Robust design method and system for fractional order PI controller of inertia and delay fractional order object

Abstract

The invention provides a robust design method and system for a fractional order PI controller 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; the feedback controller adopts a fractional order PI controller; a crossing frequency and a phase margin are given, and a proportional gain, an integral gain and a controller order of the fractional order PI controller are solely solved based on three constraint equations of the given crossing frequency, the given phase margin and zero slope of an open-loop phase of a closed-loop system at the crossing frequency; 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; and traversing the range of the traversing frequency and the phase margin to obtain a feasible region of the fractional order PI controller. According to the method, the parameters and the feasible region of the fractional order PI controller can be directly calculated, it is guaranteed that the fractional order PI controller has high robustness, and the method has practical application value.

Description

Technical Field

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

[0002] Shape (k p is the controller proportional gain, k i The fractional-order PI controller (where π is the controller integral gain and l is the integrator order) is the product of the development of fractional-order calculus. It can provide more degrees of freedom and parameter adjustment space than integer-order controllers, achieve more flexible and precise control performance, and have better robustness and adaptability to complex systems. The fractional-order object describes the dynamic characteristics of the controlled object through fractional-order differential equations. It is a generalized form of the integer-order object and can more accurately describe the dynamic characteristics of the actual system.

[0003] For fractional-order objects, the form There is a lack of research on the calculation method of the stable domain of the parameters of the fractional-order PI controller. At present, there are many studies on the tuning technology of fractional-order PI controllers, mainly focusing on methods including calculation based on the controlled object model and optimization based on evolutionary algorithms. The calculation method based on the controlled object model generally obtains the controller parameters through the transfer function of the controlled object combined with the expected closed-loop dynamic equation. This method is mainly designed for the nominal object. After designing the parameters, the robustness of the controller is checked, and there are many steps; the optimization of the parameters of the fractional-order PI controller based on the evolutionary algorithm can solve the minimum control performance index based on the robustness constraint. This method has the disadvantages of slow solution speed and easy convergence of parameters to the local optimum. It should be noted that the tuning method of the fractional-order PI controller under the constraints of typical robust indicators (such as maximum sensitivity function, phase margin, amplitude margin, phase flatness, crossover frequency, etc.) has also achieved certain results, but the current methods are mainly for integer-order objects; there is currently a lack of fractional-order PI controller parameter tuning methods for fractional-order objects.

[0004] With the development of fractional-order calculus theory and technology, more and more controlled objects are described by fractional-order transfer functions. Robust tuning of fractional-order PI controller parameters for fractional-order objects is very necessary. Summary of the invention

[0005] The purpose of the present invention is to solve the problem of robust design and feasible domain calculation of a fractional-order PI controller for a class of fractional-order objects, and to provide a robust design method and system for a fractional-order PI controller for an inertia plus delay fractional-order object.

[0006] In a first aspect, the present invention provides a robust design method for a fractional-order PI controller of an inertia-plus-delay fractional-order plant, comprising the following steps:

[0007] 1) The fractional-order PI controller of the inertia-delay fractional-order object is established as a closed-loop control system consisting of the controlled object and the feedback controller;

[0008] The controlled object adopts the inertia plus delay fractional order transfer function G p (s) Description, as follows:

[0009]

[0010] 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;

[0011] The feedback controller adopts the form of fractional-order PI controller, and its transfer function G c (s) are as follows:

[0012]

[0013] In the formula, k p is the controller proportional gain, with k p ∈[-10 10 ,10 10 ],k i is the controller integral gain, with k i ∈[-10 10 ,10 10 ], λ is the controller order, λ∈(0,2); k p , k i and λ are the fractional-order PI controller parameters to be tuned;

[0014] 2) Given the crossover frequency ω of the closed-loop control system gc and phase margin Assume that the slope of the open-loop phase of the closed-loop control system is zero at the crossover frequency. By solving equation 1, equation 2, and equation 3, the proportional gain k of the fractional-order PI controller is uniquely solved. p , integral gain k i and the controller integration order λ;

