A Parallel Interval Type-2 Fuzzy PID Controller Based on the Step-by-Step Optimization Method

Abstract

The present invention relates to the field of automation technology, and specifically provides a parallel-type interval type-2 fuzzy PID controller based on a step-by-step optimization method, including the following optimization steps: S1: Optimize the three parameters k p , k i , k d of the PID controller separately; S2: Combine a type-1 fuzzy controller with the PID controller with optimized parameters to construct a type-1 fuzzy PID controller, and optimize the five coefficients K e , #imgabs0#K up , K ui , K ud on the type-1 fuzzy PID controller; S3: Perform uncertainty optimization on the membership function of the type-1 fuzzy PID controller with optimized parameters. The uncertainty optimization method is the empirical method or the intelligent optimization algorithm. After optimization, a parallel-type interval type-2 fuzzy PID controller with optimal parameters is obtained. The step-by-step optimization method in this solution can narrow the range of optimized parameters compared with the existing methods, save a large amount of optimization time, improve the optimization efficiency, and can be effectively used in engineering applications.

Description

Technical Field

[0001] The present invention relates to the field of automation technology, and in particular, to a parallel interval type-2 fuzzy PID controller based on a step-by-step optimization method. Background Art

[0002] The PID controller, namely the proportional–integral–derivative controller, has the advantages of simple structure, convenient adjustment, good stability, reliable operation, etc. Therefore, it has been rapidly popularized in industrial control since its inception. Currently, a large number of high-end controls are based on the PID controller, and the PID controller has become one of the main technologies in industrial control. However, when the controlled object is a high-order complex system with time delay, high order, nonlinearity, and uncertain model, the PID controller will no longer have control ability.

[0003] To overcome the above problems of the PID controller, scholars at home and abroad have combined the fuzzy logic controller with the PID control to adapt to high-order complex controlled systems. In recent years, a type-1 fuzzy PID controller and an interval type-2 fuzzy PID controller have emerged successively. The results of the type-1 fuzzy controller and the interval type-2 fuzzy controller are similar. The interval type-2 fuzzy controller can be formed by adding uncertainty to the membership function of the type-1 fuzzy controller. Therefore, the interval type-2 fuzzy controller has stronger control ability than the type-1 fuzzy controller and can effectively control nonlinear and time-varying uncertain model systems. Therefore, the combination of the interval type-2 fuzzy controller and the PID controller has become a current research hotspot.

[0004] Currently, the common structures of the interval type-2 fuzzy PID controller are series type and parallel type:

[0005] 1. The series type is to perform proportional–integral operations on the outputs of the fuzzy controller respectively and then sum them to construct an interval type-2 fuzzy PID controller; when establishing the fuzzy control rules, this method does not control the parameters of the PID controller separately and does not give full play to the advantages of independent control of each parameter in the PID controller;

[0006] 2. The parallel type is a controller in which the fuzzy controller and the PID controller work in parallel at the same time; compared with the series type, this method not only retains the existing advantages of the PID controller but also utilizes the powerful control ability of the interval type-2 fuzzy controller to adjust the control parameters of the PID controller in real time, realizing the idea of using the PID controller to control high-order complex systems; therefore, the parallel type controller is more conducive to engineering applications.

[0007] However, at present, there is only the empirical method for the construction method of the parallel interval type-2 fuzzy PID controller, and there is no other optimized construction method. By analyzing the optimized construction method of the series interval type-2 fuzzy PID controller, it can be seen that when constructing an interval type-2 fuzzy PID controller, appropriate input and output coefficients and membership function parameters need to be selected. Therefore, when constructing a parallel interval type-2 fuzzy PID controller, the above-mentioned parameters also need to be selected appropriately. At present, many scholars have studied and found that the input and output coefficients are the key to affecting the performance of the interval type-2 fuzzy controller. Therefore, based on a fixed membership function, only optimizing the input and output coefficients is an efficient method for constructing a controller. Since the parallel controller retains the existing structure of the PID controller, in the dual-input mode, without optimizing the membership function, the number of parameters to be optimized is more than that of the series type. However, current research shows that it is very difficult to optimize the parameters of the series interval type-2 fuzzy PID controller simultaneously using common intelligent optimization algorithms.

