PID (Proportion Integration Differentiation) controller robust design method and system of inertia and delay fractional order object

Abstract

The invention provides a PID (Proportion Integration Differentiation) controller robust design method and system of an inertia and delay fractional order object. The method comprises the following steps: describing a controlled object by adopting an inertia and delay fractional order transfer function; a proportional-integral-differential controller is adopted to describe the controller; a crossing frequency and a phase margin are given, and a proportional gain, an integral gain and a differential gain of a proportional-integral-differential controller are uniquely solved based on three constraint equations of the given crossing frequency, the given phase margin and the condition that the slope of an open-loop phase of a closed-loop system at the crossing frequency is zero (also known as phase flatness); if a null set is solved, the values of the crossing frequency and the phase margin need to be given again, and solving is carried out; according to the method, the proportional-integral-differential controller parameters can be directly solved on the basis of three given constraint equations such as the crossing frequency, the phase margin and the phase flatness, it is guaranteed that the proportional-integral-differential controller has high robustness, and the method has practical application value.

Description

Technical Field

[0001] The invention relates to a proportional-integral-differential controller design method, and in particular to a PID controller robust design method and system for an inertia-plus-delay fractional-order object. Background Art

[0002] Proportional-Integral-Derivative (PID) controller is the most widely used controller in motion control systems, chemical control systems and energy systems, due to its advantages of easy implementation, simple structure, small number of parameters and reliable performance. Fractional-order objects describe the dynamic characteristics of the controlled object through fractional-order differential equations. It is a generalized form of integer-order objects and can more accurately describe the dynamic characteristics of the actual system.

[0003] The parameters that need to be adjusted for PID control are proportional gain, integral gain and differential gain. The current technologies mainly include methods based on the controlled object model calculation, evolutionary algorithm optimization and other methods for adjustment. The method based on the controlled object model calculation generally obtains the controller parameters through the transfer function of the controlled object combined with the expected closed-loop dynamic equation, such as the internal model method and the SIMC method. This method is mainly designed for the nominal object, and the robustness of the controller is checked after the design parameters, which has many steps.

[0004] Optimizing PID controller parameters based on evolutionary algorithms can solve the minimum control performance index based on robustness constraints. This method has the disadvantages of slow solution speed and easy convergence of parameters to local optimum. In addition, current research lacks direct calculation methods for PID controller parameters under typical robust indicators (such as maximum sensitivity function, phase margin, amplitude margin, phase flatness, crossover frequency, etc.).

[0005] It should be noted that PID controller parameter tuning methods such as those based on controlled object model calculation and evolutionary algorithm optimization are mainly for integer-order objects. Currently, there are few PID controller parameter tuning methods for fractional-order objects.

[0006] However, with the development of fractional-order calculus theory and technology, more and more controlled objects are described by fractional-order transfer functions. Therefore, it is necessary to study the robust tuning of PID controller parameters for fractional-order objects. Summary of the invention

[0007] The purpose of the present invention is to solve the problem of robust design of a PID controller for a class of fractional-order objects and to provide a method and system for robust design of a PID controller for an inertia-plus-delay fractional-order object.

[0008] In a first aspect, the present invention provides a robust design method for a PID controller of an inertia plus delay fractional-order plant, comprising the following steps:

[0009] 1) Establish a closed-loop system consisting of the controlled object and the feedback controller;

[0010] The controlled object adopts the inertia plus delay fractional order transfer function G p (s) Description, as follows:

[0011]

[0012] In the formula, G p (s) is the inertia plus delay fractional order transfer function, s is the differential operator, K is the gain of the controlled object, and K∈[-10 10 ,0∪0,10 10 ], T is the time constant of the controlled object, T∈(0,10 10 ], α is the order of the controlled object, α∈(0,2), L is the delay time constant of the controlled object, L∈(0,10 10 ], e is a natural constant;

[0013] The feedback controller adopts PID controller, and its transfer function G c (s) are as follows:

[0014]

[0015] In the formula, k p is the proportional gain of the PID controller, and k p ∈[-10 10 ,10 10 ],k i is the integral gain of the PID controller, and k i ∈[-10 10 ,10 10 ],k d is the differential gain of the PID controller, with k d ∈[-10 10 ,10 10 ]; k p , k i and k d are the PID controller parameters to be adjusted;

[0016] 2) Given the crossover frequency ω of the closed-loop system gc and phase margin Assume that the slope of the open-loop phase of the closed-loop system is zero at the crossover frequency. By solving equation 1, equation 2, and equation 3, the proportional gain k of the PID controller can be uniquely obtained. p , integral gain k iand the differential gain k d ;

