Control system based on compound controller and optimization control method

Abstract

The application relates to a control system and an optimization control method based on a composite controller and relates to the field of advanced control technology. The existing nonlinear time-delay system is generally present in complex industrial control and automation systems, and traditional control strategies are difficult to effectively cope with the problems caused by time delay and nonlinearity. The application eliminates the influence of time delay in the system by designing a Smith predictor, and introduces a fractional order controller to enhance the adaptability of the system to nonlinear behavior. The composite controller formed by combining the Smith predictor and the fractional order controller can significantly improve the dynamic response performance and control accuracy of the system. In order to further optimize the controller parameters, an improved artificial rabbit optimization algorithm is adopted. The algorithm improves the global search ability and convergence speed by introducing a dynamic adjustment factor, a Levy flight strategy and a boundary control strategy.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of advanced control technology, in particular to a control system based on a composite controller and an optimization control method. BACKGROUND

[0002] Nonlinear time-delay systems are widely present in modern control engineering, especially in complex industrial process control, communication systems, and automation control fields. For example, time delay can cause system response lag, increase overshoot, and may even lead to oscillation or instability. Nonlinear characteristics make the dynamic behavior of the system more complex, making it difficult to control effectively by traditional linear control methods. To address the time delay problem, O.J.M. Smith proposed the Smith predictor in 1957. This technology predicts the system output and compensates for the time delay in advance, significantly improving the response speed and stability of the time-delay system. Smith predictor has a significant advantage in dealing with time delay problems and has been widely used in various control systems. However, Smith predictor is mainly designed for linear systems, and its application effect is limited for systems with significant nonlinearities. On the other hand, fractional-order controllers provide more flexible adjustment means than traditional integer-order controllers, especially for handling the complex dynamic behavior of nonlinear systems. Fractional-order controllers can more accurately adapt to the nonlinear characteristics of the system and optimize control performance. However, the use of fractional-order controllers alone cannot solve the problems caused by time delay, which limits their application in some complex systems.

[0003] Therefore, the present application innovatively combines Smith predictor and fractional-order PID controller to propose a new control system design method to better address the nonlinear time delay problem in complex dynamic systems and provide a more effective solution for high-precision industrial control.

[0004] In recent years, the global search ability and efficiency of swarm intelligence algorithms have shown great potential in solving complex engineering problems. As a new type of swarm intelligence algorithm, the artificial rabbit optimization algorithm (ARO) provides a low-parameter, low-complexity optimization method by simulating the survival strategy of rabbits. However, ARO also has problems such as being prone to local optimum, slow convergence speed, and ineffective boundary processing. Therefore, the present application improves the traditional artificial rabbit algorithm to eliminate the defects and shortcomings of the traditional artificial rabbit algorithm.

[0005] In summary, these two improvements not only have important research significance but also have broad application prospects. SUMMARY

[0006] The application provides a control system based on a composite controller and an optimization control method, so as to overcome the adverse effects of nonlinearity and time delay, and significantly improve the performance and stability of a complex control system.

[0007] The control system based on the composite controller comprises a Smith predictor and a fractional order PI λ D μ controller, and forms a closed-loop control system.

[0008] The closed-loop transfer function of the closed-loop control system of the composite controller is: λ D μ

[0009]

[0010] G0(s)e -τs is a mathematical model of a controlled object, G0(s) is a non-delay term of a transfer function, e -τs is a delay term, τ is a delay time of the system, K p is a proportional gain of the fractional order PI λ D μ controller, K i is an integral gain of the fractional order PI λ D μ controller, K d is a differential gain of the fractional order PI λ D μ controller, λ is an integral order, and μ is a differential order.

[0011] The application further provides an optimization control method of the control system based on the composite controller, which optimizes parameters of the controller by using an improved artificial rabbit algorithm, and finally obtains desired controller parameters; the method is realized by the following steps.

