrigerator is a mechanical low-temperature refrigerator driven by electric power, and refrigeration is realized by utilizing Stirling reverse circulation through isothermal compression, constant volume expansion, constant volume recovery and other processes. The Stirling refrigerator has good refrigerating effect and little pollution, and is a greener efficient refrigerating mode. A free piston Stirling refrigerator (FPSC) is driven by a single-phase permanent magnet linear motor, and a piston of the free piston Stirling refrigerator is driven by the motor to do reciprocating linear motion.
However, since the Stirling refrigerator is a complex system involving machines, electricity and thermodynamics, the Stirling refrigerator has characteristics of nonlinearity, large time lag, strong coupling and the like which are unfavorable for control, is extremely easy to be influenced by ambient temperature and load disturbance, and the characteristics of the control system are dynamically changed. In addition, the refrigerating temperature area is wide, and the refrigerating process parameters at different temperature working points are different, so that the fixed PID parameters are difficult to meet the requirements of various working conditions in real time when the traditional PID control strategy is adopted, the parameter setting is complicated, and a good control effect cannot be obtained in real time.
Disclosure of Invention
In order to solve the defects in the background art, the invention aims to provide a temperature control method of a free piston Stirling refrigerator based on a model prediction algorithm.
The aim of the invention can be achieved by the following technical scheme:
a free piston Stirling refrigerator temperature control system based on a model prediction algorithm comprises a model prediction control module of a temperature loop, a PI control module of a speed loop, a PI control module of a current loop, an SPWM waveform generation and driving inverter circuit module, an LC filter module, a controlled motor and an equivalent transfer function of a motor refrigeration model.
Further, the Model Predictive Control (MPC) module includes a model predictive control algorithm, a reference trajectory, a predictive model, a rolling optimization and feedback correction unit.
The model predictive control algorithm adopted by the temperature ring comprises the following steps:
s1: at each sampling instant t=t, 2 t..nt., NT, the step response coefficient was calculated as follows:
s2: the P-step predictive model output, which represents the initial value with the control amount applied to the system in the past, is:
T(k+1)＝AΔU(k)+A 0 U(k-1)
wherein T (k+1) = [ T (k+1), T (k+2),. The term, T (k+p)] T Is the future P-step model output temperature calculated at the current moment,
ΔU＝(Δu(k),Δu(k+1),...,Δu(k+M-1)) T
U(k-1)＝(u(k-N+1),u(k-N+2),...,u(k-1)) T
s3: the effect of introducing feedback correction is that the P-step output term is:
T p (k+1)＝T(k+1)+he(k)＝AΔU(k)+A 0 U(k-1)+he(k)
wherein T is p (k+1)＝[(t p (k+1),t p (k+2),...,t p (k+p)] T e(k)＝t(k)-t p (k)
t p ＝a 1 u(k)+(a 2 -a 1 )u(k-1)+(a 3 -a 2 )u(k-2)+...+(a N -a N-1 )u(k-N+1)
S4: given the parameter h= (h 1 ,h 2 ,...,h p ) T The examination tracks are as follows:
T r ＝(t r (k+1),t r (k+2),...,t r (k+P)) T
s5: to enhance robustness, consider the effect of the control quantity u (k) at the present time on the output value at the future time of the system, while avoiding too severe a change in the control action increment Deltau applied to the system, an objective function of quadratic performance index is employed, which weights the output error and the control increment:
wherein q i ，r j Is a weighting coefficient, and w (k+i) represents a given expected value, y m (k+i|k) represents a predicted output value;
the above is rewritten into a vector form as follows:
minJ(k)＝[T r (k+1)-T p (k+1)] T Q[T r (k+1)-T p (k+1)]+ΔU T (k)RΔU(k)
＝(AΔU(k)+A 0 U(k-1)+he(k)-T r (k+1)) T Q
(AΔU(k)+A 0 U(k-1)+he(k)-T r (k+1))+ΔU(k) T RΔU(k)
s6: according to the control target of the temperature loop, the target function is minimized, and thus, the following is obtained:
s7: finally, the optimal control law can be obtained as follows:
ΔU(k)＝(AQA+R) -1 A T Q(T r (k+1)-A 0 U(k-1)-he(k))
wherein, Q and R are P, P and M, respectively, and M are the weights matrix.