[0017] Solve equation 1 as follows:

[0018]

[0019] In the formula, B 31 is the intermediate variable,

[0020] S 3 is the intermediate variable,

[0021] B 32 is the intermediate variable,

[0022] C 3 is the intermediate variable,

[0023] Solve equation 2 as follows:

[0024]

[0025] A is the gain margin;

[0026] Solve equation three as follows:

[0027]

[0028] In the formula, E 3 is the intermediate variable, E 3 =-k d ω gc 2 +k i ;

[0029] F 3 is the intermediate variable, F 3 =k p ω gc ;

[0030] E 3’ For E 3 Yes gc The derivative of E 3’ =-2k d ω gc ;

[0031] F 3’ F 3 Yes gc The derivative of 3’ =k p ;

[0032] B 31’ For B 31Yes gc The derivative of

[0033] B 32’ For B 32 Yes gc The derivative of

[0034] 3) If the proportional gain k is solved p , integral gain k i and the differential gain k d is an empty set, then the crossing frequency ω is re-given gc and phase margin Re-solve equations (3)-(5) to uniquely solve the proportional gain k of the PID controller p , integral gain k i and the differential gain k d ;

[0035] If the proportional gain k p , integral gain k i and the differential gain k d is a non-empty set, then the proportional gain k p , integral gain k i and the differential gain k d To meet the crossover frequency ω gc , Phase Margin and PID controller parameters for phase flatness constraints.

[0036] In a second aspect, the present invention provides a PID controller robust design system for an inertia plus delay fractional-order plant, comprising:

[0037] The closed-loop system establishment module is used to establish a closed-loop system consisting of a controlled object and a feedback controller; wherein,

[0038] The controlled object adopts the inertia plus delay fractional order transfer function G p (s) Description, as follows:

[0039]

[0040] In the formula, G p (s) is the inertia plus delay fractional order transfer function, s is the differential operator, K is the gain of the controlled object, and K∈[-10 10 ,0∪0,10 10 ], T is the time constant of the controlled object, T∈(0,10 10 ], α is the order of the controlled object, α∈(0,2), L is the delay time constant of the controlled object, L∈(0,10 10 ], e is a natural constant;

[0041] The feedback controller adopts PID controller, and its transfer function G c (s) are as follows:

[0042]

[0043] In the formula, k p is the proportional gain of the PID controller, and k p ∈[-10 10 ,10 10 ],k i is the integral gain of the PID controller, and k i ∈[-10 10 ,10 10 ],k d is the differential gain of the PID controller, with k d ∈[-10 10 ,10 10 ]; k p , k i and k d are the PID controller parameters to be adjusted;

[0044] The parameter solving module is connected with the closed-loop system establishment module to give the crossover frequency ω of the closed-loop system gc and phase margin Assume that the slope of the open-loop phase of the closed-loop system is zero at the crossover frequency. By solving equation 1, equation 2, and equation 3, the proportional gain k of the PID controller can be uniquely obtained. p , integral gain k i and the differential gain k d ;

[0045] If the proportional gain k p , integral gain k i and the differential gain k d is an empty set, then the crossing frequency ω is re-given gc and phase margin Re-solve equations (3)-(5) to uniquely solve the proportional gain k of the PID controller p , integral gain k i and the differential gain k d ;

[0046] If the proportional gain k p , integral gain k i and the differential gain k d is a non-empty set, then the proportional gain k p , integral gain k i and the differential gain k d To meet the crossover frequency ωgc , Phase Margin and PID controller parameters with phase flatness constraints;

[0047] Solve equation 1 as follows:

[0048]

[0049] In the formula, B 31 is the intermediate variable,

[0050] S 3 is the intermediate variable,

[0051] B 32 is the intermediate variable,

[0052] C 3 is the intermediate variable,

[0053] Solve equation 2 as follows:

[0054]

[0055] A is the gain margin;

[0056] Solve equation three as follows:

[0057]

[0058] In the formula, E 3 is the intermediate variable, E 3 =-k d ω gc 2 +k i ;

[0059] F 3 is the intermediate variable, F 3 =k p ω gc ;

[0060] E 3’ For E 3 Yes gc The derivative of E 3’ =-2k d ω gc ;

[0061] F 3’ F 3 Yes gc The derivative of 3’ =k p ;

[0062] B31’ For B 31 Yes gc The derivative of

[0063] B 32’ For B 32 Yes gc The derivative of

[0064] In a third aspect, the present invention provides a PID controller for an inertia-plus-delay fractional-order object, which is designed using the robust design method for the PID controller for an inertia-plus-delay fractional-order object.