[0012] Step one, initializing a population and parameters of the improved artificial rabbit algorithm, and calculating the fitness of initial population;

[0013] Step two, setting a loop iteration number, and requiring that the iteration number is less than a maximum iteration number;

[0014] Step three, detour foraging stage: introducing a dynamic adjustment factor, applying the dynamic adjustment factor to a mathematical model of rabbit exploration in a search space, and realizing position updating;

[0015] Step four, random hiding stage: introducing a Levy flight strategy, and performing hiding position updating;

[0016] Step five, energy contraction stage: according to a set energy factor, performing the detour foraging stage or the random hiding stage; ​

[0017] Step six, introduce boundary control strategy to ensure the position within the boundary; expressed as:

[0018]

[0019] In the formula, z i (t+1) is the position of the ith individual updated at t+1 iteration, z min is the minimum boundary value of the search space, z max is the maximum boundary value of the search space;

[0020] Step seven, judge whether the iteration number reaches the upper limit, if yes, stop iteration, obtain the optimal position and new population fitness value; otherwise, return to step two until the termination iteration condition is met; realize the optimization of the control system parameters.

[0021] The beneficial effects of the application are:

[0022] 1. The application designs a controller combining Smith predictor and fractional order PI λ D μ , which has simple structure, clear meaning at each step and is easy to apply in engineering. The application makes the system have the performance of fast response speed, high tracking accuracy and strong dynamic response, and can be effectively applied in nonlinear time delay systems.

[0023] 2. The application provides Levy flight strategy on the basis of the traditional artificial rabbit algorithm, increases the exploration depth and breadth of the search space, enhances the global search ability and avoids early local optimum.

[0024] 3. The application provides a dynamic adjustment factor on the basis of the traditional artificial rabbit algorithm, which has a larger step size in the initial stage and is beneficial to global search, and has a smaller step size in the later stage and is beneficial to local search and fine adjustment.

[0025] 4. The application provides a boundary control strategy on the basis of the traditional artificial rabbit algorithm, which controls the new position after each position update to ensure that the position is within the preset upper and lower boundaries, thereby ensuring the effectiveness of the search space and avoiding generating invalid solutions.

[0026] 5. The control system has wide application range and can be applied to complex engineering optimization, power system optimization, control system optimization, signal processing and many other control fields. BRIEF DESCRIPTION OF DRAWINGS

[0027] Figure 1 It is a flow chart of the optimization control method of the control system based on the composite controller;

[0028] Figure 2The principle block diagram of designing Smith predictor in the control system based on the composite controller described in the present application;

[0029] Figure 3 The principle block diagram of designing fractional order PI λ D μ controller in the control system based on the composite controller described in the present application;

[0030] Figure 4 The structure diagram of fusing Smith predictor and fractional order PI λ D μ controller described in the present application;

[0031] Figure 5 The flow chart of optimizing artificial rabbit algorithm. DETAILED DESCRIPTION

[0032] DETAILED DESCRIPTION Figures 1 to 4 The present embodiment is based on the control system of the composite controller, which is realized by designing Smith predictor and designing fractional order PI λ D μ controller and combining them to obtain the composite controller;

[0033] In the present embodiment, the Smith predictor is designed to eliminate the time delay problem existing in the control system. The Smith predictor is added in the liquid crystal spatial light modulator optical beam deflection control system (LCOPA) to compensate and eliminate the time delay link in the system model, so that the controlled quantity delayed by τ time is fed back to the controller in advance, the controller is actuated in advance, the control channel and the denominator of the system transfer function of the changed system do not contain pure lag link, and the delayed information can be sent to the system execution part in time, thereby reducing the system overshoot and response time, eliminating the adverse effects of time delay. The specific design process is as follows:

[0034] First, the mathematical model of the controlled object LCOPA, i.e. the transfer function G0(s)e -τs Then, the Smith predictor is designed, as shown in Figure 2 The function of the Smith predictor is to generate a delay compensation signal by introducing the non-delay term G0(s) and the delay term e -τs of the system transfer function, so as to reduce the negative effects of delay on system performance. The Smith predictor inputs the control signal U(s) to the non-delay term G0(s) of the transfer function to generate a predicted output, and then passes through the delay term e -τsThe complete predicted output is formed. The actual output Y(s) of the system and the predicted value are then compared to generate a compensation signal, so that the system behaves more like a system without delay. In this way, the system can remain stable and achieve a better dynamic response in the presence of the disturbance signal D(s).

