CN113917835A - Free piston Stirling refrigerator temperature control method based on model prediction algorithm - Google Patents
Free piston Stirling refrigerator temperature control method based on model prediction algorithm Download PDFInfo
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Abstract
The invention discloses a free piston Stirling refrigerator temperature control method based on a model prediction algorithm. The temperature ring is used as the outermost ring, in order to adapt to the characteristics of large inertia and long time delay of temperature response, the method adopts model predictive control, designs a control objective function of the temperature ring according to the dynamic response performance index of the temperature, and can timely correct the uncertainty problem caused by time delay, model mismatch and the like by utilizing a repeated optimization process; the intermediate loop is a speed loop, the innermost loop is a current loop, and P I control algorithms are adopted. Compared with the traditional P ID control, the invention effectively solves the problem of poor control effect caused by time lag and model mismatch of a 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 free piston Stirling refrigerator temperature control method based on a model prediction algorithm.
Background
The Stirling refrigerator has the characteristics of compact structure, wide refrigeration temperature range, high reliability and the like, and is widely applied to military, civil and commercial refrigeration fields requiring low-temperature refrigeration technology, such as infrared, aerospace, superconduction and the like. The Stirling refrigerator is a mechanical low-temperature refrigerator driven by electric power, and realizes refrigeration through processes of isothermal compression, constant-volume expansion, constant-volume recovery and the like by utilizing Stirling reverse circulation. The Stirling refrigerator has good refrigeration effect and little pollution, and is a more green efficient refrigeration mode. Compared with the traditional mode of 'a rotating motor and a ball screw', the free piston Stirling refrigerator (FPSC) does not need an intermediate transmission link, so that the mechanical performance is more excellent, and the free piston Stirling refrigerator has the advantages of small abrasion, low noise, high efficiency and the like, and has great development potential.
However, the stirling cryocooler is a complex system involving mechanics, electricity and thermodynamics, has characteristics of nonlinearity, large time lag, strong coupling and the like which are not beneficial to control, is very easily influenced by environmental temperature and load disturbance, and the characteristics of the control system are dynamically changed. In addition, the refrigeration temperature area is wide, and the refrigeration 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 the good control effect cannot be obtained in real time.
Disclosure of Invention
In order to solve the above-mentioned disadvantages in the background art, the present invention is directed to a method for controlling the temperature of a free-piston stirling cooler based on a model prediction algorithm.
The purpose of the invention can be realized 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 filtering 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 roll optimization and a feedback correction unit.
The model predictive control algorithm adopted by the temperature ring comprises the following steps:
s1: at each sampling time T ═ T, 2T.., NT, the step response coefficient was calculated as follows:
s2: the P-step predictive model output representing the initial value with the amount of control applied to the system in the past is:
T(k+1)＝AΔU(k)+A0U(k-1)
where T (k +1) ═ T (k +1), T (k +2),. -, T (k + p)]TIs 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: and introducing the effect of feedback correction, and then having P step output items:
Tp(k+1)＝T(k+1)+he(k)＝AΔU(k)+A0U(k-1)+he(k)
wherein, Tp(k+1)＝[(tp(k+1),tp(k+2),...,tp(k+p)]T e(k)＝t(k)-tp(k)
tp＝a1u(k)+(a2-a1)u(k-1)+(a3-a2)u(k-2)+...+(aN-aN-1)u(k-N+1)
S4: given parameter h ═ h1,h2,...,hp)TThe test trajectories are as follows:
Tr＝(tr(k+1),tr(k+2),...,tr(k+P))T
s5: in order to enhance robustness, the influence of the control quantity u (k) at the current moment on the output value of the system at the future moment is considered, and meanwhile, the control action increment delta u applied to the system is prevented from changing too severely, a target function of a quadratic performance index is adopted, and the function weights the output error and the control increment:
wherein q isi，rjAre weighting coefficients representing the suppression of the tracking error and the variation of the control action, w (k + i) representing a given desired value, ym(k + i | k) represents a prediction output value;
the above equation is rewritten into vector form as follows:
minJ(k)＝[Tr(k+1)-Tp(k+1)]TQ[Tr(k+1)-Tp(k+1)]+ΔUT(k)RΔU(k)
＝(AΔU(k)+A0U(k-1)+he(k)-Tr(k+1))TQ
(AΔU(k)+A0U(k-1)+he(k)-Tr(k+1))+ΔU(k)TRΔU(k)
s6: minimizing the objective function according to the control objective of the temperature loop, thus yielding:
s7: the optimal control law can be obtained as follows:
ΔU(k)＝(AQA+R)-1ATQ(Tr(k+1)-A0U(k-1)-he(k))
wherein Q and R are respectively P and M dimension weighting 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 a traditional PID control strategy, can be effectively solved, and the influence caused by the change of model parameters can be effectively coped with;
2. compared with the traditional PID control strategy, the dynamic performance of temperature response in the adjusting process is better, the overshoot of system response is smaller, and the adjusting time is shorter.
