CN115978856B - Whale optimized disturbance compensation Smith pre-estimated control method in air wave refrigeration process - Google Patents

Abstract

The present invention discloses a whale-optimized disturbance-compensated Smith predictive control method for a gas wave refrigeration process, comprising the following steps: S1: taking the influence of the valve opening of the gas flow entering the gas wave machine on the temperature of the refrigeration gas as the controlled object, taking the influence of the valve opening of the gas flow discharged from the heat exchanger on the temperature of the refrigeration gas as the disturbance object, and collecting the test data of the gas wave refrigeration process; S2: using the collected test data, based on the least squares method, identifying and obtaining a high-order controlled object model and a high-order disturbance model of the gas wave refrigeration process; S3: using a suboptimal order reduction algorithm, reducing the high-order model to a second-order controlled object model and a first-order disturbance model with time lag for the gas wave refrigeration process; S4: designing a disturbance-compensated Smith predictive control method for the gas wave refrigeration process; S5: realizing the optimization adjustment of the set value tracking controller and the filter parameters in the disturbance-compensated Smith predictive control method through the whale optimization algorithm, and realizing the tracking of the set value. This method is of great significance to improving the efficiency of the gas wave refrigeration.

Description

A whale-optimized disturbance compensation Smith predictive control method for gas wave refrigeration process

Technical Field

The present invention relates to the field of gas wave refrigeration process control engineering, and in particular to a whale-optimized disturbance compensation Smith predictive control method for a gas wave refrigeration process.

Background technique

The gas wave refrigeration process is a process that uses the principle of gas expansion refrigeration. It achieves the purpose of separating hot and cold fluids by injecting high-pressure gas into the oscillating tube to generate shock waves and expansion waves. Using the gas wave refrigeration process for gas refrigeration can not only make full use of the pressure energy of the gas itself, but also achieve a good and controllable refrigeration effect. Compared with turbine expander refrigeration, the gas wave refrigeration process also has the advantages of simple structure, low operating speed, and strong liquid carrying capacity. Therefore, it is widely used in important fields such as petrochemicals and aerospace.

The changes in the speed, pressure, temperature, expansion ratio and other operating parameters of the gas wave refrigeration process have an important impact on the refrigeration efficiency. Therefore, how to timely and reliably control the large-flow gas wave refrigeration device and improve the refrigeration efficiency of the gas wave refrigeration device is an urgent problem to be solved. The control of the gas wave refrigeration process usually adopts the traditional PID control scheme. However, due to the measurable disturbances and large hysteresis characteristics of the gas wave refrigeration process, simple PID control is difficult to achieve satisfactory control effects. Therefore, it is necessary to design a new control method to take into account the set value tracking characteristics and interference suppression characteristics of the system.

Summary of the invention

In order to solve the above problems, the present invention provides a technical solution adopted by the present invention: a whale optimization disturbance compensation Smith prediction control method for a gas wave refrigeration process, comprising the following steps:

S1: The influence of the valve opening of the gas flow entering the gas wave machine on the refrigerant gas temperature is taken as the controlled object, and the influence of the valve opening of the gas flow discharged from the heat exchanger on the refrigerant gas temperature is taken as the disturbance object, and the test data of the gas wave refrigeration process is collected;

S2: Using the collected test data, the high-order controlled object model and high-order disturbance model of the gas wave refrigeration process are identified based on the least squares method;

S3: Using the suboptimal order reduction algorithm, the high-order model is reduced to a second-order controlled object model with time lag and a first-order disturbance model of the gas wave refrigeration process;

S4: Design a disturbance compensation Smith predictive control method for gas wave refrigeration process;

S5: The whale optimization algorithm is used to optimize the setting value tracking controller and filter parameters in the disturbance compensation Smith predictive control method to achieve setting value tracking.

