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 application relates to a fractional order controller design method, in particular to a robust design method and system of a fractional order PI controller of an inertia plus delay fractional order object. BACKGROUND

[0002] In typical industrial process control such as chemical process and wind power generation process, there is a kind of inertia plus delay fractional order process, such as the wind power generation variable pitch control system in the wind power generation process, which is generally described by an inertia plus delay fractional order system , wherein G p (s) is an inertia plus delay fractional order transfer function, s is a differential operator, K is a controlled object gain, T is a controlled object time constant, alpha is an order of the controlled object, L is a delay time constant of the controlled object, and e is a natural constant; taking the wind power generation variable pitch control system as an example, the meanings of the parameters in the above formula are as follows: The gain K is a "control signal-pitch angle" static gain of a variable pitch actuator (such as a servo motor and a speed reducer); The time constant T is the mechanical inertia (such as the blade rotational inertia and the transmission mechanism damping) of the variable pitch system, and the greater the time constant T, the stronger the inertia, and the slower the response of the pitch angle to the control signal; The fractional order alpha is the core nonlinearity of the variable pitch system, which is derived from the blade aerodynamic characteristics: the dynamic relationship of the lift / drag of the blade when the wind speed changes cannot be accurately described by an integer order (such as a first order or a second order) linear model (for example, the difference in aerodynamic damping at low wind speed and high wind speed); and the fractional order model can more flexibly fit the "nonlinear dynamics between integer orders" through the continuously adjustable order alpha in the range of (0, 2), and has higher precision than the integer order model (such as a first order inertia with alpha = 1); The delay time L is the double delay of the variable pitch system: 1. Signal delay: time lag of wind speed detection (such as wind speed sensor sampling and data transmission); 2. Execution delay: mechanical response lag of the servo motor starting and the transmission mechanism overcoming the gap after the control signal is issued, which is completely consistent with the actual scene of "delay in wind speed fluctuation influence".

[0003] At present, the inertia plus delay fractional order system in typical industrial process control such as chemical process and wind power generation process widely uses a traditional feedback control mode based on output error, and the controller used is mainly a traditional proportional-integral-derivative (PID) controller. The traditional PID controller model is as follows, G c (s) = k p +k i / s+k d s, where k p is the proportional gain, k i is the integral gain, k d is the derivative gain.

[0004] The traditional PID controller has the advantages of simple structure and easy implementation, but for an inertial plus delay fractional order object system, it cannot provide more freedom and parameter adjustment space to meet the requirements of more flexible and accurate control performance. Therefore, it needs to be improved and extended to a fractional order PI controller. The model of the fractional order PI controller is as follows, where k p is the proportional gain, k i is the integral gain, and λ is the order. The fractional order PI controller can obtain better control performance than the traditional PID controller for an inertial plus delay fractional order system.

[0005] The fractional order PI controller in the form of (k p is the proportional gain of the controller, k i is the integral gain of the controller, and λ is the order of the integrator) is the product of the development of fractional calculus. It can provide more freedom and parameter adjustment space than the integer order controller, achieve more flexible and accurate control performance, and have better robustness and adaptability to complex systems.

[0006] The parameter stability domain calculation method of the fractional order PI controller in the form of for a fractional order object lacks research. Current fractional order PI controller tuning techniques are more focused on methods including model-based tuning and evolutionary algorithm-based optimization. The model-based tuning method generally obtains the controller parameters by combining the expected closed-loop dynamic equation with the transfer function of the controlled object. This method mainly designs for nominal objects, and the robustness of the controller is checked after the parameters are designed, which has more steps. The evolutionary algorithm-based optimization of fractional order PI controller parameters can solve the minimum control performance index based on robustness constraints. This method has the disadvantages of slow solving speed and easy convergence to local optimum. It should be noted that there are some achievements in fractional order PI controller tuning methods under the constraints of typical robustness indicators (such as maximum sensitivity function, phase margin, amplitude margin, phase flatness, and crossover frequency), 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.

[0007] With the development of fractional calculus theory and technology, more and more controlled objects are described by fractional order transfer functions. It is necessary to robustly tune the parameters of the fractional order PI controller for fractional order objects. SUMMARY

[0008] The application aims to solve the problem of robust design and parameter feasible region acquisition of fractional PI controller for a class of fractional order objects, and provides a robust design method and system of fractional PI controller for inertia plus delay fractional order objects.

