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] This invention relates to a proportional-integral-derivative (PID) controller design method, and more particularly to a robust design method and system for a fractional-order PID controller for an inertial-delayed object. Background Technology

[0002] In typical industrial process control, such as chemical processes and wind power generation processes, there exists a class of inertial plus delay fractional-order processes. For example, wind power pitch control systems are generally described using inertial plus delay fractional-order systems. In the formula, G p (s) is the fractional-order transfer function with inertia and delay, where s is the differential operator, K is the gain of the controlled object, T is the time constant of the controlled object, α is the order of the controlled object, L is the delay time constant of the controlled object, and e is the natural constant. Taking a wind power generation pitch control system as an example, the meanings of the parameters in the above formula are as follows: Gain K is the static gain of the control signal-pitch angle of a variable pitch actuator (such as a servo motor or reducer). The time constant T is the mechanical inertia of the variable pitch system (such as the blade rotational inertia and transmission mechanism damping). The larger the time constant T is, the stronger the inertia, and the slower the pitch angle responds to the control signal. The fractional order α is the core nonlinearity of the variable pitch system, which originates from the aerodynamic characteristics of the blades: when the wind speed changes, the dynamic relationship between lift and drag on the blades cannot be accurately described by integer-order (such as first-order and second-order) linear models (e.g., the difference in aerodynamic damping at low and high wind speeds); while the fractional-order model, through the continuously adjustable order α∈(0,2), can more flexibly fit this nonlinear dynamic "between integer orders", and has higher accuracy than integer-order models (such as first-order inertia with α=1); The delay time L is the double delay of the variable pitch system: 1. Signal delay: Time lag in wind speed detection (such as wind speed sensor sampling and data transmission); 2. Execution delay: After the control signal is issued, the mechanical response of the servo motor to start and the transmission mechanism to overcome the gap is delayed, which is completely consistent with the actual scenario of "delay caused by wind speed fluctuation".

[0003] Currently, in typical industrial process control applications such as chemical processes and wind power generation, inertial-delay fractional-order systems widely use traditional feedback control methods based on output error. The controllers used are primarily traditional proportional-integral-derivative (PID) controllers. The traditional PID controller model is shown below, G... c (s)=k p +k i / s+k d s, where k p For proportional gain, k i For integral gain, k d This is the differential gain.

[0004] The widespread application of PID controllers in motion control systems, chemical control systems, and energy systems is due to their advantages such as ease of implementation, simple structure, few parameters, and reliable performance. Fractional-order objects describe the dynamic characteristics of the controlled object through fractional-order differential equations. They are a generalized form of integer-order objects and can more accurately describe the dynamic characteristics of real-world systems.

[0005] PID controller control requires tuning of the proportional gain, integral gain, and derivative gain. Current technologies mainly include methods based on controlled object model calculations and evolutionary algorithm optimization. Methods based on controlled object model calculations typically obtain controller parameters by combining the control object's transfer function with the expected closed-loop dynamic equations, such as internal model methods and SIMC methods. These methods primarily focus on designing for nominal objects, and then verify the controller's robustness after parameter design, involving numerous steps. Optimizing PID controller parameters based on evolutionary algorithms can solve for the minimum control performance index based on robustness constraints. However, this method has drawbacks such as slow solution speed and the tendency for parameters to converge to local optima. Furthermore, current research lacks direct calculation methods for PID controller parameters under typical robustness indices (such as maximum sensitivity function, phase margin, gain margin, phase flatness, crossover frequency, etc.).

[0006] It should be noted that PID controller parameter tuning methods based on controlled object model calculation and evolutionary algorithm optimization are mainly for integer-order objects, and there are currently few PID controller parameter tuning methods for fractional-order objects. However, with the development of fractional calculus theory and technology, more and more controlled objects are described using fractional transfer functions. Therefore, it is essential to study the robust tuning of PID controller parameters for fractional objects. Summary of the Invention

[0007] The purpose of this invention is to solve the robust design problem of PID controllers for a class of fractional-order objects, and to provide a robust design method and system for PID controllers for inertial plus delay fractional-order objects.