Further: the process of designing the Smith predictive control method for disturbance compensation of the gas wave refrigeration process is as follows:

Assume that the closed-loop transfer function of the gas wave refrigeration process output y and the set value input r is:

Assume that the closed-loop transfer function of the gas wave refrigeration process output y and the disturbance input d is:

in, Indicates the controlled object, /> represents the controlled object model, _Gp0 (s) and _Gm0 (s) are the parts without time delay, _Gd (s) represents the disturbance object, F(s) is the set value filter, _Gc (s) is the set value tracking controller, and _Gf (s) is the disturbance compensation controller;

When the controlled object model is accurate, that is, G _m0 =G _p0 , τ _m =τ _p , the transfer functions of the gas wave refrigeration process output and the set value input and disturbance input are:

If the influence of the disturbance signal d on the output y is zero, G _yd (s) = 0, that is, G _d + G _f G _p = 0. Therefore, the set value tracking control of the gas wave refrigeration process is only related to the filter F(s) and the set value tracking controller G _c (s), and the disturbance suppression control is only related to the disturbance compensation controller G _f (s). The disturbance compensation Smith predictive control method is designed to completely decouple the set value tracking control from the disturbance suppression control, so that the gas wave refrigeration process has good set value tracking characteristics and disturbance suppression characteristics.

Further: the process of using the suboptimal order reduction algorithm to reduce the high-order model to a second-order controlled object model with time lag and a first-order disturbance model of the gas wave refrigeration process is as follows:

Assume the original model is:

The reduced-order model is:

Under the same input signal r(t), the Laplace transform of the error signal between the original model and the reduced-order model is:

E(s)＝[G(s)e ^-Ts - _Gr (s)e ^-Trs ]R(s) (7)

Where R(s) is the Laplace transform of the input r(t), and the signal h(t) = ω(t)e(t) is introduced, then the ISE index can be defined as follows:

Where ω(t) is a weight function, and the delay system is solved by approximate optimization;

Define the unknown parameter vector ξ = [α ₁ , α ₂ , …, α _k , β ₁ , β ₂ , …, β _r+1 , _Tr ], then for a given input signal, the error signal of the reduced-order model can be defined: where the error signal is explicitly written as a function of ξ,

The objective function of suboptimal reduction is defined as:

By minimizing the objective function, the second-order controlled object model of the outlet temperature of the gas wave refrigeration process is obtained as follows:

Among them, T ₁ , T ₂ , T ₃ are the time constants of the gas wave refrigeration process, K is the refrigeration process gain, and τ _p is the control delay time;

The first-order disturbance object model is obtained as:

Among them, _T4 is the disturbance process time constant, _K1 is the disturbance gain, and _τd is the disturbance control delay time.

Furthermore, the designs of the set value tracking controller and the disturbance compensation controller of the gas wave refrigeration process in the disturbance compensation Smith predictive control method are independent of each other, and the specific derivation process is as follows:

Assume that the expression of the setpoint tracking controller G _c (s) is:

Thus we can get:

Assume that the desired setpoint tracking characteristic is:

Among them, λ is the time constant, and the corresponding coefficients are equal to obtain:

Solutions have to:

From the above, we can see that the design of the filter F(s) and the controller G _c (s) is only related to the value of the parameter λ, which simplifies the design of the controller;

According to the disturbance compensation principle, in order to make the influence of disturbance on the output of gas wave refrigeration process zero, the disturbance compensation controller _Gf (s) should satisfy:

G _d +G _f G _p = 0 (17)

Further: the optimization setting of the set value tracking controller and the filter parameters in the disturbance compensation Smith predictive control method is realized by the whale optimization algorithm, as follows:

The whale optimization algorithm sets the number of individuals in the population to N and the maximum number of iterations to M. It starts from a set of random solutions. In each iteration, it selects a random search agent or the best search agent so far to guide the search. Depending on the value of a random number p between [0,1], the whale optimization algorithm switches between spiral and shrinking wrapping update positions. During the iteration process, The coefficient vector starts from 2 and decreases linearly to 0, with values between [-a, a]/> The range of change decreases accordingly. When/> When a random search agent is selected to guide the search, /> When , the optimal solution so far is selected to guide the search, and the objective function is calculated as follows:

Among them, e(t) is the system output error, u(t) is the control input, t _r is the rise time, μ ₁ , μ ₂ , μ ₄ are weighting coefficients, and in order to obtain a more satisfactory transition process, the objective function uses the integral of the absolute value of the error. In order to prevent the control amount from being too large, the square term of the control amount is introduced into the objective function;

Let ey(t) = y(t) - y(t-1). When ey(t) < 0, the above formula is updated as follows:

Among them, μ ₃ >>μ ₁ , μ ₂ , μ ₄ , in the optimization process, μ ₁ =1, μ ₂ =0.001, μ ₃ =20, μ ₄ =2 are selected;

After reaching the maximum number of iterations, the whale optimization algorithm outputs the optimal parameter λ value in the disturbance compensation Smith predictor control method, thereby calculating the setpoint filter F(s) and the setpoint tracking controller G _c (s) to realize the gas wave refrigeration process control.