[0009] In the first aspect, the application provides a robust design method of fractional PI controller for inertia plus delay fractional order objects, comprising the following steps: 1) establishing a closed-loop control system composed of a controlled object and a feedback controller; wherein, A class of actual industrial systems as controlled objects is described by an inertia plus delay fractional transfer function G p (s) as follows: (1) In the formula, G p (s) is an inertia plus delay fractional transfer function, s is a differential operator, K is the gain of the controlled object, 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 ], and e is a natural constant; The feedback controller adopts the form of fractional PI controller, and its transfer function G c (s) is as follows: (2) In the formula, k p is the proportional gain of the controller, k p ∈[-10 10 ,10 10 ], k i is the integral gain of the controller, k i ∈[-10 10 ,10 10 ], and λ is the order of the controller, λ∈(0,2); k p , k i and λ are the parameters of the fractional PI controller to be determined; 2) Given the crossover frequency ω gc and the phase margin of the closed-loop control system, and 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 p and the integral gain k iand controller integral order λ; Solving equation one as follows: (3) where B 11 is an intermediate variable, ; S1 is an intermediate variable, ; B 12 is an intermediate variable, ; C1 is an intermediate variable, ; Solving equation two as follows: (4) Solving equation three as follows: (5) where E1 is an intermediate variable, ; F1 is an intermediate variable, ; is the derivative of E1 with respect to ω gc , ; is the derivative of F1 with respect to ω gc , ; is the derivative of B 11 with respect to ω gc , ; is the derivative of B 12 with respect to ω gc , ; 3) If the solved proportional gain k p , integral gain k i and controller integral order λ are empty sets, then re-define the crossover frequency ω gc and phase margin , re-solve equations (3)-(5) to uniquely solve the fractional order PI controller's proportional gain k p , integral gain k i and controller integral order λ; If the solved proportional gain k p , integral gain k i and controller integral order λ are non-empty sets, then the obtained proportional gain k p , integral gain k i and controller integral order λ are the fractional order PI controller that meets the crossover frequency ωgc Phase margin Parameters of a fractional-order PI controller with phase flatness constraints; Record the crossover frequency ω corresponding to the non-empty set. gc and phase margin ; 4) Traversal frequency ω gc ∈(0,ω gcmax and phase margin ∈(0º,180º],ω gcmax To find the maximum shear frequency; repeat steps 2)-3) to obtain the crossover frequency ω corresponding to the non-empty set. gcmax and phase margin Distribution, i.e., the feasible region of a fractional-order PI controller; 5) The corresponding k in the feasible region of the obtained fractional-order PI controller p value, k i The values ​​of λ and λ are used as the proportional gain, integral gain, and order of the fractional-order PI controller to satisfy the constraints, thus obtaining a feedback controller that meets the control requirements.

[0010] In a second aspect, the present invention provides a robust design system for a fractional-order PI controller for an inertial-delayed fractional-order object, comprising: The closed-loop control system establishment module establishes a closed-loop control system consisting of the controlled object and a 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) describes, 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 adopts a fractional-order PI controller form, and its transfer function G c (s) are as follows: (2) In the formula, k p For the proportional gain of the controller, we have k p ∈[-10 10 10 10], k i is the integral gain of the controller, k i ∈[-10 10 ,10 10 ], λ is the order of the controller, λ∈(0, 2); k p , k i and λ are the parameters of the fractional order PI controller to be tuned; a parameter solving module, configured to uniquely solve the proportional gain k gc , the integral gain k p and the integral order λ of the fractional order PI controller by solving equation one, equation two and equation three, given the crossover frequency ω i and the phase margin of the closed-loop control system, and given that the slope of the open-loop phase of the closed-loop control system at the crossover frequency is zero; and record module determines that the proportional gain k p , the integral gain k i and the integral order λ solved are an empty set, the parameter solving module is further configured to re-given the crossover frequency ω gc and the phase margin , re-solve equations (3)-(5), and re- uniquely solve the proportional gain k p , the integral gain k i and the integral order λ of the fractional order PI controller; Equation one is solved as follows: (3) where B 11 is an intermediate variable, ; S1 is an intermediate variable, ; B 12 is an intermediate variable, ; C1 is an intermediate variable, ; Equation two is solved as follows: (4) Equation three is solved as follows: (5) where E1 is an intermediate variable, ; F1 is an intermediate variable, ; is the derivative of E1 with respect to ω gc ; ; F1 is the derivative of B gc ; ; F1 is the derivative of B 11 ; gc ; ; F1 is the derivative of B 12 ; gc ; ; The parameter judgment and recording module is connected with the parameter solving module, and is used for judging whether the proportional gain k p , the integral gain k i and the integral order λ of the fractional order PI controller solved are empty sets or not. The parameter judgment and recording module is also used for recording the crossing frequency ω gc and the phase margin corresponding to the non-empty set when judging that the proportional gain k p , the integral gain k i and the integral order λ of the fractional order PI controller solved are non-empty sets; wherein the proportional gain k p , the integral gain k i and the integral order λ obtained are fractional order PI controller parameters meeting the crossing frequency ω gc , the phase margin and the phase flatness constraint. The feasible region calculation module is connected with the parameter judgment and recording module and the parameter solving module, and is used for traversing the crossing frequency ω gc ∈(0,ω gcmax ] and the phase margin ∈(0º,180º], to obtain the distribution of the crossing frequency ω gcmax and the phase margin corresponding to the non-empty set, namely the feasible region of the fractional order PI controller; ω gcmax is the maximum shear frequency. The design module is used for setting the corresponding k p value, k i value and λ value in the feasible region of the fractional order PI controller obtained as the proportional gain, the integral gain and the order of the fractional order PI controller meeting the constraint, namely obtaining the feedback controller meeting the control requirement.