[0035] The transfer function of the Smith predictor can be expressed as:

[0036] G m (s)=G0(s)(1-e -τs ) (1)

[0037] According to the Smith predictor control strategy, the transfer function of the equivalent controlled object LCOPA is:

[0038] G0(s)=G0(s)e -τs +G m (s)

[0039] That is, G0(s)=G0(s)e -τs +G0(s)(1-e -τs )(2)

[0040] Where G0(s) is the non-delay term of the transfer function, e -τs is the delay term, and τ represents the delay time of the system.

[0041] In the Smith predictor in Figure 2 , a fractional order PI λ D μ controller is added to control the error between the reference input signal R(s) and the actual output Y(s) of the system, so as to ensure that the system has good dynamic and steady-state performance in the absence of delay. D(s) is a disturbance signal that will affect the output of the system.

[0042] As shown in Figure 3 , the fractional order PI λ D μ controller is designed to make the liquid crystal spatial light modulator have better control performance. The entire control process starts from the reference input signal R(s), and an error signal is generated by comparing the actual output Y(s) of the system. The error signal is input into the fractional order PI λ D μ controller. The fractional order PI λ D μ controller contains proportional, integral and derivative parts, which correspond to proportional gain K p , integral gain K i and derivative gain K d , respectively. Unlike the traditional integer order PID controller, the fractional order PI λ Dμ The controller adds two adjustable parameters on the basis of integer order: integral order λ and differential order μ. When λ and μ are 1, the fractional order PI λ D μ The controller is equivalent to an integer order PID controller. However, in actual design, by selecting different values of λ and μ, the response characteristics of integral and differential operations can be adjusted, so that the system performs better in dynamic performance and steady-state accuracy. In this way, the fractional order controller can more flexibly cope with the complex requirements of the LCOPA system and provide more precise control.

[0043] The fractional order PI λ D μ The mathematical model of the controller is:

[0044]

[0045] Combining the Smith predictor and the fractional order controller, a composite controller, i.e., the control system, is obtained. It can simultaneously have the characteristics of fast response and high-precision control, significantly improving the dynamic performance and beam control accuracy of the liquid crystal spatial light modulator system.

[0046] In this embodiment, in the control system composed of the Smith predictor, the system lag part can be compensated according to the degree of deviation of the output quantity from the control quantity, overcoming the adverse effects of the pure lag link, thereby improving the control effect of the system. The fractional order PI λ D μ The controller adds two adjustable parameters, making the LCOPA have better control performance, improving the flexibility of the system, and enhancing the robustness of the system.

[0047] The LCOPA fractional order model is:

[0048]

[0049] In the formula, λ0=1064 nm represents the wavelength of the laser, d=9.8 μm is the size of a single element, q=1.6×10 -19 C unit charge, C represents the unit of charge, x=9.8 μm is the thickness of the liquid crystal layer, θ p is the deflection angle of the outgoing light, k1=1.11×10 -12 N is the curvature elastic coefficient of the liquid crystal molecule, N represents the unit of Newton, k2=1.71×10 -12 N is the curvature elastic coefficient of the liquid crystal molecule, is the phase change of liquid crystal molecules after applying electric field, h1 is the splay viscosity coefficient, h2 is the bend viscosity coefficient, a1, a2 are the order, j is the fractional charge coefficient, tau is the time delay coefficient, the fractional charge coefficient j and the time delay coefficient tau are unknown parameters, and D represents the fractional calculus operation.

[0050] By using the Legendre wavelet integral operation expansion and integral operation, the fractional derivative in the model can be converted into a conventional linear system expression, so that the transfer function form of the liquid crystal spatial light modulator beam deflection control system is obtained.