The present invention provides a whale-optimized disturbance compensation Smith predictive control method for an air wave refrigeration process. The method adopts a suboptimal order reduction method to obtain a low-order model that is convenient for controller design. The set value tracking control and disturbance compensation control are realized by designing a disturbance compensation Smith predictive control structure. The controller parameters are adjusted using a whale optimization algorithm. The method of the present invention can enable the air wave mechanism refrigeration process to obtain good set value tracking and disturbance compensation control effects; it can realize the control of system set value tracking and disturbance compensation in the air wave mechanism refrigeration process and achieve good control effects, which is of great significance to improving the efficiency of air wave refrigeration.

BRIEF DESCRIPTION OF THE DRAWINGS

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

FIG1 is a flow chart of a whale-optimized disturbance compensation Smith predictive control method for a gas wave refrigeration process disclosed in the present invention;

FIG2 is a structural diagram of a whale-optimized disturbance compensation Smith predictive control method for a gas wave refrigeration process disclosed in the present invention.

Detailed ways

It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other. The present invention will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. The following description of at least one exemplary embodiment is actually only illustrative and is by no means intended to limit the present invention and its application or use. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit exemplary embodiments according to the present invention. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprising" and/or "including" are used in this specification, it indicates the presence of features, steps, operations, devices, components and/or combinations thereof.

Unless otherwise specifically stated, the relative arrangement of the parts and steps described in these embodiments, the numerical expressions and numerical values do not limit the scope of the present invention. At the same time, it should be clear that, for ease of description, the sizes of the various parts shown in the drawings are not drawn according to the actual proportional relationship. The technology, methods and equipment known to ordinary technicians in the relevant field may not be discussed in detail, but in appropriate cases, the technology, methods and equipment should be regarded as a part of the authorization specification. In all examples shown and discussed here, any specific value should be interpreted as being merely exemplary, rather than as a limitation. Therefore, other examples of exemplary embodiments may have different values. It should be noted that similar numbers and letters represent similar items in the following drawings, so once an item is defined in one drawing, it does not need to be further discussed in subsequent drawings.

In the description of the present invention, it is necessary to understand that the directions or positional relationships indicated by directional words such as "front, back, up, down, left, right", "lateral, vertical, perpendicular, horizontal" and "top, bottom" are usually based on the directions or positional relationships shown in the drawings. They are only for the convenience of describing the present invention and simplifying the description. Unless otherwise specified, these directional words do not indicate or imply that the device or element referred to must have a specific direction or be constructed and operated in a specific direction. Therefore, they cannot be understood as limiting the scope of protection of the present invention: the directional words "inside and outside" refer to the inside and outside relative to the contours of each component itself.

For ease of description, spatially relative terms such as "above", "above", "on the upper surface of", "above", etc. may be used here to describe the spatial positional relationship between a device or feature and other devices or features as shown in the figure. It should be understood that spatially relative terms are intended to include different orientations of the device in use or operation in addition to the orientation described in the figure. For example, if the device in the accompanying drawings is inverted, the device described as "above other devices or structures" or "above other devices or structures" will be positioned as "below other devices or structures" or "below their position devices or structures". Thus, the exemplary term "above" may include both "above" and "below". The device may also be positioned in other different ways (rotated 90 degrees or in other orientations), and the spatially relative descriptions used here are interpreted accordingly.

In addition, it should be noted that the use of terms such as "first" and "second" to limit components is only for the convenience of distinguishing the corresponding components. Unless otherwise stated, the above terms have no special meaning and therefore cannot be understood as limiting the scope of protection of the present invention.

