Control system based on composite controller and optimization control method

Abstract

The invention discloses a control system based on a composite controller and an optimization control method, and relates to the technical field of advanced control. The problems that an existing nonlinear time delay system generally exists in a complex industrial control and automation system, and a traditional control strategy is difficult to effectively deal with time delay and nonlinearity are solved. According to the method, the Smith predictor is designed to eliminate the time lag influence in the system, and meanwhile, the fractional order controller is introduced to enhance the adaptive capacity of the system to nonlinear behaviors. The Smith predictor and the fractional order controller are combined to form a composite controller, and the dynamic response performance and the control precision of the system can be remarkably improved. In order to further optimize controller parameters, an improved artificial rabbit optimization algorithm is adopted, and the algorithm improves the global search capability and convergence speed by introducing a dynamic adjustment factor, a Levy flight strategy and a boundary control strategy.

Description

Technical Field

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

[0002] Nonlinear time-delay systems are widely present in modern control engineering, especially in the fields of complex industrial process control, communication systems and automation control. For example, time delay can cause system response lag, increase overshoot, and may cause oscillation or instability; while nonlinear characteristics make the dynamic behavior of the system more complex and difficult to effectively control through traditional linear control methods. In order to deal with the time-delay problem, OJM Smith proposed the Smith predictor in 1957. This technology greatly improves the response speed and stability of the time-delay system by predicting the system output and compensating for the time-delay effect in advance. The Smith predictor has significant advantages in dealing with time-delay problems and has been widely used in various control systems. However, the Smith predictor is mainly designed for linear systems, and its application effect is limited for systems with significant nonlinearity. On the other hand, the fractional-order controller introduces fractional-order calculus operators, providing a more flexible adjustment method than the traditional integer-order controller, which is particularly suitable for dealing with the complex dynamic behavior of nonlinear systems. The fractional-order controller can adapt to the nonlinear characteristics of the system more accurately and optimize the control performance. However, it is difficult to solve the problems caused by time delay using the fractional-order controller alone, which limits its application in some complex systems.

[0003] Therefore, the present invention proposes a new control system design method by innovatively integrating the Smith predictor and the fractional-order PID controller to better deal with the nonlinear time-lag problem in complex dynamic systems and provide a more effective solution for high-precision industrial control.

[0004] In recent years, the global search capability and high 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 (ARO) algorithm simulates the survival strategy of rabbits for mathematical modeling, providing a low-parameter, low-complexity optimization method. However, ARO also has problems such as easy to fall into local optimality, slow convergence speed, and ineffective boundary processing. Therefore, the present invention 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 of the invention

[0006] The present invention provides a control system based on a composite controller and an optimization control method to overcome the adverse effects brought by nonlinearity and time lag and significantly improve the performance and stability of the complex control system.

[0007] A control system based on a composite controller, which consists of a Smith predictor and a fractional-order PI λ D μ The controller forms a closed-loop control system;

[0008] Combining Smith Predictor and Fractional-Order PI λ D μ The closed-loop transfer function of the closed-loop control system of the controller is:

[0009]

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

[0011] The present invention also provides an optimization control method for a control system based on a composite controller, wherein the control method uses an improved artificial rabbit algorithm to optimize the controller parameters and finally obtains the desired controller parameters; the method is implemented by the following steps:

[0012] Step 1: Initialize the population and parameters of the improved artificial rabbit algorithm and calculate the fitness of the initial population;

[0013] Step 2: Set the number of loop iterations, requiring the number of iterations to be less than the maximum number of iterations;

[0014] Step 3, detour foraging stage: introduce a dynamic adjustment factor, apply the dynamic adjustment factor to the mathematical model of the rabbit exploring in the search space, and realize position update;

[0015] Step 4: Random hiding phase: Introduce the Levy flight strategy to update the hiding position;

[0016] Step 5, energy contraction phase: execute the detour foraging phase or random hiding phase according to the set energy factor;

[0017] Step 6: Introduce boundary control strategy to ensure the position is within the boundary; it can be expressed as follows:

[0018]

[0019] In the formula, z i (t+1) is the updated position of the i-th individual at the t+1th 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 7: Determine whether the number of iterations has reached the upper limit. If so, stop the iteration to obtain the optimal position and the fitness value of the new population; otherwise, return to step 2 until the termination condition is met to achieve the optimization of the control system parameters.