[0008] In a first aspect, the present invention provides a robust design method for a PID controller for an inertial-delayed fractional-order object, comprising the following steps: 1) Establish a closed-loop system consisting of the controlled object and a feedback controller; whereby, A class of controlled actual industrial systems are taken as the controlled object, and an inertial plus delay fractional transfer function G is used. p (s) Description, as follows: (1) In the formula, G p (s) is the fractional-order transfer function with inertia and delay, s is the differential operator, and K is the gain of the controlled object, where K∈[-10]. 10 ,0)∪(0,10 10 ], T is the time constant of the controlled object, where T∈(0,10) 10 ], where α is the order of the controlled object, α∈(0,2), and L is the delay time constant of the controlled object, L∈(0,10). 10 ), where e is the natural constant; The feedback controller uses a PID controller, whose transfer function G c (s) are as follows: (2) In the formula, k p For the proportional gain of the PID controller, we have k p ∈[-10 10 10 10 ], k i For the integral gain of the PID controller, we have k i ∈[-10 10 10 10 ], k d For the derivative gain of the PID controller, we have k d ∈[-10 10 10 10 ];k p k i and k d These are the parameters of the PID controller to be tuned; 2) Given the crossover frequency ω of the closed-loop system gc and phase margin Assuming the open-loop phase of the closed-loop system has a slope of zero at the crossover frequency, the proportional gain k of the PID controller is uniquely solved by solving equations one, two, and three. p Integral gain k i and differential gain k d ; Solve equation one as follows: (3) In the formula, B 31 As an intermediate variable, ; S3 is an intermediate variable. ; B32 As an intermediate variable, ; C3 is an intermediate variable. ; Solve equation two as follows: (4) A represents the gain margin; Solve equation three as follows: (5) In the formula, E3 is an intermediate variable. ; F3 is an 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＇ For F3 to ω gc The derivative of F 3＇ =k p ; B 31＇ For B 31 For ω gc The derivative, ; B 32＇ For B 32 For ω gc The derivative, ; 3) If the calculated proportional gain k p Integral gain k i and differential gain k d If it is an empty set, then the crossing frequency ω is redefined. gc and phase margin Resolve formulas (3)-(5) to uniquely solve for the proportional gain k of the PID controller. p Integral gain k i and differential gain k d ; If the calculated proportional gain k p Integral gain k i and differential gain k d If the set is non-empty, then the proportional gain k is obtained. p Integral gain k i and differential gain k d To satisfy the crossover frequency ω gc Phase margin PID controller parameters with phase flatness constraints; 4) Obtain k p value, k i value and k d The values ​​are used as the proportional gain, integral gain, and derivative gain settings of the PID controller to satisfy the constraints, thus obtaining a feedback controller that meets the control requirements.

