Liquid crystal optical phased array beam steering method based on two-degree-of-freedom fractional order internal model PID of Smith prediction

Abstract

The method for liquid crystal optical phased array beam control based on Smith prediction two-degree-of-freedom fractional order internal model PID relates to the technical field of laser beam control, and solves the problem that the existing LCOPA beam deflection system has low control precision and stability due to environmental temperature interference and response delay. The method introduces a Smith predictor to compensate for system time delay, so as to eliminate oscillation and overshoot caused by data transmission and processing lag. Then, a two-degree-of-freedom fractional order internal model PID controller is constructed by combining fractional calculus theory and internal model control principle. Finally, the whale optimization algorithm is used to globally optimize and set the key parameters of the controller to determine the optimal control parameters. Compared with traditional control methods, the method has better robustness and dynamic performance, can effectively improve the beam pointing precision and system stability, and is suitable for precise control of laser beams in complex environments.

Description

Technical Field

[0001] This invention relates to the field of laser beam control technology, specifically to a method for controlling the beam of a liquid crystal optical phased array based on Smith-predicted two-degree-of-freedom fractional-order internal mode PID (2DOF-FOIMCPID). This method is suitable for high-precision, fast-response, and robust control of liquid crystal optical phased array (LCOPA) laser beams in complex environments. Background Technology

[0002] LCOPA, an advanced non-mechanical beam deflection technology, utilizes the electro-optic effect and birefringence of liquid crystal molecules. By adjusting the driving voltage, it changes the orientation of the liquid crystal molecules, thereby achieving precise control of the beam phase. With its significant advantages such as small size, light weight, low power consumption, no mechanical inertia, and ease of miniaturization, LCOPA has been widely applied in cutting-edge technology fields such as lidar, space optical communication, and adaptive optics.

[0003] In practical applications, LCOPA systems typically face complex operating environments, requiring high pointing accuracy, fast dynamic response, and strong robustness. However, liquid crystal materials themselves exist between solid and liquid states, possessing both the elasticity of solids and the fluidity of liquids, exhibiting significant viscoelasticity and memory effects. When the external driving voltage changes, the state recovery of liquid crystal molecules depends not only on the current external force but also on their historical states. This makes it difficult for traditional integer-order PID control methods to accurately describe and control the dynamic behavior of LCOPA.

[0004] To improve control performance, existing technologies have evolved from open-loop voltage-phase optimization to closed-loop feedback control. Researchers have proposed methods such as adaptive control, recursive least squares filters, and PID control based on BP neural networks, which have improved the pointing accuracy and anti-interference capability of the system to some extent. In particular, the introduction of fractional-order control theory (such as fractional-order PID), because its integral and derivative orders are non-integer, can describe the viscoelastic characteristics of liquid crystals more accurately than traditional integer-order PID, thus significantly improving the error suppression effect. Although existing fractional-order PID control strategies perform well in handling viscoelasticity, they are still insufficient when facing the large time delay problem that is common in LCOPA systems. The data transmission, image acquisition and processing, and the response lag of the liquid crystal molecules themselves in LCOPA systems can cause the control quantity to fail to be reflected at the output in a timely manner, resulting in increased system overshoot, prolonged settling time, and even system instability. Traditional feedback control is difficult to effectively eliminate the adverse effects of this pure time delay. While the Smith predictor is a classic solution for time-delay problems, combining it with fractional-order control theory and applying it to highly nonlinear LCOPA systems still faces challenges such as complex controller structures and severe parameter coupling. Furthermore, in complex composite control strategies (such as those combining Smith predictors, two-degree-of-freedom structures, and fractional-order internal model control), the controller contains multiple key parameters to be tuned (such as filter time constants and fractional order). These parameters interact with each other, making it difficult to find the global optimum using traditional empirical trial-and-error methods, thus failing to fully realize the controller's performance potential.

[0005] In summary, existing technologies still have limitations in simultaneously addressing the three core issues of significant time delay, nonlinear errors caused by viscoelasticity, and precise control parameter tuning in LCOPA systems. Therefore, there is an urgent need for a comprehensive control method that integrates the time delay compensation capability of the Smith predictor, the excellent dynamic performance of two-degree-of-freedom fractional internal model control, and the global optimization capability of intelligent optimization algorithms to achieve high-precision, fast, and stable beam control of LCOPA in complex environments. Summary of the Invention

[0006] The purpose of this invention is to provide a liquid crystal optical phased array beam control method based on Smith's prediction of a two-degree-of-freedom fractional-order internal mode PID, in order to solve the problems of low control accuracy, large overshoot and poor stability in existing LCOPA beam control systems caused by environmental interference, response time delay and nonlinear characteristics.

[0007] A method for beam control of liquid crystal optical phased arrays based on Smith's prediction of two-degree-of-freedom fractional-order internal mode PID is implemented by the following steps:

[0008] Step 1: Based on the beam control mechanism of liquid crystal optical phased arrays, construct a fractional transfer function model that includes a time delay term;

[0009] Step 2: Introduce the Smith predictor into the fractional transfer function model containing time delay terms described in Step 1 to compensate for the time delay terms; obtain a time delay-free equivalent model.

[0010] Step 3: Based on the time-delay-free equivalent model obtained in Step 2, and combined with the internal model control principle, design a two-degree-of-freedom fractional-order internal model PID controller. The controller includes a feedback controller and a feedforward filter. Both the feedback controller and the feedforward filter have two degrees of freedom, namely: a tracking filter and an internal anti-interference filter that further adjust the target tracking performance and anti-interference performance of the LCOPA beam deflection control system by adjusting the unknown time parameter of the PID controller.