The invention has the beneficial effects that:
compared with the prior art, the method has the following advantages:
1. the control problem of a large inertia and long-time lag system which is difficult to solve by the traditional PID control strategy can be effectively solved, and the influence on the change of model parameters can be effectively avoided;
2. compared with the traditional PID control strategy, the dynamic performance of the temperature response in the adjusting process is better, the overshoot of the system response is smaller, and the adjusting time is shorter.
Drawings
The invention is further described below with reference to the accompanying drawings.
FIG. 1 is a schematic diagram of a free piston Stirling refrigerator;
FIG. 2 is a schematic diagram of model predictive control;
FIG. 3 is a flow chart of a Stirling refrigerator temperature model predictive control;
FIG. 4 is an overall block diagram of a three closed loop control system;
FIG. 5 is a schematic diagram of a Stirling refrigerator temperature control system employing a model predictive control strategy for the temperature loop;
FIG. 6 is a temperature (MPC control) -speed (PI control) -current (PI control) cascade control block diagram;
FIG. 7 is a temperature response curve of a temperature loop using a PID control algorithm;
FIG. 8 is a temperature response curve of a temperature loop using a model predictive control algorithm.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The invention relates to a driving controller of a free piston Stirling refrigerator, which mainly comprises power modules such as a single-phase alternating current power supply, a diode uncontrolled rectifying circuit, a single-phase inverter circuit, an inverter output filter circuit and the like; the device comprises a miniature main controller, a switching power supply module, a voltage sampling and conditioning circuit, a current sampling and conditioning circuit, a temperature sampling and conditioning circuit, a serial communication module, a man-machine interaction module (an upper computer display circuit), an ice thickness detection and heating deicing circuit, an alarm display circuit and a heat dissipation device.
The rectification circuit adopts a single-phase diode for uncontrolled rectification and converts network-side single-phase alternating current into direct current;
the inverter circuit is driven by an IGBT tube and an anti-parallel diode, and converts the voltage of a direct current bus into alternating current to be supplied to the motor;
the filter circuit consists of an input inductor and an output capacitor;
the direct-current bus voltage sensor is positioned between the diode uncontrolled rectifier bridge and the H-bridge inverter circuit; the alternating-current voltage sensor is positioned between the H-bridge inverter circuit and the motor;
the central controller comprises a high-speed data processing chip, a driving circuit and an optical coupling isolation circuit;
the adopted microprocessor model is a singlechip with PIC30F4011, and the software part comprises an initialization module, a PWM signal generation module, a temperature loop adjusting module, a voltage loop adjusting module, an overvoltage and overcurrent protection module, a soft start module, a communication module between an upper computer (PC) and a chip, a communication module between a chip and a lower computer (temperature sampling plate), a display screen working module and a deicing circuit working module.
The invention adopts a single-phase H bridge inverter circuit for driving, adopts an SPWM modulation method, the sum of duty ratios of two paths of PWM waves is D, and the D is calculated in real time according to the voltage actually required. Therefore, the current applied to the stator winding of the Stirling refrigerator is approximately sine wave, and then the Stirling refrigerator is driven, and the piston is driven to do reciprocating linear motion.
The MCU generates two paths of PWM wave signals, respectively controls the conduction of diagonal IGBT tubes of an upper bridge arm and a lower bridge arm corresponding to different phase bridge arms of the H bridge circuit to form a channel, further controls the voltage waveform supplied to the motor, controls the running direction of the motor to realize the ascending and descending of the piston, and adjusts the voltage value output to the motor by controlling the duty ratio of the SPWM so as to change the actual power of the motor.
The Stirling refrigerator driving system can realize normal starting, stable running, accurate and stable temperature control and programmable parameters of the refrigerator under all environmental temperatures. When the refrigerator is started, a slow start mode is adopted. The PWM wave control signal is generated by a main control chip, and the operation parameters (including the operation speed of the linear compressor, the cold end temperature, the motor voltage and current and the like) of the refrigerator are transmitted through serial communication, and the parameters are correspondingly operated in a main program, so that the operation parameters of the refrigerator are regulated and controlled.