As shown in FIG1 , a whale-optimized disturbance compensation Smith predictive control method for a gas wave refrigeration process includes the following steps:

S1: Analyze and determine the influence of the valve opening of the gas flow entering the gas wave machine on the refrigerant gas temperature as the controlled object, and the influence of the valve opening of the gas flow discharged from the heat exchanger on the refrigerant gas temperature as the disturbance object, and collect the test data of the gas wave refrigeration process;

S2: Taking the valve opening of the gas flow entering the gas wave machine as input information and the refrigerant gas temperature as output, the least square method is used to identify the model using the collected test data of the gas wave refrigeration process to obtain a high-order controlled object model. Similarly, taking the valve opening of the gas flow discharged from the heat exchanger as input information and the refrigerant gas temperature as output, a high-order disturbance model is obtained by identification;

S3: Using a suboptimal order reduction algorithm, the high-order model obtained in S2 is reduced to a second-order controlled plant model with time lag and a first-order disturbance model;

S4: Design disturbance compensation Smith predictor control method:

Assume that the closed-loop transfer function of the gas wave refrigeration process output y and the set value input r is:

Assume that the closed-loop transfer function of the gas wave refrigeration process output y and the disturbance input d is:

in, Indicates the controlled object, /> represents the controlled object model, _Gp0 (s) and _Gm0 (s) are the parts without time delay, _Gd (s) represents the disturbance object, F(s) is the set value filter, is the set value tracking controller, and _Gf (s) is the disturbance compensation controller.

When the controlled object model is accurate, that is, G _m0 = G _p0 , τ _m = τ _p , the transfer functions of the system output and the set value input and disturbance input are:

If the influence of the disturbance signal d on the output y is zero, G _yd (s) = 0, that is, G _d + G _f G _p = 0. Therefore, the set value tracking control of the gas wave refrigeration process system is only related to the filter F(s) and the set value tracking controller G _c (s), and the disturbance suppression control is only related to the disturbance compensation controller G _f (s). The disturbance compensation Smith predictive control scheme design completely decouples the set value tracking control from the disturbance suppression control, so that the controlled system of the gas wave refrigeration process has good set value tracking characteristics and disturbance suppression characteristics.

S5: The whale optimization algorithm is used to optimize the parameters of the setpoint tracking controller and the setpoint filter in the disturbance compensation Smith predictive control scheme to achieve setpoint tracking.

Furthermore, in the process of using the suboptimal order reduction algorithm to reduce the high-order disturbance model to a second-order controlled object model with time lag and a first-order disturbance model of the gas wave refrigeration process, the following is done:

Assume the original model is:

The reduced-order model is:

Under the same input signal r(t), the Laplace transform of the error signal between the original model and the reduced-order model is:

E(s)＝[G(s)e ^-Ts - _Gr (s)e ^-Trs ]R(s) (7)

Where R(s) is the Laplace transform of the input r(t), and the signal h(t) = ω(t)e(t) is introduced, then the ISE index can be defined as follows:

Where ω(t) is a weight function;

Define the unknown parameter vector ξ = [α ₁ , α ₂ , …, α _k , β ₁ , β ₂ , …, β _r+1 , _Tr ], then for a given input signal, the error signal of the reduced-order model can be defined: The error signal is explicitly written as a function of ξ, so the suboptimal reduced-order objective function can be defined as:

By minimizing the objective function, the second-order controlled object model of the outlet temperature of the gas wave refrigeration process is obtained as follows:

Among them, T ₁ , T ₂ , T ₃ are the time constants of the gas wave refrigeration process, K is the refrigeration process gain, and τ _p is the control delay time;

The first-order disturbance object model is obtained as:

Among them, _T4 is the disturbance process time constant, _K1 is the disturbance gain, and _τd is the disturbance control delay time.

The present invention adopts a suboptimal order reduction method to obtain a low-order model with time lag, which retains the original model characteristics as much as possible and facilitates the design of subsequent control schemes.