[0011] In a third aspect, the present application provides a fractional order PI controller of an inertia plus delay fractional order object, which is designed by using the robust design method of the fractional order PI controller of the inertia plus delay fractional order object.

[0012] In a fourth aspect, the present application provides a fractional order PI controller robust design device, which comprises: one or more processors; a memory for storing one or more programs, the one or more programs, when executed by the one or more processors, cause the one or more processors to perform the steps of the method for robust design of fractional order PI controller of inertia plus delay fractional order object as claimed.

[0013] In a fifth aspect, the present application provides a computer readable storage medium storing a computer program, wherein the program, when executed by a processor, implements the steps of the method for robust design of fractional order PI controller of inertia plus delay fractional order object as claimed.

[0014] The present application has outstanding substantial features and significant progress compared with the prior art, and specifically: The present application solves the method for robust design of fractional order PI controller parameters of a class of fractional order objects, which can directly obtain the parameters (proportional gain k p , integral gain k i and controller integral order λ) of the fractional order PI controller under the direct setting of phase margin, crossover frequency and phase flatness constraints, thereby designing the fractional order PI controller with strong ability to cope with gain uncertainty of the controlled object.

[0015] 2. The method of the present application only needs to give the phase margin, crossover frequency and phase flatness constraints of the closed-loop control system, then solve the preset equation, and then obtain the parameters (proportional gain k p , integral gain k i and controller integral order λ) of the fractional order PI controller through judgment and traversal operations, and the method is simple and easy to implement. BRIEF DESCRIPTION OF DRAWINGS

[0016] Figure 1 The present application is a closed-loop system composed of a fractional order PI controller and an inertia plus delay fractional order object.

[0017] Figure 2 The control effect of the present application in Example 1.

[0018] Figure 3 The control effect of the present application in Example 1 when the controlled object has uncertainty.

[0019] Figure 4 The feasible region of the fractional order PI controller obtained by the present application in Example 1. DETAILED DESCRIPTION

[0020] In order to make the purpose, technical scheme and advantages of the present application more clear, the present application is further described in detail below in combination with the drawings and examples. It should be understood that the specific examples described herein are only used to explain the present application and not to limit the present application.

[0021] Example 1 The present example proposes a robust design method of fractional order PI controller for an inertia plus delay fractional order object, including the following steps: 1) Establish a fractional order PI controller for an inertia plus delay fractional order object as a closed-loop control system composed of a controlled object and a feedback controller, as shown in Figure 1 .

[0022] A kind of actual industrial system controlled is taken as a controlled object using an inertia plus delay fractional order transfer function G p (s) to describe as follows: (1) In the formula, G p (s) is an inertia plus delay fractional order transfer function, s is a differential operator, K is a controlled object gain, has K∈[-10 10 ,0)∪(0,10 10 ], T is a controlled object time constant, has T∈(0,10 10 ], α is the order of the controlled object, has α∈(0,2), L is the delay time constant of the controlled object, has L∈(0,10 10 ), e is a natural constant; In the present example, K=1, T=1, α=1.5 and L=1.