The refrigerating temperature of the free piston Stirling refrigerator is regulated and controlled by a controller, and the whole system is controlled by three closed loops, wherein the three closed loops consist of a temperature loop, a speed loop and a current loop. The temperature ring is used as an outermost ring, and model prediction control is adopted; the middle loop is a speed loop, the innermost loop is a current loop, and a traditional PI control algorithm is adopted.
The model prediction algorithm of the invention realizes the temperature loop control of the free piston Stirling refrigerator, and the control method comprises the following steps:
s1: at each sampling instant t=t, 2 t..nt., NT, the step response coefficient was calculated as follows:
s2: the P-step predictive model output, which represents the initial value with the control amount applied to the system in the past, is:
T(k+1)＝AΔU(k)+A 0 U(k-1)
wherein T (k+1) = [ T (k+1), T (k+2),. The term, T (k+p)] T Is the future P-step model output temperature calculated at the current moment,
ΔU＝(Δu(k),Δu(k+1),...,Δu(k+M-1)) T
U(k-1)＝(u(k-N+1),u(k-N+2),...,u(k-1)) T
s3: the effect of introducing feedback correction is that the P-step output term is:
T p (k+1)＝T(k+1)+he(k)＝AΔU(k)+A 0 U(k-1)+he(k)
wherein T is p (k+1)＝[(t p (k+1),t p (k+2),...,t p (k+p)] T ，e(k)＝t(k)-t p (k)
h＝(h 1 ,h 2 ,...,h p ) T ，t p ＝a 1 u(k)+(a 2 -a 1 )u(k-1)+(a 3 -a 2 )u(k-2)+...+(a N -a N-1 )u(k-N+1)
S4: the given reference trajectories are as follows:
T r ＝(t r (k+1),t r (k+2),...,t r (k+P)) T
s5: to enhance robustness, consider the effect of the control quantity u (k) at the present time on the output value at the future time of the system while avoiding too severe a change in the control action delta u applied to the system, an objective function of a quadratic performance index is employed that weights the output error and the control increment:
wherein q i ，r j Is a weighting coefficient, and w (k+i) represents a given expected value, y m (k+i|k) represents a predicted output value;
the above is rewritten into a vector form as follows:
minJ(k)＝[T r (k+1)-T p (k+1)] T Q[T r (k+1)-T p (k+1)]+ΔU T (k)RΔU(k)
＝(AΔU(k)+A 0 U(k-1)+he(k)-T r (k+1)) T Q
(AΔU(k)+A 0 U(k-1)+he(k)-T r (k+1))+ΔU(k) T RΔU(k)
s6: according to the control target of the temperature loop, the target function is minimized, and thus, the following is obtained:
s7: finally, the optimal control law can be obtained as follows:
ΔU(k)＝(AQA+R) -1 A T Q(T r (k+1)-A 0 U(k-1)-he(k))
wherein, Q and R are P, P and M, respectively, and M are the weights matrix.
Specifically, the Stirling refrigerator driving controller designed by the invention realizes the temperature control of the refrigerating process by adjusting the movement amplitude and frequency of the linear compressor. The specific implementation scheme of the driving controller designed by the invention is as follows: the maximum output is given to the motor in the cooling process, and the compressor is driven to work at the maximum stroke; and in the temperature control stage, controlling the stroke of the compressor to be smaller than the maximum stroke. When the controller receives a system starting instruction, in order to prevent a cylinder collision under a step voltage signal when the motor is started, the motor needs to be controlled to work under a certain amplitude and frequency, so that the motor is started by adopting a method of slowly increasing the SPWM (sinusoidal pulse width modulation) duty ratio, namely a soft start process; when the motor enters a cooling process after being started, the motor is driven by sine waves with a certain frequency to do maximum amplitude reciprocating motion, and meanwhile, the temperature change is monitored; when the measured temperature approaches the set temperature, the temperature control stage is started, the amplitude of the motor driving voltage is reduced to gradually reduce the amplitude of the reciprocating motion until the required temperature is reached, and then the motion amplitude of the motor is continuously adjusted to keep the cold end temperature of the Stirling refrigerator at the required temperature.