[0009] Secondly, the present invention provides a robust design system for a PID controller for an inertial-delayed fractional-order object, comprising: The closed-loop system establishment module is used to establish a closed-loop system consisting of the controlled object and the feedback controller; among which... A class of controlled actual industrial systems are taken as the controlled object, and an inertial plus delay fractional transfer function G is used. p (s) Description, as follows: (1) In the formula, G p (s) is the fractional-order transfer function with inertia and delay, s is the differential operator, and K is the gain of the controlled object, where K∈[-10]. 10 ,0)∪(0,10 10 ], T is the time constant of the controlled object, where T∈(0,10) 10 ], where α is the order of the controlled object, α∈(0,2), and L is the delay time constant of the controlled object, L∈(0,10). 10 ), where e is the natural constant; The feedback controller uses a PID controller, whose transfer function G c (s) are as follows: (2) In the formula, k p For the proportional gain of the PID controller, we have k p ∈[-10 10 10 10 ], k i For the integral gain of the PID controller, we have k i ∈[-10 10 10 10 ], k d For the derivative gain of the PID controller, we have k d ∈[-10 10 10 10 ];k p k i and k d These are the parameters of the PID controller to be tuned; The parameter solving module is connected to the closed-loop system establishment module and is used to provide the crossover frequency ω of the closed-loop system. gcand phase margin Assuming the open-loop phase of the closed-loop system has a slope of zero at the crossover frequency, the proportional gain k of the PID controller is uniquely solved by solving equations one, two, and three. p Integral gain k i and differential gain k d ; If the calculated proportional gain k p Integral gain k i and differential gain k d If it is an empty set, then the crossing frequency ω is redefined. gc and phase margin Resolve formulas (3)-(5) to uniquely solve for the proportional gain k of the PID controller. p Integral gain k i and differential gain k d ; If the calculated proportional gain k p Integral gain k i and differential gain k d If the set is non-empty, then the proportional gain k is obtained. p Integral gain k i and differential gain k d To satisfy the crossover frequency ω gc Phase margin PID controller parameters with phase flatness constraints; Solve equation one as follows: (3) In the formula, B 31 As an intermediate variable, ; S3 is an intermediate variable. ; B 32 As an intermediate variable, ; C3 is an intermediate variable. ; Solve equation two as follows: (4) A represents the gain margin; Solve equation three as follows: (5) In the formula, E3 is an intermediate variable. ; F3 is an intermediate variable, F3=k p ω gc ; E 3＇ For E3 to ωgc The derivative of E 3＇ =-2k d ω gc ; F 3＇ For F3 to ω gc The derivative of F 3＇ =k p ; B 31＇ For B 31 For ω gc The derivative, ; B 32＇ For B 32 For ω gc The derivative, ; The design module is used to obtain k p value, k i value and k d The values ​​are used as the proportional gain, integral gain, and derivative gain settings of the PID controller to satisfy the constraints, thus obtaining a feedback controller that meets the control requirements.

[0010] Thirdly, the present invention provides a PID controller for an inertial plus delay fractional-order object, which is designed using the robust design method for the PID controller of the inertial plus delay fractional-order object.

[0011] Fourthly, the present invention provides a robust design apparatus for a PID controller, comprising: One or more processors; Memory, used to store one or more programs. When the one or more programs are executed by the one or more processors, the one or more processors perform the steps of the robust design method for a PID controller for an inertial plus delay fractional-order object as described above.

[0012] Fifthly, the present invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the robust design method for a PID controller of an inertial plus delay fractional-order object as described above.

[0013] This invention has outstanding substantive features and significant progress compared to the prior art, specifically: 1. This invention solves a robust design method for PID parameters of a class of fractional-order objects. This method can directly tune the PID controller parameters (proportional gain k) under constraints of phase margin, crossover frequency, and phase flatness. p Integral gain k i and differential gain k dThis leads to the design of a PID controller with strong ability to cope with the uncertainty of the controlled object's gain.

[0014] 2. The method of this invention only requires providing the phase margin, crossover frequency, and phase flatness constraint of the closed-loop control system, and then calculating to obtain the parameters (proportional gain k) of the fractional-order [PI] controller. p Integral gain k i With order r), the method is simple and easy to implement.

[0015] 3. Compared with existing PID controller parameter tuning methods, this invention can uniquely determine the proportional gain, integral gain and derivative gain of the PID controller through the calculation of three equations, which can guarantee the uniqueness of the obtained PID controller parameters and avoid the local optimum problem that exists when using evolutionary algorithms to optimize fractional-order [PI] controllers. Attached Figure Description

[0016] Figure 1 These are the implementation steps of the method of the present invention.

[0017] Figure 2 The present invention is a closed-loop system consisting of a PID controller and an inertial-delayed fractional-order object.

[0018] Figure 3 This describes the control effect of the method in Example 1.