[0023] The feedback controller adopts the form of fractional order PI controller, and its transfer function G c (s) is as follows: (2) In the formula, k p is a controller proportional gain, has k p ∈[-10 10 ,10 10 ], k i is a controller integral gain, has k i ∈[-10 10 ,10 10 ], λ is a controller order, has λ∈(0,2); k p , k i and λ are fractional order PI controller parameters to be tuned.

[0024] 2) Given the crossover frequency ω gc and the phase margin and the open loop phase of the closed loop control system has a slope of zero at the crossover frequency (also known as phase flatness), the fractional order PI controller is uniquely solved by solving Equation One, solving Equation Two and solving Equation Three to obtain the proportional gain k p , the integral gain k i and the integral order of the controller λ. In this embodiment, the initial given crossover frequency ω gc = 0.05 Hz and the phase margin = 83°. The solved proportional gain k p = 0.4623, the integral gain k i = 0.2306 and the integral order of the controller λ = 1.1300.

[0025] Solving Equation One is as follows: (3) where B 11 is an intermediate variable, ; S1 is an intermediate variable, ; B 12 is an intermediate variable, ; C1 is an intermediate variable, ; Solving Equation Two is as follows: (4) Solving Equation Three is as follows: (5) where E1 is an intermediate variable, ; F1 is an intermediate variable, ; is the derivative of E1 with respect to ω gc ; ; is the derivative of F1 with respect to ω gc ; ; is the derivative of B 11 with respect to ω gc ; ; is the derivative of B 12 with respect to ω gc .

[0026] 3) If the solved proportional gain k p ​, integral gain k i and controller integral order λ is empty set, re-set the crossover frequency ω gc and phase margin , re-solve equation (3) - (5), re-solve the fractional order PI controller proportional gain k p , integral gain k i and controller integral order λ; If the proportional gain k p , integral gain k i and controller integral order λ is non-empty set, the proportional gain k p , integral gain k i and controller integral order λ is the fractional order PI controller parameters that meet the crossover frequency ω gc , phase margin and phase flatness constraints; Record the non-empty set corresponding to the crossover frequency ω gc and phase margin .

[0027] 4) traverse the crossover frequency ω gc ∈(0,ω gcmax ] and phase margin ∈(0º,180º], ω gcmax is the maximum shear frequency; repeat steps 2) - 3), get the non-empty set corresponding to the crossover frequency ω gcmax and phase margin distribution, that is, the feasible region of the fractional order PI controller; In this embodiment, the crossover frequency ω gcmax =1.5Hz.

[0028] In this embodiment, the crossover frequency ω gc =0.05Hz, phase margin =83°, phase flatness constraint fractional order PI controller parameters: proportional gain k p =0.4623, integral gain k i =0.2306 and controller integral order λ=1.1300.

[0029] 5) the fractional order PI controller in the feasible region of the proportional gain k p =0.4623, k i =0.2306 and λ=1.1300 obtained as the fractional order PI controller that meets the constraints of proportional gain, integral gain and order set to the fractional order PI controller, that is, to obtain the feedback controller that meets the control requirements.

[0030] The feedback controller obtained in this embodiment can be combined with the controlled object to obtainFigure 1 The tracking and anti-interference performance of the closed-loop control system shown in the figure is as follows Figure 2 The specific simulation process is as shown in the figure: At the beginning of the simulation, the system is in a steady state, the set value is changed from 0 to 1 at 0s, and a disturbance of the control quantity is applied to the closed-loop circuit from 0 to 1 at 20s, until the simulation ends at 40s; Through the simulation, it can be known that the closed-loop control system after the parameters of the fractional order PI controller are directly calculated based on the given phase margin, the crossing frequency and the phase flatness constraint has relatively fast tracking capability and relatively strong anti-interference capability.