[0021] Beneficial effects of the present invention:

[0022] 1. The present invention designs a fusion Smith predictor and fractional-order PI λ D μ The controller has a simple structure, each step has a clear meaning, and is easy to apply in engineering. The invention enables the system to 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 present invention provides a Levy flight strategy based on the traditional artificial rabbit algorithm, which increases the exploration depth and breadth of the search space, enhances the global search capability, and avoids falling into the local optimum at an early stage.

[0024] 3. The present invention provides a dynamic adjustment factor on the traditional artificial rabbit algorithm. In the initial stage, the step size is large, which is conducive to global search; in the later stage, the step size is reduced, which is conducive to local search and fine adjustment.

[0025] 4. The present invention provides a boundary control strategy based on the traditional artificial rabbit algorithm. After each position update, the new position is boundary controlled to ensure that the position is within the preset upper and lower boundaries, thereby ensuring the validity of the search space and avoiding the generation of invalid solutions.

[0026] 5. The control system described in the present invention has a wide range of applications and can be applied to many control fields such as complex engineering optimization, power system optimization, control system optimization, signal processing, etc. BRIEF DESCRIPTION OF THE DRAWINGS

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

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

[0029] Figure 3 Design of fractional-order PI in the control system based on composite controller of the present invention λ D μ Controller block diagram;

[0030] Figure 4 To fuse the Smith predictor with the fractional-order PI λ D μ Controller structure diagram;

[0031] Figure 5 Flowchart for optimizing the Artificial Rabbit algorithm. DETAILED DESCRIPTION

[0032] Specific implementation method 1. Combination Figures 1 to 4 The control system based on the composite controller is described in this embodiment. The system is implemented by designing a Smith predictor and a fractional-order PI λ D μ controllers and combine them to obtain a composite controller composition;

[0033] In this embodiment, a Smith predictor is designed to eliminate the time delay problem in the control system. A Smith predictor is added to the liquid crystal spatial light modulator beam deflection control system (LCOPA), and the predictor is used to compensate and eliminate the delay link in the system model, so that the controlled quantity delayed by τ time is fed back to the controller in advance, so that the controller acts in advance, so that the control channel of the changed system and the denominator of the system transfer function do not contain a 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, and eliminating the adverse effects of time lag. The specific design process is:

[0034] First, the mathematical model of the controlled object LCOPA is established, that is, the transfer function G0(s)e -τs , and then design the Smith estimator, such as Figure 2 As shown in the figure, the Smith predictor works by introducing the delay-free term G0(s) and the delay term e in the system transfer function. -τs , to generate a delay compensation signal to reduce the negative impact of delay on system performance. The Smith predictor inputs the control signal U(s) into the delay-free term G0(s) of the transfer function, generates a predicted output, and then passes through the delay term e -τsThe system then compares the actual output Y(s) of the system with the predicted value to generate a compensation signal, making the system behave closer to a situation without delay. In this way, the system can maintain stability and obtain better dynamic response in the presence of a 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 predictive 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 delay-free term of the transfer function, e -τs is the delay term, and τ represents the delay time of the system.

[0041] exist Figure 2 The Smith predictor in the λ D μ The controller controls the error between the reference input signal R(s) and the actual output Y(s) of the system to ensure that the system obtains better dynamic and steady-state performance without delay. D(s) is the disturbance signal, which will affect the output of the system.