[0019] Figure 4 This demonstrates the control effect of the method in Example 1 when the controlled object exhibits uncertainty. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0021] Example 1 This embodiment proposes a robust design method for a PID controller for an inertial-delayed fractional-order object, the process of which is as follows: Figure 1 As shown, it includes the following steps: 101: Establish a closed-loop system consisting of the controlled object and a feedback controller, such as... Figure 2 As shown; where, A class of controlled actual industrial systems are taken as the controlled object, and an inertial plus delay fractional transfer function G is used. p (s) Description, as follows: (1) In the formula, G p(s) is the fractional-order transfer function with inertia and delay, s is the differential operator, and K is the gain of the controlled object, where K∈[-10]. 10 ,0)∪(0,10 10 ], T is the time constant of the controlled object, where T∈(0,10) 10 ], where α is the order of the controlled object, α∈(0,2), and L is the delay time constant of the controlled object, L∈(0,10). 10 ), where e is the natural constant.

[0022] In this embodiment, K=1, T=1, α=0.5, L=0.1; 102: The feedback controller uses a PID controller, and its transfer function G c (s) are as follows: (2) In the formula, k p For the proportional gain of the PID controller, we have k p ∈[-10 10 10 10 ], k i For the integral gain of the PID controller, we have k i ∈[-10 10 10 10 ], k d For the derivative gain of the PID controller, we have k d ∈[-10 10 10 10 ];k p k i and k d These are the parameters of the PID controller to be tuned; 103: Given the crossover frequency ω of the control system gc and phase margin ; In this embodiment, ω gc =0.1HZ and =73º; 104: The solution equation for the PID controller parameters is given below: (3) In the formula, B 31 As an intermediate variable, ; S3 is an intermediate variable. ; B 32 As an intermediate variable, ; C3 is an intermediate variable. ; 105: The second equation for solving the PID controller parameters is given below: (4) A represents the gain margin; in this embodiment, A = 1.

[0023] 106: The following is the third equation for solving the parameters of a PID controller with an open-loop phase slope of zero (also known as phase flatness) at the crossover frequency of a closed-loop system: (5) In the formula, E3 is an intermediate variable. ; F3 is an 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＇ For F3 to ω gc The derivative of F 3＇ =k p ; B 31＇ For B 31 For ω gc The derivative, ; B 32＇ For B 32 For ω gc The derivative, ; 107: Based on the given crossover frequency ω of the closed-loop system gc and phase margin Solving formulas (3)-(5) allows us to uniquely determine the proportional gain k of the PID controller. p Integral gain k i and 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; 108: If the solution results in an empty set, restart steps 104-107 and re-define the crossing frequency ω. gc and phase margin Resolve formulas (3)-(5) to uniquely determine the proportional gain k of the new PID controller. p Integral gain k i and differential gain k dIf the solution yields a non-empty set, then the crossover frequency ω is obtained. gc Phase margin PID controller parameters subject to constraints such as phase flatness.

[0024] In this embodiment, the proportional gain k of the PID controller, which is subject to constraints such as crossover frequency (Hz), phase margin, and phase flatness, can be obtained. p =0.1836, Integral gain k i =1.2880 and differential gain k d =0.6400.

[0025] 109: The obtained k p =0.1836, k i =1.2880 and k d =0.6400 is used as the proportional gain, integral gain and derivative gain of the PID controller to satisfy the constraints, thus obtaining a feedback controller that meets the control requirements.

[0026] By combining the feedback controller with the controlled object, we can obtain... Figure 2 The tracking and anti-interference performance of the closed-loop system shown is as follows: Figure 3 As shown, the specific simulation process is as follows: At the start of the simulation, the system is in steady state. At 0s, the setpoint is changed from 0 to 1. At 20s, the control variable is perturbed in the closed-loop circuit, changing from 0 to 1. The simulation ends at 40s. Simulation results show that the closed-loop system proposed in this invention, which directly calculates the PID controller parameters based on given phase margin, crossover frequency, and phase flatness constraints, exhibits relatively fast tracking capability and strong anti-interference ability. To analyze the ability of the tuned PID controller to cope with the uncertainty of the controlled object's gain, G is modified... p In (s), the controlled object gain K is 120%K and 80%K respectively. Repeating the above simulation, we can obtain... Figure 4 The results shown are from Figure 4 As can be seen, the tuned PID controller has a strong ability to cope with the uncertainty of the controlled object's gain.