[0008] In summary, the empirical method alone cannot meet the design of the parallel interval type-2 fuzzy PID controller. How to propose a practical design method for the parallel interval type-2 fuzzy PID controller and efficiently and quickly optimize multiple parameters of the parallel interval type-2 fuzzy PID controller is an urgent problem to be solved by those skilled in the art at present. Summary of the Invention

[0009] To solve the above problems, the present invention provides a parallel interval type-2 fuzzy PID controller based on a step-by-step optimization method. First, the three parameters of the PID controller are optimized separately. After completion, the PID controller is combined with a type-1 fuzzy controller, and five input and output coefficients are optimized simultaneously. After completion, the membership function of the type-1 fuzzy PID controller is fuzzified to construct an interval type-2 fuzzy PID controller. This solution can improve the optimization efficiency, reduce the optimization time, and narrow the optimization range of the parameters.

[0010] To achieve the above object, the present invention proposes the following technical solution: A parallel interval type-2 fuzzy PID controller based on a step-by-step optimization method, characterized by including the following optimization steps:

[0011] S1: Optimize the parameters of the PID controller separately;

[0012] S2: Combine a type-1 fuzzy controller with the PID controller after parameter optimization to construct a type-1 fuzzy PID controller, and perform parameter optimization on the type-1 fuzzy PID controller;

[0013] S3: Perform uncertainty optimization on the membership function of the type-1 fuzzy PID controller after parameter optimization, and obtain a parallel interval type-2 fuzzy PID controller with optimal parameters.

[0014] Preferably, in step S1, the three parameters k p 、k i 、k d of the PID controller are optimized simultaneously, where k p is the proportional coefficient, k i is the integral coefficient, and k d is the derivative coefficient; during the optimization process, only the PID controller participates in the optimization.

[0015] Preferably, the optimization formula of the PID controller in step S1 is:

[0016]

[0017] where u(k) is the output of the PID controller and e(k) is the error value.

[0018] Preferably, in step S3, the method for optimizing the membership function uncertainty of the type-1 fuzzy PID controller is the empirical method or the intelligent optimization algorithm.

[0019] Preferably, the optimization steps of the PID controller in step S1 are:

[0020] S11: Set the expected value to Firef, the initial e(k) to Firef, and the intelligent optimization algorithm randomly assigns three parameter values k p 、k i 、k d to obtain the initial u(k) value;

[0021] S12: Substitute the u(k) value into the controlled system and perform feedback;

[0022] S13: Compare the feedback value output by the controlled system with the expected value Firef; when the feedback value output by the controlled system is consistent and stable with Firef, the parameters of the PID controller do not need to be changed; when the feedback value output by the controlled system is stable but inconsistent with Firef, the intelligent optimization algorithm selects a set of better k p 、k i 、k d values and substitute them into the PID controller until the feedback value output by the controlled system is stable and consistent with Firef.

[0023] Preferably, in step S2, the five coefficients K e 、 K up 、K ui 、K ud of the type-1 fuzzy PID controller are optimized simultaneously, where K e is the error input coefficient, is the error change rate input coefficient, and K upis the proportionality coefficient output scale factor, K ui is the integral coefficient output scale factor, K ud is the derivative coefficient output scale factor.

[0024] Preferably, during the optimization process, the type-1 fuzzy controller in step S2 adjusts △k p 、△k i 、△k d and the type-2 fuzzy controller in step S3 adjusts △k p 、△k i 、△k d to perform online real-time parameter tuning for the PID controller.

[0025] The beneficial effects of the present invention are as follows:

[0026] 1. In the existing series type, usually only 4 parameters need to be optimized. However, even so, it is very difficult to optimize the 4 parameters of the series type interval type-2 fuzzy PID controller using common intelligent optimization algorithms. In the dual-input mode, without optimizing the membership function, the parameters to be optimized for the parallel type interval type-2 fuzzy PID controller are 8, including the proportionality coefficient, integral coefficient, derivative coefficient of the PID controller, and the error input coefficient, error change rate input coefficient, proportionality coefficient output factor, integral coefficient output factor, and derivative coefficient output factor of the interval type-2 fuzzy controller. The parallel type interval type-2 fuzzy PID controller in the present invention can optimize 8 parameters.