[0015] Solve equation 1 as follows:

[0016]

[0017] In the formula, B 11 is the intermediate variable,

[0018] S1 is the intermediate variable,

[0019] B 12 is the intermediate variable,

[0020] C1 is the intermediate variable,

[0021] Solve equation 2 as follows:

[0022]

[0023] Solve equation three as follows:

[0024]

[0025] In the formula, E1 is the intermediate variable,

[0026] F1 is the intermediate variable,

[0027] E1, is E1 to ω gc The derivative of

[0028] F1, is F1 to ω gc The derivative of

[0029] B 11 , for B 11 Yes gc The derivative of

[0030] B 12 , for B 12 Yes gc The derivative of

[0031] 3) If the proportional gain k is solved p , integral gain k i If the controller integral order λ is an empty set, then the crossover frequency ω is re-given gc and phase margin Resolve equations (3)-(5) to uniquely solve the proportional gain k of the fractional-order PI controller p , integral gain k iand the controller integration order λ;

[0032] If the proportional gain k p , integral gain k i and the controller integral order λ is a non-empty set, then the proportional gain k p , integral gain k i and the controller integral order λ is to satisfy the crossover frequency ω gc , Phase Margin Parameters of fractional-order PI controller with constraints such as phase flatness;

[0033] Record the crossing frequency ω corresponding to the non-empty set gc and phase margin

[0034] 9) Traverse the crossing frequency ω gc ∈(0,ω gcmax ] and phase margin ω gcmax is the maximum shear frequency; repeat steps 2)-3) to obtain the crossing frequency ω corresponding to the non-empty set gc and phase margin Distribution, that is, the feasible domain of the fractional-order PI controller.

[0035] In a second aspect, the present invention provides a robust design system for a fractional-order PI controller of an inertia-plus-delay fractional-order plant, comprising:

[0036] The closed-loop control system establishment module is used to establish the fractional-order PI controller of the inertia plus delay fractional-order object into a closed-loop control system consisting of a controlled object and a feedback controller; wherein,

[0037] The controlled object adopts the inertia plus delay fractional order transfer function G p (s) Description, as follows:

[0038]

[0039] 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;

[0040] The feedback controller adopts the form of fractional-order PI controller, and its transfer function G c (s) are as follows:

[0041]

[0042] In the formula, k p is the controller proportional gain, with k p ∈[-10 10 ,10 10 ],k i is the controller integral gain, with k i ∈[-10 10 ,10 10 ], λ is the controller order, λ∈(0,2); k p , k i and λ are the fractional-order PI controller parameters to be tuned;

[0043] The parameter solving module is used to calculate the crossover frequency ω of a given closed-loop control system. gc and phase margin Assuming that the open-loop phase of the closed-loop control system has a slope of zero at the crossover frequency, the proportional gain k of the fractional-order PI controller can be uniquely obtained by solving equations 1, 2, and 3. p , integral gain k i and the controller integration order λ;

[0044] It is also used to determine the proportional gain k solved in the parameter determination and recording module. p , integral gain k i When the controller integral order λ is an empty set, the crossover frequency ω is re-given gc and phase margin Resolve equations (3)-(5) to uniquely solve the proportional gain k of the fractional-order PI controller p , integral gain k i and the controller integration order λ;

[0045] Solve equation 1 as follows:

[0046]

[0047] In the formula, B 11 is the intermediate variable,

[0048] S1 is the intermediate variable,

[0049] B 12 is the intermediate variable,

[0050] C1 is the intermediate variable,

[0051] Solve equation 2 as follows:

[0052]

[0053] Solve equation three as follows:

[0054]

[0055] In the formula, E1 is the intermediate variable,

[0056] F1 is the intermediate variable,

[0057] E1, is E1 to ω gc The derivative of

[0058] F1, is F1 to ω gc The derivative of

[0059] B 11 , for B 11 Yes gc The derivative of

[0060] B 12 , for B 12 Yes gc The derivative of

[0061] The parameter judgment and recording module is connected to the parameter solving module to judge the proportional gain k of the solved fractional-order PI controller. p , integral gain k i and whether the controller integral order λ is an empty set;