[0027] Example 2 This embodiment provides a robust design system for a PID controller for an inertial-delayed fractional-order object, including: The closed-loop system establishment module is used to establish a closed-loop system consisting of the controlled object and the feedback controller; among which... A class of controlled actual industrial systems are taken as the controlled object, and an inertial plus delay fractional transfer function G is used. p (s) Description, as follows: (1) In the formula, G p (s) is the fractional-order transfer function with inertia and delay, s is the differential operator, and K is the gain of the controlled object, where K∈[-10]. 10 ,0)∪(0,10 10 ], T is the time constant of the controlled object, where T∈(0,10) 10 ], where α is the order of the controlled object, α∈(0,2), and L is the delay time constant of the controlled object, L∈(0,10). 10 ), where e is the natural constant; The feedback controller uses a PID controller, whose transfer function G c (s) are as follows: (2) In the formula, k p For the proportional gain of the PID controller, we have k p ∈[-10 10 10 10 ], k i For the integral gain of the PID controller, we have k i ∈[-10 10 10 10 ], k d For the derivative gain of the PID controller, we have k d ∈[-10 10 10 10 ];k p k i and k d These are the parameters of the PID controller to be tuned; The parameter solving module is connected to the closed-loop system establishment module and is used to provide the crossover frequency ω of the closed-loop system. gc and phase margin Assuming the open-loop phase of the closed-loop system has a slope of zero at the crossover frequency, the proportional gain k of the PID controller is uniquely solved by solving equations one, two, and three. p Integral gain k i and differential gain k d ; If the calculated proportional gain k p Integral gain k i and differential gain k d If it is an empty set, then the crossing frequency ω is redefined. gc and phase margin Resolve formulas (3)-(5) to uniquely solve for the proportional gain k of the PID controller. p Integral gain k i and differential gain k d ; If the calculated proportional gain kp Integral gain k i and differential gain k d If the set is non-empty, then the proportional gain k is obtained. p Integral gain k i and differential gain k d To satisfy the crossover frequency ω gc Phase margin PID controller parameters with phase flatness constraints; Solve equation one as follows: (3) In the formula, B 31 As an intermediate variable, ; S3 is an intermediate variable. ; B 32 As an intermediate variable, ; C3 is an intermediate variable. ; Solve equation two as follows: (4) A represents the gain margin; Solve equation three as follows: (5) In the formula, E3 is an intermediate variable. ; F3 is an 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＇ For F3 to ω gc The derivative of F 3＇ =k p ; B 31＇ For B 31 For ω gc The derivative, ; B 32＇ For B 32 For ω gc The derivative, ; The design module is used to obtain k p value, k i value and k dThe values ​​are used as the proportional gain, integral gain, and derivative gain settings of the PID controller to satisfy the constraints, thus obtaining a feedback controller that meets the control requirements.

[0028] In this embodiment, the solution to the problem of the robust design system for the PID controller of the inertial plus delay fractional order object is similar to the solution described in Embodiment 1, and will not be repeated here.

[0029] Example 3 This embodiment provides a PID controller for an inertial plus delay fractional-order object, which is designed using the robust design method for the PID controller of the inertial plus delay fractional-order object described in Embodiment 1.

[0030] Example 4 In Example 2, each module in the system can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device, or stored in the memory of a computer device as software, so that the processor can call and execute the operations corresponding to each module.