[0051] The fractional order model of LCOPA is changed into the transfer function form as follows:

[0052]

[0053] As shown in Figure 4 , Figure 4 is the fractional order PI λ D μ controller, according to Mason gain formula, the Smith predictor and fractional order PI λ D μ controller are fused, and the closed-loop transfer function of the closed-loop control system of the controller is:

[0054]

[0055] wherein, represents the fractional order integral term, and lambda is the integral order; K d s μ represents the fractional order differential term, and mu is the differential order. From the design process of the fractional order PI λ D μ controller, it can be seen that the Smith predictor is designed based on the system model, and it does not contain adjustable parameters. On the contrary, the fractional order PI λ D μ controller parameters K p , K i , K d , lambda, mu are unknown. Therefore, the improved artificial rabbit algorithm is used to optimize the parameters of the control system, and the expected controller parameters are obtained.

[0056] Specific embodiment two, in combination Figure 5 with the specific embodiment one, the optimization control method of the control system based on the composite controller is described, the improved artificial rabbit algorithm is used to optimize the parameters of the control system, and the final expected controller parameters are obtained. The following steps are realized:

[0057] Step 1, initialize the population and parameters of the improved artificial rabbit algorithm, and calculate the initial group fitness;

[0058] Step 2, set the number of loop iterations, and require the number of iterations < maximum number of iterations;

[0059] Step 3, detour foraging stage: introduce dynamic adjustment factor, position update;

[0060] The detour foraging simulates the exploration behavior of rabbits when they are looking for food. In this stage, the rabbit finds the possible food source by extensive exploration in the search space, and the mathematical model is:

[0061]

[0062] R = L-c(k) (5)

[0063]

[0064] g = randperm(d) (8)

[0065] wherein, is the new position calculated according to the positions of other individuals (such as reference position and optimal position) and dynamic adjustment factor, is the reference position of the i-th rabbit at the t-th iteration, is the reference position of the j-th rabbit at the t-th iteration, g is a random permutation from 1 to d generated by the function, used to randomly select the updated dimension in the artificial rabbit detour foraging stage, r1, r2 and r3 are random numbers between 0 and 1; n is the population size; d is the problem dimension; T is the maximum number of iterations; R is the running operator; L is the running length; c is 0 or 1, used to randomly select individuals for mutation; n1 is a random number following the standard normal distribution. In this stage, the dynamic adjustment factor is introduced, which gradually changes the step size in the iteration process to control the search range, so that the algorithm has a larger search step in the early stage to enhance the global search ability, and gradually reduces the step size in the later stage to enhance the local search precision. The mathematical model is as follows:

[0066]

[0067] wherein, α(t) is the t-th dynamic adjustment factor; α min is the minimum adjustment factor; α max is the maximum adjustment factor; t is the current iteration number; T is the maximum iteration number;

[0068] Apply the formula to equation (4):

[0069]

[0070] where R is a running operator; Z i (t) is the current position of the ith individual, Z best (t) is the best position found so far.

[0071] Step 4, random hiding phase: Levy flight strategy is introduced to update the hiding position;

[0072] The random hiding simulates the random hiding behavior of rabbits in the natural environment to avoid predators. In each iteration, the rabbit will generate m holes around itself along the dimension of the search space to reduce the probability of being preyed upon. The position of the bth hiding hole of the ith rabbit is:

[0073]

[0074] where b = 1, ···, m

[0075]

[0076] where, represents the hiding hole position randomly selected from the m holes; g(k') represents the selection of a specific hole for the rabbit's hiding position update operation; r4 is a random number 0 or 1, and H is a hidden parameter.

[0077] When the rabbits are chased, they will randomly hide in a hole. The position update formula for random hiding is:

[0078]

[0079]

[0080] where, is a hole randomly selected from the m holes, f r is a step scaling factor, r4 and r5 are random numbers from 0 to 1. After completing the detour foraging and random hiding, the rabbit position update is:

[0081]

[0082] where, represents the fitness value at time t+1 (current solution); represents the fitness value at time t (previous solution).

[0083] In this phase, Levy flight strategy is introduced. Levy flight strategy is a random walk strategy based on Levy distribution.