[0031] In order to analyze the response capability of the tuned fractional order PI controller to the gain uncertainty of the controlled object, the G p (s) is modified, the gain K of the controlled object is 120%K and 80%K respectively, the above simulation is repeated, and the following results can be obtained Figure 3 The results are shown in the figure, and it can be known from the figure that the tuned fractional order PI controller has relatively strong response capability to the gain uncertainty of the controlled object. Figure 3 The feasible region of the fractional order PI controller is plotted as shown in the figure, thereby verifying the effectiveness of the method for calculating the feasible region of the fractional order PI controller. Figure 4

[0032] Embodiment 2 The embodiment provides a robust design system of a fractional order PI controller of an inertia plus delay fractional order object, and the system comprises: A closed-loop control system establishment module is configured to establish a closed-loop control system composed of a controlled object and a feedback controller; wherein, A kind of controlled actual industrial system is taken as controlled object using inertia plus delay fractional order transfer function G p (s) is described as follows: (1) In the formula, G p (s) is inertia plus delay fractional order transfer function, s is differential operator, K is controlled object gain, has K∈[-10 10 ,0)∪(0,10 10 ], T is controlled object time constant, has T∈(0,10 10 ], α is the order of controlled object, has α∈(0,2), L is controlled object delay time constant, has L∈(0,10 10 ), e is natural constant; The feedback controller adopts fractional order PI controller form, and its transfer function G c (s) is as follows: (2) In the formula, k​p For the proportional gain of the controller, we have k p ∈[-10 10 10 10 ], k i For the controller integral gain, we have k i ∈[-10 10 10 10 ], where λ is the order of the controller, and λ∈(0,2); k p k i λ and λ are the parameters of the fractional-order PI controller to be tuned; The parameter solving module is used to solve for the crossover frequency ω of a given closed-loop control system. gc and phase margin Assuming the open-loop phase of the closed-loop control system has a zero slope at the crossover frequency, the proportional gain k of the fractional-order PI controller is uniquely solved by solving equations one, two, and three. p Integral gain k i and the integral order λ of the controller; It is also used in the parameter judgment and recording module to judge the calculated proportional gain k. p Integral gain k i When the integral order λ of the controller is an empty set, the crossover frequency ω is redefined. gc and phase margin Resolve formulas (3)-(5) to uniquely solve for the proportional gain k of the fractional-order PI controller. p Integral gain k i and the integral order λ of the controller; Solve equation one as follows: (3) In the formula, B 11 As an intermediate variable, ; S1 is an intermediate variable. ; B 12 As an intermediate variable, ; C1 is an intermediate variable. ; Solve equation two as follows: (4) Solve equation three as follows: (5) In the formula, E1 is an intermediate variable. ; F1 is an intermediate variable. ; derivative of F1 with respect to ω gc ; derivative of F1 with respect to ω gc ; derivative of B 11 with respect to ω gc ; derivative of B 12 with respect to ω gc ; The parameter judgment and recording module is connected with the parameter solving module, and is used for judging whether the proportional gain k p , the integral gain k i and the integral order λ of the fractional order PI controller solved are empty sets or not. The parameter judgment and recording module is further used for recording the crossing frequency ω gc and the phase margin corresponding to the non-empty set when judging that the proportional gain k p , the integral gain k i and the integral order λ of the fractional order PI controller solved are non-empty sets; wherein the proportional gain k p , the integral gain k i and the integral order λ obtained are the fractional order PI controller parameters meeting the crossing frequency ω gc , the phase margin and the phase flatness constraint. The feasible region calculation module is connected with the parameter judgment and recording module and the parameter solving module, and is used for traversing the crossing frequency ω gc ∈(0, ω gcmax ] and the phase margin ∈(0º, 180º], to obtain the distribution of the crossing frequency ω gcmax and the phase margin corresponding to the non-empty set, that is, the feasible region of the fractional order PI controller; ω gcmax is the maximum shear frequency. The design module is used for setting the corresponding k p value, k i value and λ value in the feasible region of the fractional order PI controller obtained as the proportional gain, the integral gain and the order of the fractional order PI controller meeting the constraint to the fractional order PI controller, that is, obtaining the feedback controller meeting the control requirement.

[0033] ​​​​In this embodiment, the solution to the problem of the robust design system of the fractional order PI controller of the inertia plus delay fractional order object is similar to the implementation described in the method of embodiment 1, and will not be repeated here.

[0034] Embodiment 3 This embodiment provides a fractional order PI controller of an inertia plus delay fractional order object, which is designed by using the robust design method of the fractional order PI controller of the inertia plus delay fractional order object described in embodiment 1.

[0035] Embodiment 4 Each module in the system of embodiment 2 can be implemented by software, hardware and a combination thereof in whole or in part. Each module described above can be embedded in or independent of the processor in the computer device in hardware form, or can be stored in the memory in the computer device in software form, so as to be called and executed by the processor to perform the operations corresponding to each module.