[0027] 2. In the first step of the present invention, the parameters of the PID controller are optimized separately first. The structure is simple, which can greatly accelerate the optimization speed and efficiency, avoid the situation of simultaneously optimizing too many parameters, and efficiently determine the optimal PID parameters.

[0028] 3. Due to the uncertainty of the membership function of the interval type-2 fuzzy controller, directly optimizing the input and output coefficients on it takes a lot of time and affects work efficiency. In the second step of the present invention, a type-1 fuzzy PID controller is constructed by combining a type-1 fuzzy controller with the PID controller after parameter optimization, and parameter optimization is performed on the type-1 fuzzy PID controller. Compared with the scheme of directly building an interval type-2 fuzzy PID controller to optimize 5 coefficients, the optimization time can be greatly reduced.

[0029] 4. In the third step of the present invention, the uncertainty of the membership function of the type-1 fuzzy PID controller after parameter optimization is optimized, and a parallel type interval type-2 fuzzy PID controller with optimal parameters is obtained. Here, only the uncertainty factor is optimized. Compared with the scheme of simultaneously optimizing all parameters, the optimization efficiency is higher, and the overall optimization efficiency of the type-2 fuzzy PID controller can be greatly improved.

[0030] 5. Since the optimal PID controller parameters have been determined, during the optimization process, the type-1 fuzzy controller and the type-2 fuzzy controller only adjust △k p 、△k i 、△k d . Compared with the optimization range of the parameters of the series-connected interval type-2 fuzzy PID controller, the parameter optimization range is greatly reduced, which can save a large amount of optimization time and provide support for the PID controller to realize online real-time parameter tuning and control time-varying nonlinear complex systems. Description of the Drawings

[0031] Figure 1 is the step-by-step optimization flowchart of the parallel-connected interval type-2 fuzzy PID controller provided by the embodiment of the present invention. Detailed Embodiments

[0032] In order to make the objectives, technical solutions and advantages of the present invention clearer, the following further describes the present invention in detail with reference to the accompanying Figure 1 drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and do not constitute a limitation to the present invention.

[0033] A parallel-connected interval type-2 fuzzy PID controller based on a step-by-step optimization method, characterized by including the following optimization steps:

[0034] S1: Optimize the parameters of the PID controller alone; specifically, optimize the three parameters k p 、k i 、k d of the PID controller simultaneously, where k p is the proportionality coefficient, k i is the integral coefficient, and k d is the differential coefficient; during this optimization process, only the PID controller participates in the optimization, and the optimal PID parameters can be efficiently determined.

[0035] The optimization formula of the PID controller is:

[0036]

[0037] where u(k) is the output of the PID controller and e(k) is the error value.

[0038] As Figure 1 shown, the optimization steps of the PID controller are:

[0039] S11: Set the desired value as Firef, the initial e(k) as Firef, and the intelligent optimization algorithm randomly assigns three parameter values k p 、k i 、k d, the initial value of u(k) is obtained;

[0040] S12: Substitute the value of u(k) into the controlled system and perform feedback;

[0041] S13: Compare the feedback value output by the controlled system with the expected value Firef; when the feedback value output by the controlled system is consistent and stable with Firef, the parameters of the PID controller do not need to be changed; when the feedback value output by the controlled system is stable but inconsistent with Firef, the intelligent optimization algorithm selects a set of better k p 、k i 、k d values and substitute them into the PID controller until the feedback value output by the controlled system is stable and consistent with Firef.

[0042] S2: Combine a type-1 fuzzy controller with the PID controller with optimized parameters to construct a type-1 fuzzy PID controller, and perform parameter optimization on the type-1 fuzzy PID controller; specifically, optimize the five coefficients K e 、 K up 、K ui 、K ud 、K e of the type-1 fuzzy PID controller simultaneously, where K is the error input coefficient, up is the error change rate input coefficient, K ui is the proportional coefficient output scale factor, K ud is the integral coefficient output scale factor, and K

[0043] S3: Perform uncertainty optimization on the membership function of the type-1 fuzzy PID controller with optimized parameters. The uncertainty optimization method of the membership function is the empirical method or an intelligent optimization algorithm including the particle swarm algorithm, ant colony algorithm, or genetic algorithm. Those skilled in the art can also select other intelligent optimization algorithms according to actual needs, and obtain a parallel type-2 fuzzy PID controller with optimal parameters.