Drawings
The invention will be further described with reference to the accompanying drawings.
FIG. 1 is a schematic diagram of a free piston Stirling cryocooler configuration;
FIG. 2 is a model predictive control schematic;
FIG. 3 is a flow chart of Stirling cooler 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 with a temperature loop employing a model predictive control strategy;
FIG. 6 is a block diagram of temperature (MPC control) -speed (PI control) -current (PI control) cascade control;
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 technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention relates to a free piston Stirling refrigerator drive controller, 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 micro 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 port communication module, a man-machine interaction module (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 single-phase diode uncontrolled rectification to convert the 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 direct-current bus voltage into alternating current to supply 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 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 is a single chip microcomputer with the model of PIC30F4011, and the software part comprises an initialization module, a PWM signal generation module, a temperature ring regulation module, a voltage ring regulation module, an overvoltage and overcurrent protection module, a soft start module, an upper computer (PC) and chip communication module, a chip and lower computer (temperature sampling plate) communication module, 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 (sinusoidal pulse width modulation) method, and obtains the sum of the duty ratios of two paths of PWM waves as D through real-time calculation according to the voltage actually required. Therefore, the current acting on 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, diagonal IGBT pipes of an upper bridge arm and a lower bridge arm corresponding to different phase bridge arms of the H-bridge circuit are respectively controlled to be conducted to form a channel, further, the voltage waveform supplied to the motor is controlled, the running direction of the motor is controlled to achieve the ascending and descending of the piston, and the duty ratio of the SPWM is controlled to adjust the voltage value output to the motor so as to change the actual power of the motor.
The Stirling refrigerator driving system can realize normal starting and stable operation of the refrigerator at various environmental temperatures, accurate and stable temperature control and programmable parameters. When the refrigerator is started, a slow start mode is adopted. The PWM wave control signal is generated by a main control chip, the operation parameters (including the operation speed of the linear compressor, the temperature of a cold end, the voltage and the current of a motor 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 refrigeration temperature of the free piston Stirling refrigerator is regulated and controlled by a controller, the whole system is controlled by three closed loops, and the three closed loops comprise a temperature loop, a speed loop and a current loop. The temperature ring is used as the outermost ring and is subjected to model prediction control; the middle loop is a speed loop, the innermost loop is a current loop, and the 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 time T ═ T, 2T.., NT, the step response coefficient was calculated as follows:
s2: the P-step predictive model output representing the initial value with the amount of control applied to the system in the past is:
T(k+1)＝AΔU(k)+A0U(k-1)
where T (k +1) ═ T (k +1), T (k +2),. -, T (k + p)]TIs 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: and introducing the effect of feedback correction, and then having P step output items:
Tp(k+1)＝T(k+1)+he(k)＝AΔU(k)+A0U(k-1)+he(k)
wherein, Tp(k+1)＝[(tp(k+1),tp(k+2),...,tp(k+p)]T，e(k)＝t(k)-tp(k)
h＝(h1,h2,...,hp)T，tp＝a1u(k)+(a2-a1)u(k-1)+(a3-a2)u(k-2)+...+(aN-aN-1)u(k-N+1)
S4: the reference trajectory is given as follows:
Tr＝(tr(k+1),tr(k+2),...,tr(k+P))T
s5: in order to enhance robustness, the influence of the control quantity u (k) at the current moment on the output value of the system at the future moment is considered, and the control action increment delta u applied to the system is prevented from changing too severely, and a target function of a quadratic performance index is adopted, and the function weights the output error and the control increment:
wherein q isi，rjAre weighting coefficients representing the suppression of the tracking error and the variation of the control action, w (k + i) representing a given desired value, ym(k + i | k) represents a prediction output value;
the above equation is rewritten into vector form as follows:
minJ(k)＝[Tr(k+1)-Tp(k+1)]TQ[Tr(k+1)-Tp(k+1)]+ΔUT(k)RΔU(k)
＝(AΔU(k)+A0U(k-1)+he(k)-Tr(k+1))TQ
(AΔU(k)+A0U(k-1)+he(k)-Tr(k+1))+ΔU(k)TRΔU(k)
s6: minimizing the objective function according to the control objective of the temperature loop, thus yielding:
s7: the optimal control law can be obtained as follows:
ΔU(k)＝(AQA+R)-1ATQ(Tr(k+1)-A0U(k-1)-he(k))
wherein Q and R are respectively P and M dimension weighting matrix.