[0036] In one exemplary embodiment, a fractional order PI controller robust design apparatus is provided, and the computer device can 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 through a system bus, and the communication interface, the display unit and the input device are connected to the system bus through the input / output interface. The processor of the computer device is configured 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 operating system and the computer program in the non-volatile storage medium to run. The input / output interface of the computer device is configured to exchange information between the processor and external devices. The communication interface of the computer device is configured to perform wired or wireless communication with external terminals, and the wireless communication can be achieved by WIFI, mobile cellular network, NFC (near field communication) or other technologies. The computer program is executed by the processor to implement the steps of the robust design method of the fractional order PI controller of the inertia plus delay fractional order object. The display unit of the computer device is configured to form a visually visible picture, which can 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 overlaid on the display screen, or can be a key, a trackball or a touchpad arranged on the shell of the computer device, or can be an external keyboard, a touchpad or a mouse, etc.

[0037] Those skilled in the art can understand that the structure of the computer device described above is only part of the structure related to the scheme of the present application, and does not constitute a limitation on the computer device to which the scheme of the present application is applied. A specific computer device can include more or fewer components, or combine certain components, or have a different arrangement of components.

[0038] In one exemplary embodiment, a computer readable storage medium is provided, having stored thereon a computer program which, when executed by a processor, implements the steps of the method for robust design of a fractional order PI controller of a fractional order plus time delay object.

[0039] Those of ordinary skill in the art can understand that all or part of the processes in the above-mentioned embodiments can be completed by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer readable storage medium and can include the processes of the above-mentioned embodiments when executed. Any reference to a memory, database, or other medium used in the embodiments provided by the present application can include at least one of a non-volatile and volatile memory. The non-volatile memory can include a read-only memory (ROM), a magnetic tape, a floppy disk, a flash memory, an optical memory, a high-density embedded non-volatile memory, a resistive memory (ReRAM), a magnetoresistive random access memory (MRAM), a ferroelectric memory (FRAM), a phase change memory (PCM), a graphene memory, etc. The volatile memory can include a random access memory (RAM) or an external cache memory, etc. As an illustration but not as a limitation, the RAM can be in various forms such as a static random access memory (SRAM) or a dynamic random access memory (DRAM), etc. The database involved in the embodiments provided by the present application can include at least one of a relational database and a non-relational database. The non-relational database can include a distributed database based on a block chain, etc., without being limited thereto. The processor involved in the embodiments provided by the present application can be a general-purpose processor, a central processing unit, a graphics processing unit, a digital signal processor, a programmable logic device, a data processing logic device based on quantum computing, etc., without being limited thereto.

[0040] Any technical features in the above embodiments can be combined, and for the sake of brevity, not all possible combinations are described above, however, any combination of the technical features is deemed to be within the scope of the present disclosure.

[0041] The above merely provides the specific implementation of the present application, but the protection scope of the present application is not limited thereto, any person skilled in the art can easily think of the changes or replacements within the technical range disclosed by the present application, which should be covered within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A method for robust design of a fractional order PI controller for an inertial plus time-delay fractional order plant, characterized in that, The method comprises the following steps: 1) establishing a closed-loop control 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 takes the form of a fractional order PI controller whose transfer function G c (s) is as follows: （2） where k p is the controller proportional gain, k p ∈[-10 10 ,10 10 ], k i is the controller integral gain, k i ∈[-10 10 ,10 10 ], and λ is the controller order, λ∈(0, 2); k p , k i , and λ are the tuning fractional PI controller parameters; 2) the crossover frequency ω of the given closed-loop control system gc and the phase margin and the open-loop phase of the closed-loop control system has a slope of zero at the crossover frequency, the proportional gain k p , the integral gain k i and the integral order λ of the fractional-order PI controller are uniquely solved by solving Equation One, Equation Two and Equation Three. Solving equation one as follows: （3） In the formula, B 11 is an intermediate variable, ; S1 is an intermediate variable, ; B 12 is an intermediate variable, ; C1 is an intermediate variable, ; Solving equation two as follows: （4） Solving equation three as follows: （5） In the formula, E1 is an intermediate variable, ; F1 is an intermediate variable, ; E1 for ω gc derivative of ; F1 for ω gc derivative of, ; B for 11 derivative of ω gc ;​ B for 12 derivative of ω gc , the derivative of ; 3) if the solved proportional gain k p , integral gain k i and controller integral order λ are empty set, then re-define the crossover frequency ω gc and phase margin , re-solve equations (3)-(5) and re-solve uniquely the proportional gain k p , integral gain k i and controller integral order λ of the fractional order PI controller; If the solved proportional gain k p , integral gain k i and controller integral order λ are non-empty set, the obtained proportional gain k p , integral gain k i and controller integral order λ are fractional order PI controller parameters satisfying the constraints of crossover frequency ω gc , phase margin and phase flatness. Record the crossing frequency ω for the non-empty set gc and phase margin ; 4) traversing frequencies ω gc ∈(0, ω gcmax and phase margin ∈(0º, 180º], ω gcmax is the maximum shear frequency; repeat steps 2)-3) to obtain the set of traversing frequencies ω gcmax and phase margin distribution, i.e. the feasible region of the fractional order PI controller; 5) The corresponding k in the feasible region of the obtained fractional-order PI controller p value, k i The values ​​of λ and λ are used as the proportional gain, integral gain, and order of the fractional-order PI controller to satisfy the constraints, thus obtaining a feedback controller that meets the control requirements.