[0065] In a fourth aspect, the present invention provides a PID controller robust design device, comprising:

[0066] one or more processors;

[0067] a memory for storing one or more programs,

[0068] When the one or more programs are executed by the one or more processors, the one or more processors are caused to perform the steps of the method for robust design of a PID controller for an inertia-plus-delay fractional-order plant.

[0069] In a fifth aspect, the present invention provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of the robust design method of a PID controller for an inertia-plus-delay fractional-order object as described above.

[0070] Compared with the prior art, the present invention has outstanding substantive features and significant progress, specifically:

[0071] 1. The present invention solves a PID parameter robust design method for a class of fractional-order objects. The method can directly calculate the parameters of the PID controller under the constraints of phase margin, crossover frequency and phase flatness. It has the advantages of clear principle and easy implementation. The PID controller with calculated parameters has a strong ability to cope with the gain uncertainty of the controlled object.

[0072] 2. Compared with the existing PID controller parameter tuning method, the present invention can uniquely determine the proportional gain, integral gain and differential gain of the PID controller through three equations, which can ensure the uniqueness of the PID controller parameters and avoid the local optimal solution of the PID controller based on the evolutionary algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] Figure 1 These are the implementation steps of the method of the present invention.

[0074] Figure 2The invention discloses a closed-loop system composed of a PID controller and an inertia-plus-delay fractional-order object.

[0075] Figure 3 This is the control effect of the method in Example 1.

[0076] Figure 4 This is the control effect of the method in Example 1 when there is uncertainty in the controlled object. DETAILED DESCRIPTION

[0077] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0078] Example 1

[0079] This embodiment proposes a robust design method for a PID controller of an inertia plus delay fractional-order plant. The process is as follows: Figure 1 As shown, the following steps are included:

[0080] 101: Establish a closed-loop system consisting of a controlled object and a feedback controller, such as Figure 2 As shown; among them,

[0081] The controlled object adopts the inertia plus delay fractional order transfer function G p (s) Description, as follows:

[0082]

[0083] In the formula, G p (s) is the inertia plus delay fractional order transfer function, s is the differential operator, K is the gain of the controlled object, and K∈[-10 10 ,0∪0,10 10 ], T is the time constant of the controlled object, T∈(0,10 10 ], α is the order of the controlled object, α∈(0,2), L is the delay time constant of the controlled object, L∈(0,10 10 ], e is a natural constant.

[0084] In this embodiment, K=1, T=1, a=0.5 and L=0.1;

[0085] 102: The feedback controller uses a PID controller, and its transfer function G c (s) are as follows:

[0086]

[0087] In the formula, k p is the proportional gain of the PID controller, and kp ∈[-10 10 ,10 10 ],k i is the integral gain of the PID controller, and k i ∈[-10 10 ,10 10 ],k d is the differential gain of the PID controller, with k d ∈[-10 10 ,10 10 ]; k p , k i and k d are the PID controller parameters to be adjusted;

[0088] 103: The crossover frequency w of a given control system gc and phase margin f m In this embodiment, gc =0.1HZ and f m =73°;

[0089] 104: The solution equation for the PID controller parameters is given as follows:

[0090]

[0091] In the formula, B 31 is the intermediate variable,

[0092] S 3 is the intermediate variable,

[0093] B 32 is the intermediate variable,

[0094] C 3 is the intermediate variable,

[0095] 105: The solution equation for the PID controller parameters is given as follows:

[0096]

[0097] A is the gain margin. In this embodiment, A=1.

[0098] 106: The solution equation 3 for the PID controller parameters of the closed-loop system with a slope of zero (also known as phase flatness) at the crossover frequency is as follows:

[0099]

[0100] In the formula, E 3is the intermediate variable, E 3 =-k d ω gc 2 +k i ;

[0101] F 3 is the intermediate variable, F 3 =k p ω gc ;

[0102] E 3’ For E 3 Yes gc The derivative of E 3’ =-2k d ω gc ;

[0103] F 3’ F 3 Yes gc The derivative of 3’ =k p ;

[0104] B 31’ For B 31 Yes gc The derivative of

[0105] B 32’ For B 32 Yes gc The derivative of

[0106] 107: Based on the crossover frequency ω of a given closed-loop system gc and phase margin Solving equations (3)-(5) can uniquely solve the proportional gain k of the PID controller: p , integral gain k i and the differential gain k d In this embodiment, the proportional gain k of the PID controller can be uniquely solved p =0.1185, integral gain k i =1.1833 and differential gain k d =1.5800;

[0107] 108: If the solution is an empty set, restart steps 104-107 and re-set the crossing frequency ω gc and phase margin Re-solve equations (3)-(5) to uniquely solve the new proportional gain k of the PID controller p , integral gain k i and the differential gain k d; If the solution is a non-empty set, then the crossing frequency ω is obtained. gc , Phase Margin PID controller parameters for constraints such as phase flatness.