The control scheme adopted by the invention controls the refrigeration process in a starting stage, a cooling stage and a temperature control stage. The following scheme is adopted: the temperature ring is used as the outermost ring, the middle ring is a speed ring, and the innermost ring is a current ring. In the start-up phase: in order to prevent the motor from knocking the cylinder caused by sudden voltage, the optimal amplitude and frequency combination of the linear motor are obtained by using an MPC algorithm by taking the motor motion frequency and amplitude as controlled quantities, so that the motor is ensured to be started quickly and stably; in the cooling stage: keeping the frequency fixed, outputting the motor with maximum power, and operating the motor under the maximum amplitude under the mechanical constraint; in the temperature control stage: the frequency is fixed, and the amplitude of the motor is regulated by utilizing an MPC algorithm according to the actual temperature requirement, so that the requirements of short regulating time, small overshoot and small steady-state fluctuation in the temperature control process are met. And obtaining an optimal motion track according to the optimal amplitude and frequency combination obtained by calculation in the control strategy, and calculating the motor motion speed. And then the PI controller of the speed ring and the current ring are used for adjusting the motor to do corresponding linear motion.
In the description of the present specification, the descriptions of the terms "one embodiment," "example," "specific example," and the like, mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiments or examples. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
The foregoing has shown and described the basic principles, principal features and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, and that the above embodiments and descriptions are merely illustrative of the principles of the present invention, and various changes and modifications may be made without departing from the spirit and scope of the invention, which is defined in the appended claims.
Claims (1)
1. A free piston Stirling refrigerator temperature control system based on a model prediction algorithm is characterized in that: the system comprises a model prediction control module of a temperature loop, a PI control module of a speed loop, a PI control module of a current loop, an SPWM waveform generation and driving inverter circuit module, an LC filter module, a controlled motor and an equivalent transfer function of a motor refrigeration model;
the model prediction control module adopts a model prediction control algorithm and comprises a reference track, a prediction model, a rolling optimization unit and a feedback correction unit;
the model predictive control algorithm adopted by the temperature ring comprises the following steps:
s1: at each sampling instant t=t, 2 t..nt., NT, the step response coefficient was calculated as follows:
s2: the P-step predictive model output, which represents the initial value with the control amount applied to the system in the past, is:
T(k+1)＝AΔU(k)+A 0 U(k-1)
wherein T (k+1) = [ T (k+1), T (k+2),. The term, T (k+p)] T Is the future P-step model output temperature calculated at the current moment,
ΔU＝(Δu(k),Δu(k+1),...,Δu(k+M-1)) T
U(k-1)＝(u(k-N+1),u(k-N+2),...,u(k-1)) T
s3: the effect of introducing feedback correction is that the P-step output term is:
T p (k+1)＝T(k+1)+he(k)＝AΔU(k)+A 0 U(k-1)+he(k)
wherein T is p (k+1)＝[(t p (k+1),t p (k+2),...,t p (k+p)] T ，e(k)＝t(k)-t p (k)，h＝(h 1 ,h 2 ,...,h p ) T ，t p ＝a 1 u(k)+(a 2 -a 1 )u(k-1)+(a 3 -a 2 )u(k-2)+...+(a N -a N-1 )u(k-N+1)，
S4: the given reference trajectories are as follows:
T r ＝(t r (k+1),t r (k+2),...,t r (k+P)) T
s5: to enhance robustness, consider the effect of the control quantity u (k) at the present time on the output value at the future time of the system, while avoiding too severe a change in the control action delta u applied to the system, an objective function of a quadratic performance index is used, which weights the output error and the control increment:
wherein q i ，r j Is a weighting coefficient, and T represents the suppression of the tracking error and the control action change r (k+i) represents a given desired value, T p (k+i|k) represents a predicted output value;
the above is rewritten into a vector form as follows:
min J(k)＝[T r (k+1)-T p (k+1)] T Q[T r (k+1)-T p (k+1)]+ΔU T (k)RΔU(k)
＝(AΔU(k)+A 0 U(k-1)+he(k)-T r (k+1)) T Q(AΔU(k)+A 0 U(k-1)+he(k)-T r (k+1))+ΔU(k) T RΔU(k)
s6: according to the control target of the temperature loop, the target function is minimized, and thus, the following is obtained:
s7: finally, the optimal control law can be obtained as follows:
ΔU(k)＝(AQA+R) -1 A T Q(T r (k+1)-A 0 U(k-1)-he(k))
wherein, Q and R are P, P and M, respectively, and M are the weights matrix.
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