[0044] In addition, since the optimal PID controller parameters have been determined, the type-1 fuzzy controller in step S2 only adjusts △k p 、△k i 、△k d , and the type-2 fuzzy controller in step S3 only adjusts △k p 、△k i 、△k d , which greatly reduces the parameter optimization range, can save a large amount of optimization time, and provides support for the PID controller to achieve online real-time parameter tuning and control time-varying nonlinear complex systems.

[0045] Although the embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those of ordinary skill in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present invention.

[0046] The above specific embodiments of the present invention do not constitute a limitation on the protection scope of the present invention. Any other corresponding changes and deformations made according to the technical concept of the present invention should be included within the protection scope of the claims of the present invention.

Claims

1. A parallel interval type-2 fuzzy PID controller based on the step-by-step optimization method, characterized in that It includes the following optimization steps: S1: Optimize the parameters of the PID controller separately; S2: Combine a type-1 fuzzy controller with the PID controller after parameter optimization to construct a type-1 fuzzy PID controller, and optimize the parameters on the type-1 fuzzy PID controller; S3: Perform uncertainty optimization on the membership function of the type-1 fuzzy PID controller after parameter optimization, and obtain a parallel-connected interval type-2 fuzzy PID controller with optimal parameters.

2. The parallel type interval type-2 fuzzy PID controller based on the step-by-step optimization method according to claim 1, characterized in that, In step S1, the three parameters k p , k i , k d of the PID controller are optimized simultaneously, where k p is the proportionality coefficient, k i is the integral coefficient, and k d is the derivative coefficient; during the optimization process, only the PID controller participates in the optimization.

3. The parallel interval type-2 fuzzy PID controller based on the step-by-step optimization method according to claim 2, wherein, The optimization formula of the PID controller in step S1 is: where u(k) is the output of the PID controller, and e(k) is the error value.

4. The parallel interval type-2 fuzzy PID controller based on the step-by-step optimization method according to claim 3, wherein The method for uncertainty optimization of the membership function of the type-1 fuzzy PID controller in step S3 is the empirical method or the intelligent optimization algorithm.

5. The parallel type interval type-2 fuzzy PID controller based on the step-by-step optimization method according to claim 4, wherein The optimization steps of the PID controller in step S1 are: S11: Set the expected value as Firef, the initial e(k) as Firef, and the intelligent optimization algorithm randomly assigns three parameter values k p , k i , k d , and obtain the initial u(k) value; S12: Substitute the value of u(k) into the controlled system and perform feedback; S13: Compare the feedback value output by the controlled system with the expected value Firef; When the feedback value of the controlled system output is consistent and stable with Firef, the parameters of the PID controller do not need to be changed; when the feedback value of the controlled system output is stable but inconsistent with Firef, the intelligent optimization algorithm selects a set of better k p , k i , k d values and substitutes them into the PID controller until the feedback value of the controlled system output is stable and consistent with Firef.

6. The parallel type interval type-2 fuzzy PID controller based on the step-by-step optimization method according to any one of claims 1-5, characterized in that, In step S2, five coefficients of the type-1 fuzzy PID controller, namely K e , K up , K ui , K ud , are optimized. Among them, K e is the error input coefficient, is the error change rate input coefficient, K up is the proportional coefficient output scale factor, K ui is the integral coefficient output scale factor, K ud is the differential coefficient output scale factor.

7. The parallel type interval type-2 fuzzy PID controller based on the step-by-step optimization method according to claim 6, characterized in that, During the optimization process, the type-1 fuzzy controller in step S2 adjusts △k p , △k i , △k d , and the type-2 fuzzy controller in step S3 adjusts △k p , △k i , △k d to adjust the parameters of the PID controller online in real time.

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