[0062] It is also used to determine the proportional gain k p , integral gain k i When the controller integral order λ is a non-empty set, record the crossover frequency ω corresponding to the non-empty set gc and phase margin Among them, the proportional gain k p , integral gain k i and the controller integral order λ is to satisfy the crossover frequency ω gc , Phase Margin Parameters of fractional-order PI controller with constraints such as phase flatness;

[0063] The feasible domain calculation module is connected with the parameter judgment and recording module and the parameter solution module to traverse the crossing frequency ω gc ∈(0,ω gcmax ] and phase margin Get the crossing frequency ω corresponding to the non-empty set gc and phase margin Distribution, that is, the feasible domain of the fractional-order PI controller; ω gcmax is the maximum shear frequency.

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

[0065] In a fourth aspect, the present invention provides a robust design device for a fractional-order PI controller, 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 fractional-order PI 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, characterized in that when the program is executed by a processor, the steps of the robust design method of the fractional-order PI controller of the inertia-plus-delay fractional-order object as described above are implemented.

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

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

[0072] 2. The method for calculating the feasible region of the fractional-order PI controller for fractional-order objects provided by the present invention has the advantages of being simple and easy to implement. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] Figure 1 The invention discloses a closed-loop system composed of a fractional-order PI controller and an inertia-plus-delay fractional-order object.

[0074] Figure 2 This is the control effect of the present invention in Example 1.

[0075] Figure 3This is the control effect of the present invention in Example 1 when there is uncertainty in the controlled object.

[0076] Figure 4 This is the feasible domain of the fractional-order PI controller obtained by the present invention in Example 1. 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 provides a robust design method for a fractional-order PI controller of an inertia-plus-delay fractional-order plant, comprising the following steps:

[0080] 1) The fractional-order PI controller of the inertia-delay fractional-order object is established as a closed-loop control system consisting of the controlled object and the feedback controller, such as Figure 1 shown.

[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, α=1.5 and L=1.

[0085] The feedback controller adopts the form of fractional-order PI controller, and its transfer function G c (s) are as follows:

[0086]

[0087] In the formula, k p is the controller proportional gain, with k p ∈[-10 10 ,10 10 ],k iis the controller integral gain, with k i ∈[-10 10 ,10 10 ], λ is the controller order, λ∈(0,2); k p , k i and λ are the fractional-order PI controller parameters to be tuned.

[0088] 2) Given the crossover frequency ω of the closed-loop control system gc and phase margin Assume that the slope of the open-loop phase of the closed-loop control system is zero at the crossover frequency (also known as phase flatness). By solving equation 1, equation 2, and equation 3, the proportional gain k of the fractional-order PI controller can be uniquely obtained. p , integral gain k i and the controller integration order λ;

[0089] In this embodiment, the initially given crossover frequency ω gc = 0.05Hz and phase margin

[0090] The solved proportional gain k p =0.4623, integral gain k i =0.2306 and the controller integral order λ=1.1300.

[0091] Solve equation 1 as follows:

[0092]

[0093] In the formula, B 11 is the intermediate variable,

[0094] S1 is the intermediate variable,

[0095] B 12 is the intermediate variable,

[0096] C1 is the intermediate variable,

[0097] Solve equation 2 as follows:

[0098]

[0099] Solve equation three as follows:

[0100]

[0101] In the formula, E1 is the intermediate variable,

[0102] F1 is the intermediate variable,

[0103] E 1, E1 to ω gc The derivative of

[0104] F 1, For F1 to ω gc The derivative of

[0105] B 11, For B 11 Yes gc The derivative of

[0106] B 12, For B 12 Yes gc The derivative of

[0107] 3) If the proportional gain k is solved p , integral gain k i If the controller integral order λ is an empty set, then the crossover frequency ω is re-given gc and phase margin Resolve equations (3)-(5) to uniquely solve the proportional gain k of the fractional-order PI controller p , integral gain k i and the controller integration order λ;