[0108] In this embodiment, the crossover frequency w can be obtained gc =0.1HZ, phase margin f m =73°, phase flatness and other constraints of the PID controller parameters proportional gain k p =0.1836, integral gain k i =1.2880 and differential gain k d =0.6400. Combined with the controlled object, we can get Figure 2 The tracking and anti-interference performance of the closed-loop system is shown in Figure 3 As shown in the figure, the specific simulation process is:

[0109] At the beginning of the simulation, the system is in a steady state. At 0s, the set value is changed from 0 to 1. At 20s, the closed-loop control quantity is disturbed from 0 to 1, and the simulation ends at 40s. Through simulation, it can be seen that the closed-loop system proposed by the method of the present invention, which directly calculates the parameters of the PID controller based on the given phase margin, crossover frequency and phase flatness constraints, has a relatively fast tracking ability and strong anti-interference ability. In order to analyze the ability of the adjusted PID to cope with the gain uncertainty of the controlled object, G is modified p In (s), the gains K of the controlled objects are 120%K and 80%K respectively. Repeating the above simulation, we can get Figure 4 The results shown are from Figure 4 It can be seen that the tuned PID controller has a strong ability to cope with the gain uncertainty of the controlled object.

[0110] Example 2

[0111] This embodiment provides a PID controller robust design system for an inertia plus delay fractional-order plant, including:

[0112] The closed-loop system establishment module is used to establish a closed-loop system consisting of a controlled object and a feedback controller; wherein,

[0113] The controlled object adopts the inertia plus delay fractional order transfer function G p (s) Description, as follows:

[0114]

[0115] In the formula, G p (s) is the inertia plus delay fractional order transfer function, s is the differential operator, K is the gain of the controlled object, and K∈[-10 10 ,0∪0,10 10], T is the time constant of the controlled object, T∈(0,10 10 ], α is the order of the controlled object, α∈(0,2), L is the delay time constant of the controlled object, L∈(0,10 10 ], e is a natural constant;

[0116] The feedback controller adopts PID controller, and its transfer function G c (s) are as follows:

[0117]

[0118] In the formula, k p is the proportional gain of the PID controller, and k p ∈[-10 10 ,10 10 ],k i is the integral gain of the PID controller, and k i ∈[-10 10 ,10 10 ],k d is the differential gain of the PID controller, with k d ∈[-10 10 ,10 10 ]; k p , k i and k d are the PID controller parameters to be adjusted;

[0119] The parameter solving module is connected with the closed-loop system establishment module to give the crossover frequency ω of the closed-loop system gc and phase margin Assume that the slope of the open-loop phase of the closed-loop system is zero at the crossover frequency. By solving equation 1, equation 2, and equation 3, the proportional gain k of the PID controller can be uniquely obtained. p , integral gain k i and the differential gain k d ;

[0120] If the proportional gain k p , integral gain k i and the differential gain k d is an empty set, then the crossing frequency ω is re-given gc and phase margin Re-solve equations (3)-(5) to uniquely solve the proportional gain k of the PID controller p , integral gain k i and the differential gain k d ;

[0121] If the proportional gain k p , integral gain ki and the differential gain k d is a non-empty set, then the proportional gain k p , integral gain k i and the differential gain k d To meet the crossover frequency ω gc , Phase Margin and PID controller parameters with phase flatness constraints;

[0122] Solve equation 1 as follows:

[0123]

[0124] In the formula, B 31 is the intermediate variable,

[0125] S 3 is the intermediate variable,

[0126] B 32 is the intermediate variable,

[0127] C 3 is the intermediate variable,

[0128] Solve equation 2 as follows:

[0129]

[0130] Solve equation three as follows:

[0131]

[0132] In the formula, E 3 is the intermediate variable, E 3 =-k d ω gc 2 +k i ;

[0133] F 3 is the intermediate variable, F 3 =k p ω gc ;

[0134] E 3’ For E 3 Yes gc The derivative of E 3’ =-2k d ω gc ;

[0135] F 3’ F 3 Yesgc The derivative of 3’ =k p ;

[0136] B 31’ For B 31 Yes gc The derivative of

[0137] B 32’ For B 32 Yes gc The derivative of

[0138] In this embodiment, the implementation scheme of the robust design system of the PID controller for the inertia plus delay fractional-order plant to solve the problem is similar to the implementation scheme described in the method of Embodiment 1, and will not be repeated here.