[0042] like Figure 3 As shown, the fractional-order PI λ D μ The controller makes the liquid crystal spatial light modulator have better control performance. The entire control process starts with the reference input signal R(s), and generates an error signal after comparing it with the actual output Y(s) of the system. The error signal is connected to the fractional order PI λ D μ Controller, Fractional Order PI λ D μ The controller consists of three parts: proportional, integral and differential, corresponding to the proportional gain K p , integral gain K i and differential gain K d Unlike traditional integer-order PID controllers, 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 the values ​​of 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 λ and μ values, the response characteristics of the 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 respond to the complex requirements of the LCOPA system and provide more sophisticated control.

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

[0044]

[0045] Combining the Smith predictor with the fractional-order controller, a composite controller, i.e., a 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 composed control system, the Smith predictor can compensate for the lag part of the system according to the degree to which the output quantity deviates from the control quantity, overcome the adverse effects of the pure lag link, and thus improve the control effect of the system. λ D μ The controller adds two adjustable parameters, which makes LCOPA have better control performance, improves the flexibility of the system and enhances the robustness of the system.

[0047] Among them, the LCOPA fractional-order model is:

[0048]

[0049] Where λ0 = 1064 nm represents the laser wavelength, d = 9.8 μm single element size, q = 1.6 × 10 -19 C is the unit charge, C represents coulomb, which is the unit of charge, x = 9.8 μm is the thickness of the liquid crystal layer, θ p is the deflection angle of the emitted light, k1=1.11×10 -12 N is the elastic coefficient of liquid crystal molecules. N represents the unit of force, Newton, k2 = 1.71 × 10 -12 N is the bending elastic coefficient of the liquid crystal molecules, is the phase change of the liquid crystal molecules after the electric field is applied, η1 is the flexural viscosity coefficient, η2 is the bending viscosity coefficient, α1 and α2 are the orders, j is the volume charge fraction coefficient, τ is the hysteresis coefficient, the volume charge fraction coefficient j and the hysteresis coefficient τ are both unknown parameters, and D represents the fractional calculus operation.

[0050] By using Legendre wavelet integral operation expansion and integral operation, the fractional-order derivatives in the model can be converted into conventional linear system expressions, thereby obtaining the transfer function form of the liquid crystal spatial light modulator beam deflection control system.

[0051] The LCOPA fractional-order model is changed into a transfer function form:

[0052]

[0053] like Figure 4 As shown, Figure 4 To fuse the Smith predictor and fractional-order PI λ D μ The control system structure of the controller is obtained by combining the Smith predictor and fractional-order PI according to the Mason gain formula. λ D μ The closed-loop transfer function of the closed-loop control system of the controller is:

[0054]

[0055] in, represents the fractional integral term, λ is the integral order; K d s μ represents the fractional-order differential term, μ is the differential order. λ D μ The controller design process shows that the Smith predictor is designed based on the system model and does not contain adjustable parameters. λ D μ Controller parameter K p , K i , K d , λ, and μ are all unknown. Therefore, the improved artificial rabbit algorithm is used to tune the control system parameters and obtain the desired controller parameters.

[0056] Specific implementation method 2: Combination Figure 5 This embodiment is an optimization control method for the control system based on the composite controller described in the first embodiment. The method uses an improved artificial rabbit algorithm to optimize the control system parameters to obtain the final desired controller parameters. This is achieved by the following steps:

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

[0058] Step 2: Set the number of loop iterations, requiring the number of iterations to be less than the maximum number of iterations;

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

[0060] Detour foraging simulates the exploratory behavior of rabbits when looking for food. In this stage, the rabbit searches for possible food sources by conducting extensive exploration in the search space. The mathematical model is:

[0061]

[0062] R=L·c(k) (5)

[0063]

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

[0065] in, It is a new position calculated based on the positions of other individuals (such as reference position and optimal position) and dynamic adjustment factors. is the reference position of the i-th rabbit at the t-th iteration, is the reference position of the jth rabbit at the tth iteration, g is a random arrangement from 1 to d generated by a function, which is used to randomly select the updated dimension during the artificial rabbit detour foraging stage, r1, r2 and r3 are random numbers between [0,1]; n is the population size; d is the problem latitude; 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 that obeys the standard normal distribution. In this stage, a dynamic adjustment factor is introduced to control the search range by gradually changing the step size during the iteration process, so that the algorithm has a larger search step size 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 accuracy. Its mathematical model is as follows:

[0066]

[0067] Among them, α(t) is the dynamic adjustment factor of generation t; α min is the minimum adjustment factor; α max is the maximum adjustment factor; t is the current number of iterations; T is the maximum number of iterations;

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

[0069]

[0070] Where R is the running operator; Z i (t) is the current position of the i-th individual, Z best (t) is the best position currently found.