[0108] If the proportional gain k p , integral gain k i and the controller integral order λ is a non-empty set, then the proportional gain k p , integral gain k i and the controller integral order λ is to satisfy the crossover frequency ω gc , Phase Margin Parameters of fractional-order PI controller with constraints such as phase flatness;

[0109] Record the crossing frequency ω corresponding to the non-empty set gc and phase margin

[0110] 9) Traverse the crossing frequency ω gc ∈(0,ω gcmax ] and phase margin ω gcmax is the maximum shear frequency; repeat steps 2)-3) to obtain the crossing frequency ω corresponding to the non-empty set gc and phase margin Distribution, i.e., the feasible domain of the fractional-order PI controller;

[0111] In this embodiment, the crossover frequency ω gc =1.5Hz.

[0112] In this embodiment, the crossover frequency ω can be obtained gc =0.05Hz, phase margin Phase flatness constrained fractional-order PI controller parameters: proportional gain k p =0.4623, integral gain k i =0.2306 and the controller integral order λ=1.1300.

[0113] Combined with the controlled object, we can get Figure 1 The tracking and anti-interference performance of the closed-loop control system is shown in Figure 2 As shown in the figure, the specific simulation process is:

[0114] 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, until the simulation ends at 40s.

[0115] Through simulation, it can be seen that the closed-loop control system proposed by the method of this embodiment, which directly calculates the parameters of the fractional-order PI controller based on a given phase margin, crossover frequency and phase flatness constraint, has a relatively fast tracking capability and a strong anti-interference ability.

[0116] In order to analyze the ability of the adjusted fractional-order PI controller to cope with the uncertainty of the controlled object gain, G 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 3 The results shown are from Figure 3 It can be seen that the adjusted fractional-order PI controller has a strong ability to deal with the gain uncertainty of the controlled object. The feasible domain of the fractional-order PI controller is shown in Figure 4 As shown, the effectiveness of the method of the present invention in calculating the feasible region of the fractional-order PI controller is verified.

[0117] Example 2

[0118] This embodiment provides a robust design system for a fractional-order PI controller of an inertia-plus-delay fractional-order plant, including:

[0119] The closed-loop control system establishment module is used to establish the fractional-order PI controller of the inertia plus delay fractional-order object into a closed-loop control system consisting of a controlled object and a feedback controller; wherein,

[0120] The controlled object adopts the inertia plus delay fractional order transfer function G p (s) Description, as follows:

[0121]

[0122] 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;

[0123] The feedback controller adopts the form of fractional-order PI controller, and its transfer function G c (s) are as follows:

[0124]

[0125] In the formula, k p is the controller proportional gain, with k p ∈[-10 10 ,10 10 ],k i is the controller integral gain, with k i ∈[-10 10 ,10 10 ], λ is the controller order, λ∈(0,2); k p , k i and λ are the fractional-order PI controller parameters to be tuned;

[0126] The parameter solving module is used to calculate the crossover frequency ω of a given closed-loop control system. gc and phase margin Assuming that the open-loop phase of the closed-loop control system has a slope of zero at the crossover frequency, the proportional gain k of the fractional-order PI controller can be uniquely obtained by solving equations 1, 2, and 3. p , integral gain k i and the controller integration order λ;

[0127] It is also used to determine the proportional gain k solved in the parameter determination and recording module. p , integral gain k i When the controller integral order λ is an empty set, the crossover frequency ω is re-given gc and phase margin Resolve equations (3)-(5) to uniquely solve the proportional gain k of the fractional-order PI controller p , integral gain k i and the controller integration order λ;

[0128] Solve equation 1 as follows:

[0129]