[0139] Example 3

[0140] This embodiment provides a PID controller for an inertia-plus-delay fractional-order object, which is designed using the robust design method for the PID controller for an inertia-plus-delay fractional-order object described in Embodiment 1.

[0141] Example 4

[0142] Each module in the embodiment 2 system can be implemented in whole or in part by software, hardware, or a combination thereof. Each of the above modules can be embedded in or independent of a processor in a computer device in the form of hardware, or can be stored in a memory in a computer device in the form of software, so that the processor can call and execute operations corresponding to each of the above modules.

[0143] In an exemplary embodiment, a PID controller robust design device is provided, and the computer device may be a terminal. The computer device further includes a processor, a memory, an input / output interface, a communication interface, a display unit, and an input device. The processor, the memory, and the input / output interface are connected via a system bus, and the communication interface, the display unit, and the input device are connected to the system bus via the input / output interface. The processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The input / output interface of the computer device is used to exchange information between the processor and an external device. The communication interface of the computer device is used to communicate with an external terminal in a wired or wireless manner, and the wireless manner may be implemented through WIFI, a mobile cellular network, NFC (near field communication) or other technologies. When the computer program is executed by the processor, the steps of the robust design method of the PID controller for an inertial plus delayed fractional-order object are implemented. The display unit of the computer device is used to form a visually visible picture, which may be a display screen, a projection device, or a virtual reality imaging device. The display screen can be a liquid crystal display screen or an electronic ink display screen, and the input device of the computer device can be a touch layer covering the display screen, or a button, trackball or touchpad set on the computer device shell, or an external keyboard, touchpad or mouse.

[0144] Those skilled in the art will appreciate that the structure of the above-mentioned computer device is only a partial structure related to the solution of the present application, and does not constitute a limitation on the computer device to which the solution of the present application is applied. The specific computer device may include more or fewer components, or combine certain components, or have a different arrangement of components.

[0145] In an exemplary embodiment, a computer-readable storage medium is provided, on which a computer program is stored. When the computer program is executed by a processor, the steps of a robust design method of a PID controller for an inertia-plus-delay fractional-order plant are implemented.

[0146] Those of ordinary skill in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to the memory, database or other medium used in the embodiments provided in the present application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. As an illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM). The database involved in each embodiment provided in this application may include at least one of a relational database and a non-relational database. Non-relational databases may include distributed databases based on blockchains, etc., but are not limited thereto. The processors involved in each embodiment provided in this application may be general-purpose processors, central processing units, graphics processors, digital signal processors, programmable logic devices, data processing logic devices based on quantum computing, etc., but are not limited thereto.

[0147] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0148] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art can easily think of changes or substitutions within the technical scope disclosed by the present invention, which should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A robust design method for a PID controller for an inertia plus delay fractional-order plant, characterized in that: The following steps are involved: 1) Establish a closed-loop system consisting of the controlled object and the feedback controller; The controlled object adopts the inertia plus delay fractional order transfer function G p (s) Description, as follows: In the formula, G p (s) is the inertia plus delay fractional order transfer function, s is the differential operator, K is the gain of the controlled object, and K∈[-10 10 ,0∪0,10 10 ], T is the time constant of the controlled object, T∈(0,10 10 ], α is the order of the controlled object, α∈(0,2), L is the delay time constant of the controlled object, L∈(0,10 10 ], e is a natural constant; The feedback controller adopts PID controller, and its transfer function G c (s) are as follows: In the formula, k p is the proportional gain of the PID controller, k p ∈[-10 10 ,10 10 ],k i is the integral gain of the PID controller, and k i ∈[-10 10 ,10 10 ],k d is the differential gain of the PID controller, and k d ∈[-10 10 ,10 10 ]; k p , k i and k d are the PID controller parameters to be adjusted; 2) Given the crossover frequency ω of the closed-loop system gc and phase margin Assume that the slope of the open-loop phase of the closed-loop system is zero at the crossover frequency. By solving equation 1, equation 2, and equation 3, the proportional gain k of the PID controller can be uniquely obtained. p , integral gain k i and the differential gain k d ; Solve equation 1 as follows: In the formula, B 31 is the intermediate variable, S3 is the intermediate variable, B 32 is the intermediate variable, C3 is the intermediate variable, Solve equation 2 as follows: A is the gain margin; Solve equation three as follows: In the formula, E3 is the intermediate variable, E3 = -k d ω gc 2 +k i ; F3 is the intermediate variable, F3 = k p ω gc ; E 3’ For E3 to ω gc The derivative of E 3’ =-2k d ω gc ; F 3’ F3 to ω gc The derivative of 3’ =k p ; B 31’ For B 31 Yes gc The derivative of B 32’ For B 32 Yes gc The derivative of 3) If the proportional gain k is solved p , integral gain k i and the differential gain k d is an empty set, then the crossing frequency ω is re-given gc and phase margin Re-solve equations (3)-(5) to uniquely solve the proportional gain k of the PID controller p , integral gain k i and the differential gain k d ; If the proportional gain k p , integral gain k i and the differential gain k d is a non-empty set, then the proportional gain k p , integral gain k i and the differential gain k d To meet the crossover frequency ω gc , Phase Margin and PID controller parameters for phase flatness constraints.