2. A system for robust design of a fractional order PI controller for an inertial plus delayed fractional order plant, characterized by, The method comprises the following steps: The closed-loop control system establishing module establishes a closed-loop control 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 takes the form of a fractional order PI controller whose transfer function G c (s) is as follows: （2） where 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 ], and λ is the controller order, with λ∈(0,2); k p , k i and λ are the tuning fractional PI controller parameters; a parameter solving module, configured to solve the proportional gain k gc and the phase margin of the fractional order PI controller uniquely by solving the equation one, the equation two and the equation three under the condition that the slope of the open loop phase of the closed loop control system at the cross-over frequency is zero p , the integral gain k i and the integral order λ of the controller; Also used in parameter judgment and record module to judge the proportional gain k p , integral gain k i and controller integral order λ is empty set, redefined crossing frequency ω gc and phase margin , re-solve formula (3) - (5), re-solve the fractional order PI controller proportional gain k p , integral gain k i and controller integral order λ; Solving equation one as follows: （3） In the formula, B 11 is an intermediate variable, ; S1 is an intermediate variable, ; B 12 is an intermediate variable, ; C1 is an intermediate variable, ; Solving equation two as follows: （4） Solving equation three as follows: （5） In the formula, E1 is an intermediate variable, ; F1 is an intermediate variable, ; E1 for ω gc derivative of ; F1 for ω gc derivative of ; B for 11 derivative of ω gc ;​ B for 12 derivative of ω gc ;​ The parameter judging and recording module is connected with the parameter solving module, and is used for judging whether the proportional gain k p , the integral gain k i and the integral order λ of the fractional order PI controller are empty sets or not. Also used for judging the proportional gain k p , integral gain k i and controller integral order λ is a non-empty set, record the non-empty set corresponding to the crossing frequency ω gc and phase margin ; wherein the proportional gain k p , integral gain k i and controller integral order λ is the fractional order PI controller parameters that meet the crossing frequency ω gc , phase margin and phase flatness constraints; The feasible region calculation module is connected with the parameter judgment and record module and the parameter solution module, and is used for traversing the crossing frequency ω gc ∈(0,ω gcmax ] and the phase margin ∈(0º,180º] to obtain the non-empty set corresponding to the crossing frequency ω gcmax and the phase margin distribution, i.e. the feasible region of the fractional order PI controller; ω gcmax is the maximum shear frequency; a design module for setting the corresponding k p value, k i value and the value of λ as the proportional gain, the integral gain and the order of the fractional order PI controller satisfying the constraints into the fractional order PI controller, i.e. obtaining the feedback controller satisfying the control requirements.

3. A fractional order PI controller for an inertial plus delayed fractional order object, characterized by: The fractional order PI controller for the inertial plus delay fractional order object is designed by using the robust design method of the fractional order PI controller for the inertial plus delay fractional order object according to claim 1.

4. A fractional order PI controller robust design apparatus, characterized by, The method comprises the following steps: One or more processors; 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 execute the steps of the robust design method of the fractional order PI controller for the inertial plus delay fractional order object according to claim 1.

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

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