[0130] In the formula, B 11 is the intermediate variable,

[0131] S1 is the intermediate variable,

[0132] B 12 is the intermediate variable,

[0133] C1 is the intermediate variable, C1=cos(f m +Lw gc );

[0134] Solve equation 2 as follows:

[0135]

[0136] Solve equation three as follows:

[0137]

[0138] In the formula, E1 is the intermediate variable,

[0139] F1 is the intermediate variable,

[0140] E 1, E1 to ω gc The derivative of

[0141] F 1, For F1 to ω gc The derivative of

[0142] B 11, For B 11 Yes gc The derivative of

[0143] B 12, For B 12 Yes gc The derivative of

[0144] The parameter judgment and recording module is connected to the parameter solving module to judge the proportional gain k of the solved fractional-order PI controller. p , integral gain k iand whether the controller integral order λ is an empty set;

[0145] It is also used to determine the proportional gain k p , integral gain k i When the controller integral order λ is a non-empty set, record the crossover frequency ω corresponding to the non-empty set gc and phase margin Among them, the proportional gain k p , integral gain k i and the controller integral order λ is to satisfy the crossover frequency ω gc , Phase Margin Parameters of fractional-order PI controller with constraints such as phase flatness;

[0146] The feasible domain calculation module is connected with the parameter judgment and recording module and the parameter solution module to traverse the crossing frequency ω gc ∈(0,ω gcmax ] and phase margin Get the crossing frequency ω corresponding to the non-empty set gc and phase margin Distribution, that is, the feasible domain of the fractional-order PI controller; ω gcmax is the maximum shear frequency.

[0147] In this embodiment, the implementation scheme for solving the problem of the robust design system of the fractional-order PI controller of the inertia plus delay fractional-order plant is similar to the implementation scheme described in the method of Example 1, which will not be repeated here.

[0148] Example 3

[0149] This embodiment provides a fractional-order PI controller for a fractional-order object with inertia and delay, which is designed using the robust design method of the fractional-order PI controller for a fractional-order object with inertia and delay described in Example 1.

[0150] Example 4

[0151] 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.

[0152] In an exemplary embodiment, a robust design device for a fractional-order PI controller 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 fractional-order PI controller of the inertial plus delay 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.

[0153] 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.

[0154] 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 fractional-order PI controller for an inertia-plus-delay fractional-order plant are implemented.

[0155] Those skilled 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), magnetoresistive 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 to this. The processor involved in each embodiment provided in this application may be a general-purpose processor, a central processing unit, a graphics processor, a digital signal processor, a programmable logic device, a data processing logic device based on quantum computing, etc., but are not limited to this.

[0156] 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.

[0157] 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 fractional-order PI controller for an inertia-plus-delay fractional-order plant, characterized in that: The following steps are involved: 1) Establish a closed-loop control system consisting of a controlled object and a 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 the form of fractional-order PI controller, and its transfer function G c (s) are as follows: In the formula, k p is the controller proportional gain, with k p ∈[-10 10 ,10 10 ],k i is the controller integral gain, with k i ∈[-10 10 ,10 10 ], λ is the controller order, λ∈(0,2); k p , k i and λ are the fractional-order PI controller parameters to be tuned; 2) Given the crossover frequency ω of the closed-loop control system gc and phase margin Assume that the slope of the open-loop phase of the closed-loop control system is zero at the crossover frequency. By solving equation 1, equation 2, and equation 3, the proportional gain k of the fractional-order PI controller is uniquely solved. p , integral gain k i and the controller integration order λ; Solve equation 1 as follows: In the formula, B 11 is the intermediate variable, S1 is the intermediate variable, B 12 is the intermediate variable, C1 is the intermediate variable, Solve equation 2 as follows: Solve equation three as follows: In the formula, E1 is the intermediate variable, F1 is the intermediate variable, E 1, E1 to ω gc The derivative of F 1, For F1 to ω gc The derivative of B 11’ For B 11 Yes gc The derivative of B 12’ For B 12 Yes gc The derivative of 3) If the proportional gain k is solved p , integral gain k i If the controller integral order λ is an empty set, then the crossover frequency ω is re-given gc and phase margin Resolve equations (3)-(5) to uniquely solve the proportional gain k of the fractional-order PI controller p , integral gain k i and the controller integration order λ; If the proportional gain k p , integral gain k i and the controller integral order λ is a non-empty set, then the proportional gain k p , integral gain k i and the controller integral order λ is to satisfy the crossover frequency ω gc , Phase Margin Parameters of fractional-order PI controller with constraints such as phase flatness; Record the crossing frequency ω corresponding to the non-empty set gc and phase margin 9) Traverse the crossing frequency ω gc ∈(0,ωg cmax ] and phase margin ω gcmax is the maximum shear frequency; repeat steps 2)-3) to obtain the crossing frequency ω corresponding to the non-empty set gc and phase margin Distribution, that is, the feasible domain of the fractional-order PI controller.