[0031] In an exemplary embodiment, a robust design apparatus for a PID controller is provided, the computer device being a terminal. The computer device further includes a processor, memory, an input / output interface, a communication interface, a display unit, and an input device. The processor, memory, and input / output interface are connected via a system bus, and the communication interface, display unit, and input device are also connected to the system bus via the input / output interface. The processor of the computer device provides computational and control capabilities. The memory of the computer device includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores an operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage medium. The input / output interface of the computer device is used for exchanging information between the processor and external devices. The communication interface of the computer device is used for wired or wireless communication with external terminals; wireless communication can be achieved through Wi-Fi, mobile cellular networks, NFC (Near Field Communication), or other technologies. When the computer program is executed by the processor, it implements the steps of a robust design method for a PID controller for an inertial-delayed fractional-order object. The display unit of the computer device is used to form a visually visible image and can be a display screen, a projection device, or a virtual reality imaging device. The display screen can be an LCD screen or an e-ink screen. The input device of the computer device can be a touch layer covering the display screen, or buttons, trackballs, or touchpads set on the casing of the computer device, or external keyboards, touchpads, or mice, etc.

[0032] Those skilled in the art will understand that the structure of the computer device described above is only a partial structure related to the solution of this application, and does not constitute a limitation on the computer device to which the solution of this application is applied. A specific computer device may include more or fewer components, or combine certain components, or have different component arrangements.

[0033] In one exemplary embodiment, a computer-readable storage medium is provided having a computer program stored thereon that, when executed by a processor, implements the steps of a robust design method for a PID controller for an inertial plus-delay fractional-order object.

[0034] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments described above. Any references to memory, databases, or other media used in the embodiments provided in this 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. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM). The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0035] The technical features of the above embodiments can be combined in any way. For the sake of brevity, 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.

[0036] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for robust design of a PID controller for an inertial plus delayed fractional order plant, characterized in that, The method comprises the following steps: 1) establishing a closed loop system composed of a controlled object and a feedback controller; wherein, A class of actual industrial systems as controlled object is taken as controlled object to adopt inertia plus delay fractional order transfer function G p (s) description, as follows: （1） In the formula, G p (s) is an inertial plus delay fractional order transfer function, s is a differential operator, K is a gain of the controlled object, has K ∈ [-10 10 , 0)∪(0, 10 10 ], T is a time constant of the controlled object, has T ∈ (0, 10 10 ], α is an order of the controlled object, has α ∈ (0, 2), L is a delay time constant of the controlled object, has L ∈ (0, 10 10 ], and e is a natural constant; The feedback controller employs a PID controller whose transfer function G c (s) is as follows: （2） where k p is the PID controller proportional gain, k p ∈[-10 10 ,10 10 ], k i is the PID controller integral gain, k i ∈[-10 10 ,10 10 ], and k d is the PID controller derivative gain, k d ∈[-10 10 ,10 10 ]; k p , k i , and k d are the PID controller parameters to be tuned. 2) the crossover frequency ω of the given closed loop system gc and the phase margin and given that the open loop phase of the closed loop system has a slope of zero at the crossover frequency, the proportional gain k p , the integral gain k i and the derivative gain k d of the PID controller are uniquely solved by solving equation one, equation two and equation three; Solving equation one as follows: （3） In the formula, B 31 is an intermediate variable, ; S3 is an intermediate variable, ; B 32 is an intermediate variable, ; C3 is an intermediate variable, ; Solving equation two as follows: （4） A is a gain margin; Solving equation three as follows: （5） E3 = E2 + E1 ; F3 is an intermediate variable, F3 = k p ω gc ; E 3＇ For E3, the derivative of ω gc , E 3＇ =-2k d ω gc ; F 3＇ F3= F2- F1 gc F1= F2- F3 3＇ F1= F2- F3 p F1= F2- F3 B 31＇ For B 31 Derivative of ω gc ;​ B 32＇ For B 32 Derivative of ω gc ;​ 3) if the solved proportional gain k p , integral gain k i and differential gain k d are empty set, then re-define the cross-over frequency ω gc and phase margin , re-solve the equations (3)-(5) to uniquely solve the proportional gain k p , integral gain k i and differential gain k d ; If the solved proportional gain k p , integral gain k i and differential gain k d are non-empty sets, then the obtained proportional gain k p , integral gain k i and differential gain k d are the PID controller parameters that satisfy the crossing frequency ω gc , phase margin and phase flatness constraints; 4) The obtained k p value, k i value and k d value are set to the PID controller as the proportional gain, the integral gain and the derivative gain of the PID controller satisfying the constraint, i.e. a feedback controller satisfying the control requirement is obtained.