Further, in the above technical solution, the disturbance compensation Smith predictive control structure is shown in FIG2 . In the disturbance compensation Smith predictive controller solution, the set value tracking controller and the disturbance compensation controller of the gas wave refrigeration process system are designed independently of each other. The specific method derivation process is as follows:

Assume that the expression of the setpoint tracking controller G _c (s) is:

Thus we can get:

Assume that the desired setpoint tracking characteristic is:

Among them, λ is the time constant, and the corresponding coefficients are equal to obtain:

Solutions have to:

From the above, we can see that the design of the filter F(s) and the controller G _c (s) is only related to the value of the parameter λ, which greatly simplifies the design of the controller;

According to the disturbance compensation principle, in order to make the influence of disturbance on the output of gas wave refrigeration process zero, the disturbance compensation controller _Gf (s) should satisfy:

G _d +G _f G _p = 0 (17)

Right now:

Furthermore, the whale optimization algorithm is used to optimize the setting value tracking controller and filter parameters in the disturbance compensation Smith predictive control scheme, as follows:

The whale optimization algorithm sets the number of individuals in the population to N, which can be 30, the number of iterations to M, which can be 200, and starts from a set of random solutions. In each iteration, a random search agent or the best search agent so far can be selected to guide the search. Depending on the value of a random number p between [0,1], the whale optimization algorithm can switch between spiral and shrinking wrapping update positions. During the iteration process, The coefficient vector starts from 2 and decreases linearly to 0, with values between [-a, a]/> The range of change decreases accordingly. When/> When a random search agent is selected to guide the search, /> When , the optimal solution so far is selected to guide the search, and the objective function is calculated as follows:

Among them, e(t) is the system output error, u(t) is the control input, t _r is the rise time, μ ₁ , μ ₂ , μ ₄ are weighting coefficients, and in order to obtain a more satisfactory transition process, the objective function uses the integral of the absolute value of the error. In order to prevent the control amount from being too large, the square term of the control amount is introduced into the objective function;

In order to avoid overshoot, let ey(t) = y(t) - y(t-1). When ey(t) < 0, the above formula is updated as follows:

Wherein μ ₃ >>μ ₁ , μ ₂ , μ ₄ , the present invention selects μ ₁ =1, μ ₂ =0.001, μ ₃ =20, μ ₄ =2 during the optimization process;

After reaching the maximum number of iterations, the whale optimization algorithm outputs the set value tracking controller and the optimal parameter λ value of the filter, thereby calculating the set value filter F(s) and the set value tracking controller G _c (s) to achieve the set value tracking control of the system.

The experimental results of the comparison between the present invention and Smith predictive control and PID control are shown in Table 1. The method of the present invention enables the system to have better set value tracking characteristics and greatly reduces the influence of disturbance input on the gas wave refrigeration process.

Table 1 Comparison of dynamic response of gas wave refrigeration process control

Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein by equivalents. However, these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims (1)