[0071] Step 4, random hiding phase: introduce Levy flight strategy and update hiding position;

[0072] 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 on. The location of the bth hiding hole of the i-th rabbit is:

[0073]

[0074] Where b=1,···,m

[0075]

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

[0077] When rabbits are being hunted, they will randomly hide in a cave, and the formula for updating the random hiding position is:

[0078]

[0079]

[0080] in, is a cave randomly selected from m caves, f r is the step size scaling factor, r4 and r5 are random numbers from 0 to 1. After completing the detour foraging and random hiding, the rabbit's position is updated:

[0081]

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

[0083] The Levy flight strategy is introduced at this stage. The Levy flight strategy is a random walk strategy based on Levy distribution.

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

[0085]

[0086] in: The step size factor σ u and σ v The calculation formula is:

[0087]

[0088] σ v =1 (20)

[0089] Where λ is taken as 1.5; Γ is used to calculate the fractional-order calculus term in the fractional-order controller.

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

[0091]

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

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

[0094] Energy contraction simulates the behavior of a rabbit concentrating its energy on careful foraging after finding a food source, i.e., this search mechanism is determined by the rabbit's energy, which gradually decreases over time. The energy factor in ARO is defined as follows:

[0095]

[0096] Among them, r is a random number between 0 and 1. When A(t)>1, the individuals in the population implement a detour foraging strategy; otherwise, the individuals in the population implement a random hiding strategy.

[0097] Step 6: Introduce boundary control strategy to ensure the position is within the boundary;

[0098] The boundary control strategy adjusts the individual position 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] Among them, z i(t+1) represents the updated position of the i-th individual, t represents the number of iterations, 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: Determine whether the number of iterations has reached the upper limit. If so, stop the iteration and get the optimal position Z. best (t) and the fitness value of the new population Otherwise, the number of iterations is increased by 1, and steps 2 to 6 are repeated until the termination condition is met.

[0102] In this implementation, the parameters of the control system are optimized by using the improved artificial rabbit algorithm, and the number of iterations is set to 20. The parameters of LCOPA are tuned using the optimized artificial rabbit algorithm, and the controller parameters after tuning are K p =40.7324,K i =42.5622,K d =79.5144,λ=0.98,μ=0.2653. The adjusted controller parameters were applied to the LCOPA system, which significantly improved the dynamic response performance of the system, reduced the overshoot and response time; enhanced the tracking accuracy of the beam deflection, and ensured that the system can still operate stably in complex environments; and optimized the robustness of the system, so that it can still maintain high accuracy and reliability under external disturbances and uncertainties. In addition, the adjusted parameters effectively coped with the nonlinear time lag problem in LCOPA, providing accurate and stable beam control capabilities for high-demand industrial applications such as optical control, laser processing and optical communications.

[0103] The technical features of the above-described embodiments may be arbitrarily combined. To make the description concise, not all possible combinations of the technical features in the above-described embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0104] The above-mentioned embodiments only express several implementation methods of the present invention, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention patent. It should be pointed out that, for ordinary technicians in this field, several variations and improvements can be made without departing from the concept of the present invention, and these all belong to the protection scope of the present invention. Therefore, the protection scope of the patent of the present invention shall be subject to the attached claims.

Claims

1. A control system based on a composite controller, characterized by: The control system consists of a Smith predictor and a fractional-order PI λ D μ The controller forms a closed-loop control system; Combining 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 the mathematical model of the controlled object, G0(s) is the delay-free term of the transfer function, e -τs is the delay term, τ is the system delay time, K p is fractional PI λ D μ Proportional gain of the controller, K i is fractional PI λ D μ The integral gain of the controller, K d is fractional PI λ D μ The differential gain of the controller, λ is the integral order, and μ is the differential order.