[0084] The step formula of Levy flight strategy is as follows:

[0085]

[0086] wherein: the scale factor of step size σ u and σ v The calculation formula is:

[0087]

[0088] σ v = 1 (20)

[0089] In the formula, λ is 1.5; Γ is used to calculate the fractional calculus item in the fractional order controller.

[0090] The Levy flight strategy is introduced into the optimal position of the artificial rabbit in formula (14), and the improved ARO greatly reduces the risk of the artificial rabbit falling into local optimum and can fully perform local search. The improved formula is as follows:

[0091]

[0092] Where s' is the step size generated by Levy distribution, and α is the step size scaling factor used to control the scale of the step size. By introducing the Levy flight strategy, local search and global search can be balanced, and falling into local optimum can be avoided.

[0093] Step 5, energy contraction phase: update based on energy factor;

[0094] The energy contraction simulates the behavior of the rabbit concentrating on detailed foraging after finding the food source, that is, this search mechanism is determined by the energy of the rabbit, and the energy of the rabbit gradually decreases over time. The energy factor in ARO is defined as follows:

[0095]

[0096] Wherein, r is a random number between 0 and 1, when A(t) > 1, the population individual executes the detour foraging strategy; otherwise, the population individual executes the random hiding strategy.

[0097] Step 6, introduce boundary control strategy to ensure the position within the boundary;

[0098] The boundary control strategy adjusts the position of the individual to ensure that it moves within the effective search range, thereby improving the stability and effectiveness of the algorithm. In the existing artificial rabbit optimization algorithm, the boundary control strategy needs to be added to the position update formula, that is, formula (17). The improved formula is as follows:

[0099]

[0100] Wherein, z i(t+1) represents the updated position of the i-th individual, t represents the iteration number, z min is the minimum boundary value of the search space, z max is the maximum boundary value of the search space.

[0101] Step 7, judge whether the iteration number reaches the upper limit, if yes, stop iteration, and get the optimal position Z best (t) and the new population fitness value Otherwise, the iteration number is increased by 1, and steps 2-6 are repeated until the iteration termination condition is met.

[0102] In this embodiment, the improved artificial rabbit algorithm is used to optimize the parameters of the control system, and the iteration number is set to 20. The optimized artificial rabbit algorithm is used to set the parameters of the LCOPA, and the controller parameters after setting are K p = 40.7324, K i = 42.5622, K d = 79.5144, λ = 0.98, μ = 0.2653. The controller parameters after setting are applied to the LCOPA system, which significantly improves the dynamic response performance of the system, reduces the overshoot and response time, enhances the tracking accuracy of beam deflection, ensures the stable operation of the system in complex environment, and optimizes the robustness of the system, so that it can still maintain high precision and reliability under external disturbance and uncertainty. In addition, the optimized parameters effectively deal with the nonlinear time delay problem in LCOPA, and provide precise and stable beam control capability for high requirement industrial applications such as optical regulation, laser processing and optical communication.

[0103] The technical features of the above-described embodiments can be combined in any manner. To make the description concise, all possible combinations of the technical features in the above-described embodiments are not described, but as long as the combinations of the technical features do not exist contradictory, they should be considered as the scope of the present disclosure.

[0104] The above-described embodiments only express several embodiments of the present application, and the description is more specific and detailed, but it should not be understood as limiting the scope of the patent. It should be noted that for ordinary skilled in the art, without departing from the concept of the present application, a number of modifications and improvements can be made, which are within the scope of the present application. Therefore, the scope of protection of the present application should be subject to the appended claims.