2. A robust design system for PID controller of inertia plus delay fractional-order plant, characterized in that: include: The closed-loop system establishment module is used to establish a closed-loop system consisting of a controlled object and a feedback controller; wherein, The controlled object adopts the inertia plus delay fractional order transfer function G p (s) Description, as follows: In the formula, G p (s) is the inertia plus delay fractional order transfer function, s is the differential operator, K is the gain of the controlled object, and K∈[-10 10 ,0∪0,10 10 ], T is the time constant of the controlled object, T∈(0,10 10 ], α is the order of the controlled object, α∈(0,2), L is the delay time constant of the controlled object, L∈(0,10 10 ], e is a natural constant; The feedback controller adopts PID controller, and its transfer function G c (s) are as follows: In the formula, k p is the proportional gain of the PID controller, and k p ∈[-10 10 ,10 10 ],k i is the integral gain of the PID controller, and k i ∈[-10 10 ,10 10 ],k d is the differential gain of the PID controller, with k d ∈[-10 10 ,10 10 ]; k p , k i and k d are the PID controller parameters to be adjusted; The parameter solving module is connected with the closed-loop system establishment module to give the crossover frequency ω of the closed-loop system gc and phase margin Assume that the slope of the open-loop phase of the closed-loop system is zero at the crossover frequency. By solving equation 1, equation 2, and equation 3, the proportional gain k of the PID controller can be uniquely obtained. p , integral gain k i and the differential gain k d ; If the proportional gain k p , integral gain k i and the differential gain k d is an empty set, then the crossing frequency ω is re-given gc and phase margin Re-solve equations (3)-(5) to uniquely solve the proportional gain k of the PID controller p , integral gain k i and the differential gain k d ; If the proportional gain k p , integral gain k i and the differential gain k d is a non-empty set, then the proportional gain k p , integral gain k i and the differential gain k d To meet the crossover frequency ω gc , Phase Margin and PID controller parameters with phase flatness constraints; Solve equation 1 as follows: In the formula, B 31 is the intermediate variable, S3 is the intermediate variable, B 32 is the intermediate variable, C3 is the intermediate variable, Solve equation 2 as follows: A is the gain margin; Solve equation three as follows: In the formula, E3 is the intermediate variable, E3 = -k d ω gc 2 +k i ; F3 is the intermediate variable, F3 = k p ω gc ; E 3’ For E3 to ω gc The derivative of E 3’ =-2k d ω gc ; F 3’ F3 to ω gc The derivative of 3’ =k p ; B 31’ For B 31 Yes gc The derivative of B 32’ For B 32 Yes gc The derivative of 3. A PID controller for an inertia plus delay fractional-order plant, characterized in that: The robust design method of the PID controller for the inertia plus delay fractional-order object described in claim 1 is used for design.

4. A PID controller robust design device, characterized in that: include: one or more processors; a memory for storing one or more programs, When the one or more programs are executed by the one or more processors, the one or more processors are caused to perform the steps of the method for robust design of a PID controller for an inertia-plus-delay fractional-order plant as claimed in claim 1 .

5. A computer-readable storage medium storing a computer program, characterized in that: When the program is executed by a processor, the steps of the robust design method of a PID controller for an inertia-plus-delay fractional-order plant as claimed in claim 1 are implemented.

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