2. A robust design system for fractional-order PI controllers for inertia-plus-delay fractional-order plants, characterized in that: include: The closed-loop control system establishment module establishes a closed-loop control 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 the form of fractional-order PI controller, and its transfer function G c (s) are as follows: In the formula, k p is the controller proportional gain, with k p ∈[-10 10 ,10 10 ],k i is the controller integral gain, with k i ∈[-10 10 ,10 10 ], λ is the controller order, λ∈(0,2); k p , k i and λ are the fractional-order PI controller parameters to be tuned; The parameter solving module is used to calculate the crossover frequency ω of a given closed-loop control system. gc and phase margin Assuming that the open-loop phase of the closed-loop control system has a slope of zero at the crossover frequency, the proportional gain k of the fractional-order PI controller can be uniquely obtained by solving equations 1, 2, and 3. p , integral gain k i and the controller integration order λ; It is also used to determine the proportional gain k solved in the parameter determination and recording module. p , integral gain k i When the controller integral order λ is an empty set, the crossover frequency ω is re-given gc and phase margin Resolve equations (3)-(5) to uniquely solve the proportional gain k of the fractional-order PI controller p , integral gain k i and the controller integration order λ; Solve equation 1 as follows: In the formula, B 11 is the intermediate variable, S1 is the intermediate variable, B 12 is the intermediate variable, C1 is the intermediate variable, C1=cos(f m +Lw gc ); Solve equation 2 as follows: Solve equation three as follows: In the formula, E1 is the intermediate variable, F1 is the intermediate variable, E 1’ E1 to ω gc The derivative of F 1’ For F1 to ω gc The derivative of B 11’ For B 11 Yes gc The derivative of B 12’ For B 12 Yes gc The derivative of The parameter judgment and recording module is connected to the parameter solving module to judge the proportional gain k of the solved fractional-order PI controller. p , integral gain k i and whether the controller integral order λ is an empty set; It is also used to determine the proportional gain k p , integral gain k i When the controller integral order λ is a non-empty set, record the crossover frequency ω corresponding to the non-empty set gc and phase margin Among them, the proportional gain k p , integral gain k i and the controller integral order λ is to satisfy the crossover frequency ω gc , Phase Margin Parameters of fractional-order PI controller with constraints such as phase flatness; The feasible domain calculation module is connected with the parameter judgment and recording module and the parameter solution module to traverse the crossing frequency ω gc ∈(0,ω gcmax ] and phase margin Get the crossing frequency ω corresponding to the non-empty set gc and phase margin Distribution, that is, the feasible domain of the fractional-order PI controller; ω gcmax is the maximum shear frequency.

3. A fractional-order PI controller for an inertia-plus-delay fractional-order plant, characterized in that: The design is performed using the robust design method for a fractional-order PI controller for an inertia-plus-delay fractional-order object as described in claim 1.

4. A robust design device for a fractional-order PI controller, 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 robust design method for a fractional-order PI controller of 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 fractional-order PI controller for an inertia-plus-delay fractional-order plant as claimed in claim 1 are implemented.

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