Claims

1. A method for optimal control of a control system based on a composite controller, characterized by: The control method is used for optimizing control of a control system based on a composite controller, which is composed of a Smith predictor and a fractional order PI λ D μ controller to form a closed-loop control system; Fusion Smith predictor and fractional order PI λ D μ The closed-loop transfer function of the closed-loop control system of the controller is: In the formula, G0(s)e -τs is a mathematical model of the controlled object, G0(s) is a non-delay term of a transfer function, e -τs is a delay term, τ is a delay time of the system, K p is a fractional order PI λ D μ is a proportional gain of the controller, K i is a fractional order PI λ D μ is an integral gain of the controller, K d is a fractional order PI λ D μ is a differential gain of the controller, λ is an integral order, and μ is a differential order. The transfer function of the Smith predictor is expressed as: G m (s) = G0(s)(1 - e -τs ) According to the Smith prediction control strategy, the transfer function of the equivalent controlled object is: G0(s) = G0(s) e -τs +G m (s) The control method adopts an improved artificial rabbit algorithm to optimize the parameters of the controller, and finally obtains the desired controller parameters; the method is realized by the following steps: Step one, initialize the population and parameters of the improved artificial rabbit algorithm, and calculate the initial group fitness; Step two, set the number of iterations, and require the number of iterations < maximum number of iterations; Step three, detour foraging stage: introduce a dynamic adjustment factor, apply the dynamic adjustment factor to the mathematical model of the rabbit exploring the search space, and realize position updating; Step four, random hiding stage: introduce Levy flight strategy, and perform hiding position updating; Step five, energy contraction stage: according to the set energy factor, execute the detour foraging stage or the random hiding stage; Step six, introduce a boundary control strategy to ensure that the position is within the boundary; expressed as: wherein z i (t+1) is the updated position of the ith individual at the t+1 iteration, z min is the minimum boundary value of the search space, z max is the maximum boundary value of the search space; Step seven, judge whether the number of iterations reaches the upper limit, if yes, stop iteration, obtain the optimal position and new population fitness value; otherwise, return to step two until the termination iteration condition is met; realize the optimization of the control system parameters.

2. The optimization control method of a composite controller-based control system according to claim 1, characterized by: The specific process of step three is: Set the rabbit to explore the search space, and the mathematical model is: where i, j = 1, ···, n, j≠i, is a new position calculated from the positions of other individuals and a dynamic adjustment factor, is the reference position of the ith rabbit at the tth iteration, is the reference position of the jth rabbit at the tth iteration, t is the current iteration number, R is the running operator, r1 is a random number between [0, 1], round() is a function of rounding to the specified number of digits, and n1 is a random number following a standard normal distribution; Introduce a dynamic adjustment factor, expressed as: In the formula, a(t) is a dynamic adjustment factor of tth iteration; a min is a minimum adjustment factor; T is a maximum iteration number; a max is a maximum adjustment factor; Apply the dynamic adjustment factor to the mathematical model, expressed as: wherein Z i (t) and Z best (t) are the current position of the i-th individual and the best position found so far at the t-th iteration, respectively.

3. The optimization control method of a composite controller-based control system according to claim 1, characterized by: The specific process of step four is: When the rabbit is chased, it will randomly hide in a cave, and the random hiding position formula is as follows: wherein, is a new position calculated from the positions of other individuals and a dynamic adjustment factor, is the reference position of the ith rabbit at the tth iteration, is the reference position of the jth rabbit at the tth iteration, t is the current iteration number, R is the running operator, and r4 is a random number between [0, 1]; is a randomly selected cave from m caves; After random hiding, the rabbit position updating formula is as follows: wherein is the fitness value at iteration t+1; is the fitness value at iteration t; Apply Levy flight strategy to the random hiding position updating formula, and the position updating formula is as follows: Where s' is the step length generated by Levy distribution, and alpha is the step length scaling factor, used to control the scale of the step length.

4. The optimization control method of the composite controller-based control system according to claim 3, characterized in that: Set the step length formula of Levy flight strategy as follows: wherein: Step size scale factor σ u and σ v The formula for calculating σ is: σ v = 1 Where λ is 1.5, and Γ is used to calculate the fractional order differential term and integral term in the fractional order controller.

5. The optimization control method of a composite controller-based control system according to claim 1, characterized by: In step five, set the formula of energy factor A(t) as follows: Where r is a random number between 0 and 1, and T is the maximum number of iterations; when A(t)>1, the population individual executes the detour foraging stage; otherwise, the population individual executes the random hiding stage.

Images