2. The control system based on the composite controller according to claim 1, characterized in that: The transfer function of the Smith predictor is expressed as: G m (s)=G0(s)(1-e -τs ) According to the Smith predictive control strategy, the transfer function of the equivalent controlled object is: G0(s)=G0(s)e -τs +G m (s)。 3. An optimization control method for a control system based on a composite controller, characterized in that: The control method is used to optimize the control system based on the composite controller described in claim 1 or 2. The control method uses an improved artificial rabbit algorithm to optimize the controller parameters and finally obtains the desired controller parameters. The method is implemented by the following steps: Step 1: Initialize the population and parameters of the improved artificial rabbit algorithm and calculate the fitness of the initial population; Step 2: Set the number of loop iterations, requiring the number of iterations to be less than the maximum number of iterations; Step 3, detour foraging stage: introduce a dynamic adjustment factor, apply the dynamic adjustment factor to the mathematical model of the rabbit exploring in the search space, and realize position update; Step 4: Random hiding phase: Introduce the Levy flight strategy to update the hiding position; Step 5, energy contraction phase: execute the detour foraging phase or random hiding phase according to the set energy factor; Step 6: Introduce boundary control strategy to ensure the position is within the boundary; it can be expressed as follows: In the formula, z i (t+1) is the updated position of the i-th individual at the t+1th iteration, z min is the minimum boundary value of the search space, z max is the maximum boundary value of the search space; Step 7: Determine whether the number of iterations has reached the upper limit. If so, stop the iteration to obtain the optimal position and the fitness value of the new population; otherwise, return to step 2 until the termination condition is met to achieve the optimization of the control system parameters.

4. The optimization control method of the control system based on the composite controller according to claim 3 is characterized in that: The specific process of step three is: Assume that the rabbit explores in the search space, and the mathematical model is: Where, i, j = 1, · · ·, n, j ≠ i, It is the new position calculated based on the positions of other individuals and the dynamic adjustment factor. is the reference position of the i-th rabbit at the t-th 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 that rounds to a specified number of digits, and n1 is a random number that follows a standard normal distribution; Introducing a dynamic adjustment factor, it is expressed as follows: Where α(t) is the dynamic adjustment factor for the tth iteration; min is the minimum adjustment factor; T is the maximum number of iterations; α max is the maximum adjustment factor; The dynamic adjustment factor is applied to the mathematical model and is expressed as follows: In the formula, Z i (t) and Z best (t) are the current position of the i-th individual at the t-th iteration and the best position found so far.

5. The optimization control method of the control system based on the composite controller according to claim 3 is characterized in that: The specific process of step 4 is as follows: When being chased, the rabbit will hide in a random cave. The formula for the random hiding position is as follows: In the formula, It is the new position calculated based on the positions of other individuals and the 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, t is the current iteration number, R is the running operator, and r4 is a random number between [0,1]; is a cave randomly selected from m caves; After randomly hiding, the rabbit's position update formula is as follows: In the formula, is the fitness value at t+1 iteration; is the fitness value at t iterations; Applying the Levy flight strategy to the random hiding position update formula, the position update formula is as follows: Among them, s' is the step size generated by Levy distribution, and α is the step size scaling factor, which is used to control the scale of the step size.

6. The optimization control method of the control system based on the composite controller according to claim 5 is characterized in that: The step length formula for setting the Levy flight strategy is as follows: in: The step size factor σ u and σ v The calculation formula is: s v =1 Where λ is taken as 1.5, and Γ is used to calculate the fractional-order differential and integral terms in the fractional-order controller.

7. The optimization control method of a control system based on a composite controller according to claim 1, characterized in that: In step 5, the formula for setting the energy factor A(t) is 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 individuals in the population execute the detour foraging phase; otherwise, the individuals in the population execute the random hiding phase.

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