Specifically, the Stirling refrigerator driving controller designed by the invention realizes temperature control of a refrigeration process by adjusting the motion 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 in the maximum stroke; and in the temperature control stage, controlling the stroke of the compressor to be smaller than the maximum stroke. After the controller receives a system starting instruction, in order to prevent the motor from colliding with a cylinder under a step voltage signal when the motor is started, the motor needs to be controlled to work under certain amplitude and frequency, so that the motor is started by adopting a method of slowly increasing the SPWM modulation duty ratio, namely a soft starting process; when the motor enters a cooling process after being started, the motor is driven to do reciprocating motion with maximum amplitude by sine waves with certain frequency, and the change of temperature is monitored; and entering a temperature control stage when the actually measured temperature is close to the set temperature, gradually reducing the amplitude of the reciprocating motion by reducing the amplitude of the driving voltage of the motor until the required temperature is reached, and then continuously adjusting the motion amplitude of the motor to keep the temperature of the cold end of the Stirling refrigerator at the required temperature.
The control scheme adopted by the invention is divided into a starting stage, a cooling stage and a temperature control stage to control the refrigeration process. The following scheme is adopted: the temperature loop is taken as the outermost loop, the intermediate loop is the velocity loop, and the innermost loop is the current loop. In the starting stage: in order to prevent the motor from colliding with the cylinder due to sudden voltage, the optimal amplitude and frequency combination of the linear motor are obtained by using the 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 at the 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 motor amplitude is adjusted by using an MPC algorithm according to the actual temperature requirement so as to meet the requirements of short adjustment time, small overshoot and small steady-state fluctuation in the temperature control process. And combining the optimal amplitude and frequency obtained by calculation in the control strategy to obtain an optimal motion track, and calculating the motion speed of the motor. And then the motors are regulated to do corresponding linear motion through PI controllers of the speed ring and the current ring.
In the description herein, references to the description of "one embodiment," "an example," "a specific example" or the like are intended to 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 invention. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. 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 shows and describes the general principles, essential 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, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed.
Claims (3)
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 ring, a PI control module of a speed ring, a PI control module of a current ring, 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.
2. The model predictive algorithm-based free-piston stirling cooler temperature control system of claim 1 wherein: and the Model Prediction Control (MPC) module comprises a model prediction control algorithm, a reference track, a prediction model and a rolling optimization and feedback correction unit.
3. A model predictive algorithm-based free-piston stirling cooler temperature control system according to claim 2 wherein the model predictive control algorithm employed by the temperature loop comprises the steps of:
s1: at each sampling time T ═ T, 2T.., NT, the step response coefficient was calculated as follows:
s2: the P-step predictive model output representing the initial value with the amount of control applied to the system in the past is:
T(k+1)＝AΔU(k)+A0U(k-1)
where T (k +1) ═ T (k +1), T (k +2),. -, T (k + p)]TIs 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: and introducing the effect of feedback correction, and then having P step output items:
Tp(k+1)＝T(k+1)+he(k)＝AΔU(k)+A0U(k-1)+he(k)
wherein, Tp(k+1)＝[(tp(k+1),tp(k+2),...,tp(k+p)]T e(k)＝t(k)-tp(k)h＝(h1,h2,...,hp)T tp＝a1u(k)+(a2-a1)u(k-1)+(a3-a2)u(k-2)+...+(aN-aN-1)u(k-N+1)
S4: the reference trajectory is given as follows:
Tr＝(tr(k+1),tr(k+2),...,tr(k+P))T
s5: in order to enhance robustness, the influence of the control quantity u (k) at the current moment on the output value of the system at the future moment is considered, and meanwhile, the control action increment delta u applied to the system is prevented from changing too severely, a target function of a quadratic performance index is adopted, and the function weights the output error and the control increment:
wherein q isi，rjAre weighting coefficients representing the suppression of the tracking error and the variation of the control action, w (k + i) representing a given desired value, ym(k + i | k) represents a prediction output value;
the above equation is rewritten into vector form as follows:
min J(k)＝[Tr(k+1)-Tp(k+1)]TQ[Tr(k+1)-Tp(k+1)]+ΔUT(k)RΔU(k)
＝(AΔU(k)+A0U(k-1)+he(k)-Tr(k+1))TQ(AΔU(k)+A0U(k-1)+he(k)-Tr(k+1))+ΔU(k)TRΔU(k)
s6: minimizing the objective function according to the control objective of the temperature loop, thus yielding:
s7: the optimal control law can be obtained as follows:
ΔU(k)＝(AQA+R)-1ATQ(Tr(k+1)-A0U(k-1)-he(k))
wherein Q and R are respectively P and M dimension weighting matrix.
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