1. A whale-optimized disturbance compensation Smith predictive control method for a gas wave refrigeration process, characterized in that it comprises the following steps: S1: The influence of the valve opening of the gas flow entering the gas wave machine on the refrigerant gas temperature is taken as the controlled object, and the influence of the valve opening of the gas flow discharged from the heat exchanger on the refrigerant gas temperature is taken as the disturbance object, and the test data of the gas wave refrigeration process is collected; S2: Using the collected test data, the high-order controlled object model and high-order disturbance model of the gas wave refrigeration process are identified based on the least squares method; S3: Using the suboptimal order reduction algorithm, the high-order model is reduced to a second-order controlled object model with time lag and a first-order disturbance model of the gas wave refrigeration process; S4: Design a disturbance compensation Smith predictive control method for gas wave refrigeration process; S5: The whale optimization algorithm is used to optimize the setting value tracking controller and filter parameters in the disturbance compensation Smith predictive control method to achieve setting value tracking; The process of designing the Smith predictive control method for disturbance compensation of the gas wave refrigeration process is as follows: Assume that the closed-loop transfer function of the gas wave refrigeration process output y and the set value input r is: Assume that the closed-loop transfer function of the gas wave refrigeration process output y and the disturbance input d is: in, Indicates the controlled object, /> represents the controlled object model, _Gp0 (s) and _Gm0 (s) are the parts without time delay, _Gd (s) represents the disturbance object, F(s) is the set value filter, _Gc (s) is the set value tracking controller, and _Gf (s) is the disturbance compensation controller; When the controlled object model is accurate, that is, G _m0 =G _p0 , τ _m =τ _p , the transfer functions of the gas wave refrigeration process output and the set value input and disturbance input are: If the influence of the disturbance signal d on the output y is zero, G _yd (s) = 0, that is, G _d + G _f G _p = 0. Therefore, the set value tracking control of the gas wave refrigeration process is only related to the filter F(s) and the set value tracking controller G _c (s), and the disturbance suppression control is only related to the disturbance compensation controller G _f (s). The disturbance compensation Smith predictive control method is designed to completely decouple the set value tracking control from the disturbance suppression control, so that the gas wave refrigeration process has good set value tracking characteristics and disturbance suppression characteristics at the same time. The process of using the suboptimal order reduction algorithm to reduce the high-order model to a second-order controlled object model with time lag and a first-order disturbance model of the gas wave refrigeration process is as follows: Assume the original model is: The reduced-order model is: Under the same input signal r(t), the Laplace transform of the error signal between the original model and the reduced-order model is: Where R(s) is the Laplace transform of the input r(t), and the signal h(t) = ω(t)e(t) is introduced, then the ISE index can be defined as follows: Where ω(t) is a weight function, and the delay system is solved by approximate optimization; Define the unknown parameter vector ξ = [α ₁ , α ₂ , …, α _k , β ₁ , β ₂ , …, β _r+1 , _Tr ], then for a given input signal, the error signal of the reduced-order model can be defined: where the error signal is explicitly written as a function of ξ, The objective function of suboptimal reduction is defined as: By minimizing the objective function, the second-order controlled object model of the outlet temperature of the gas wave refrigeration process is obtained as follows: Among them, T ₁ , T ₂ , T ₃ are the time constants of the gas wave refrigeration process, K is the refrigeration process gain, and τ _p is the control delay time; The first-order disturbance object model is obtained as: Among them, T ₄ is the disturbance process time constant, K ₁ is the disturbance gain, and τ _d is the disturbance control delay time; The designs of the set value tracking controller and the disturbance compensation controller of the gas wave refrigeration process in the disturbance compensation Smith predictive control method are independent of each other. The specific derivation process is as follows: Assume that the expression of the setpoint tracking controller G _c (s) is: Thus we can get: Assume that the desired setpoint tracking characteristic is: Among them, λ is the time constant, and the corresponding coefficients are equal to obtain: Solutions have to: From the above, we can see that the design of the filter F(s) and the controller G _c (s) is only related to the value of the parameter λ, which simplifies the design of the controller; According to the disturbance compensation principle, in order to make the influence of disturbance on the output of gas wave refrigeration process zero, the disturbance compensation controller _Gf (s) should satisfy: G _d +G _f G _p = 0 (17) Right now: The optimization setting of the set value tracking controller and the filter parameters in the disturbance compensation Smith predictive control method is realized by the whale optimization algorithm, as follows: The whale optimization algorithm sets the number of individuals in the population to N and the maximum number of iterations to M. It starts from a set of random solutions. In each iteration, it selects a random search agent or the best search agent so far to guide the search. Depending on the value of a random number p between [0,1], the whale optimization algorithm switches between spiral and shrinking wrapping update positions. During the iteration process, The coefficient vector starts from 2 and decreases linearly to 0, with values between [-a, a]/> The range of change decreases accordingly. When/> When a random search agent is selected to guide the search, /> When , the optimal solution so far is selected to guide the search, and the objective function is calculated as follows: Among them, e(t) is the system output error, u(t) is the control input, t _r is the rise time, μ ₁ , μ ₂ , μ ₄ are weighting coefficients, and in order to obtain a more satisfactory transition process, the objective function uses the integral of the absolute value of the error. In order to prevent the control amount from being too large, the square term of the control amount is introduced into the objective function; Let ey(t) = y(t) - y(t-1). When ey(t) < 0, the above formula is updated as follows: Among them, μ ₃ >>μ ₁ , μ ₂ , μ ₄ , in the optimization process, μ ₁ =1, μ ₂ =0.001, μ ₃ =20, μ ₄ =2 are selected; After reaching the maximum number of iterations, the whale optimization algorithm outputs the optimal parameter λ value in the disturbance compensation Smith predictor control method, thereby calculating the setpoint filter F(s) and the setpoint tracking controller G _c (s) to realize the gas wave refrigeration process control.