2. A system for robust design of a PID controller for an inertial plus delayed fractional order plant, characterized by, comprise: a closed loop system establishing module, configured to establish a closed loop system composed of a controlled object and a feedback controller; wherein, A class of actual industrial systems as controlled object is taken as controlled object to adopt inertia plus delay fractional order transfer function G p (s) description, as follows: （1） In the formula, G p (s) is an inertial plus delay fractional order transfer function, s is a differential operator, K is a gain of a controlled object, has K ∈ [-10 10 , 0)∪(0, 10 10 ], T is a time constant of the controlled object, has T ∈ (0, 10 10 ], α is an order of the controlled object, has α ∈ (0, 2), L is a delay time constant of the controlled object, has L ∈ (0, 10 10 ], and e is a natural constant; The feedback controller employs a PID controller whose transfer function G c (s) is as follows: （2） where k p is the PID controller proportional gain, k p ∈ [-10 10 , 10 10 ], k i is the PID controller integral gain, k i ∈ [-10 10 , 10 10 ], k d is the PID controller derivative gain, k d ∈ [-10 10 , 10 10 ]; k p , k i and k d are the PID controller parameters to be tuned. The parameter solving module is connected with the closed loop system establishing module, and is used for solving the through frequency ω gc and the phase margin of the given closed loop system, and setting the slope of the open loop phase of the closed loop system at the through frequency to be zero, so as to uniquely solve the proportional gain k p , the integral gain k i and the differential gain k d of the PID controller through solving equation one, solving equation two and solving equation three. If the solved proportional gain k p , integral gain k i and differential gain k d are empty sets, then the crossover frequency ω gc and phase margin are redefined, the formula (3)-(5) are solved again, and the proportional gain k p , integral gain k i and differential gain k d of the PID controller are uniquely solved again. If the solved proportional gain k p , integral gain k i and differential gain k d are non-empty sets, then the obtained proportional gain k p , integral gain k i and differential gain k d are the PID controller parameters that satisfy the crossing frequency ω gc , phase margin and phase flatness constraints; Solving equation one as follows: （3） In the formula, B 31 is an intermediate variable, ; S3 is an intermediate variable, ; B 32 is an intermediate variable, ; C3 is an intermediate variable, ; Solving equation two as follows: （4） A is a gain margin; Solving equation three as follows: （5） E3 = E2 + E1 ; F3 is an intermediate variable, F3 = k p ω gc ; E 3＇ For E3, the derivative of ω gc , E 3＇ =-2k d ω gc ; F 3＇ F3= F2- F1 gc F1= F0 3＇ F0= k p ; B 31＇ For B 31 Derivative of ω gc ;​ B 32＇ For B 32 Derivative of ω gc , ; a design module for setting the obtained k p value, k i value and k d value as the proportional gain, the integral gain and the derivative gain of the PID controller that satisfies the constraints, i.e. obtaining a feedback controller that satisfies the control requirements.

3. A PID controller for an inertial plus delayed fractional order plant characterized by: The PID controller robust design method for the inertial plus delay fractional order object is designed by using the PID controller robust design method for the inertial plus delay fractional order object in claim 1.

4. A PID controller robust design apparatus, characterized by, comprise: 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 execute the steps of the PID controller robust design method for the inertial plus delay fractional order object in claim 1.

5. A computer readable storage medium storing a computer program, characterized in that, The programs are executed by the processors to implement the steps of the PID controller robust design method for the inertial plus delay fractional order object in claim 1.

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