[0011] Step 4: Use the whale optimization algorithm to globally optimize and tune the unknown time parameters in the PID controller described in Step 3; use the integral time absolute error as the objective function, iteratively update the parameters by simulating the whale's behavior of surrounding prey, searching for prey, and attacking with a spiral bubble net, and finally output the optimal control parameters for beam control.

[0012] The beneficial effects of this invention are:

[0013] 1. Significantly eliminates time delay effects: This invention applies the Smith predictor to the LCOPA control system, effectively compensating for the inherent response delay of the system. Experimental results show that this method can completely eliminate overshoot in the step response (overshoot is 0), ensuring the stability of beam control.

[0014] 2. Improved dynamic response speed: Compared with traditional fractional-order PID (response time 28.685ms) and integer-order PID (response time 38.916ms), the response time of the method of this invention is shortened to 7.68ms, which greatly enhances the application potential of LCOPA in high-speed beam scanning.

[0015] 3. Enhanced System Robustness: Through the design of a two-degree-of-freedom internal model structure, independent adjustment of tracking performance and disturbance rejection performance is achieved. Combined with parameters optimized by the whale algorithm, the system can recover to steady state faster than traditional methods when faced with external sudden disturbances, demonstrating extremely strong robustness.

[0016] 4. High-precision intelligent control: The system automatically finds the optimal control parameters using the whale optimization algorithm, avoiding the blindness of manual tuning, resulting in minimal steady-state error and achieving precise control of the laser beam deflection angle. Attached Figure Description

[0017] Figure 1This is a schematic diagram of the Smith predictor design principle in the liquid crystal optical phased array beam control method based on Smith prediction and two-degree-of-freedom fractional-order internal mode PID described in this invention.

[0018] Figure 2 This is a schematic diagram of the system architecture of a fractional-order internal model PID controller based on the Smith predictor;

[0019] Figure 3 This is a structural diagram of a two-degree-of-freedom fractional-order internal model PID control system.

[0020] Figure 4 This is the block diagram of an equivalent two-degree-of-freedom fractional-order PID control system;

[0021] Figure 5 A flowchart for controller parameter tuning based on the whale optimization algorithm;

[0022] Figure 6 The diagram shows the structure of a 2DOF-FOIMCPID and Smith predictive compensation control system tuned based on the whale optimization algorithm.

[0023] Figure 7 This is a graph showing the effect of the ITAE value change curve in the controller parameter tuning of this invention;

[0024] Figure 8 This is a diagram showing the step response effect of the laser beam control system in this invention;

[0025] Figure 9 This is a diagram showing the effect of the absolute error curve of the step response of the laser beam control system in this invention.

[0026] Figure 10 This is a diagram illustrating the control effect of the laser beam manipulation system tracking the square wave signal in this invention.

[0027] Figure 11 This is a diagram showing the absolute error of the laser beam control system tracking the square wave signal in this invention.

[0028] Figure 12 This is a diagram illustrating the effect of +0.2° disturbance control in the laser beam modulation system of this invention.

[0029] Figure 13 This is a diagram showing the effect of the laser beam control system in this invention with a -0.2° disturbance. Detailed Implementation

[0030] Specific Implementation Method 1: Combination Figures 1 to 7 This embodiment describes a liquid crystal optical phased array beam control method based on Smith's predicted two-degree-of-freedom fractional-order internal mode PID. This method is implemented through the following steps:

[0031] Step 1. Construct a fractional-order mathematical model of the liquid crystal optical phased array system. Based on the beam control mechanism of the liquid crystal optical phased array, considering the viscoelastic properties of the liquid crystal material and the system response hysteresis, construct a fractional-order transfer function model including a time delay term. This is used to describe the dynamic response characteristics of the deflection angle of the output beam of a liquid crystal optical phased array under the action of a driving voltage. The specific process is as follows:

[0032] Step 11. Construct a fractional-order mathematical model of the liquid crystal optical phased array beam deflection control system:

[0033] (1)

[0034] In the formula, The angle at which the emitted light from the liquid crystal molecules deflects. For systems with time delay Phase modulation amount The wavelength of the laser. For the size of a single array element, It is a unit charge. It refers to the thickness of the liquid crystal layer; , These are the viscosity coefficients for unfolding and bending, respectively. , These are the elastic moduli for unfolding and bending, respectively. , For fractional derivatives, It is a fractional calculus operator;

[0035] Step 12. Establish the fractional transfer function model of the LCOPA beam deflection control system;

[0036] For the LCOPA beam deflection control system, a dynamic model is first performed. Considering that liquid crystal materials possess both solid elasticity and liquid viscosity, their orientation behavior under an electric field exhibits fractional-order dynamic characteristics; therefore, the transfer function of the fractional dynamic model in the frequency domain is expressed as:

[0037] (2)

[0038] In the formula, It is a fractional transfer function model. For the Laplace operator, The system gain coefficient is represented by the denominator, which includes a fractional differential term, describing the viscoelastic properties and memory effect of the liquid crystal material.

[0039] In this embodiment, data on input voltage and output deflection angle are collected experimentally, and a genetic algorithm is used for system identification to obtain the actual fractional-order transfer function model of the LCOPA beam deflection control system. :

[0040] (3)

[0041] In the formula, This indicates that the system exists. The pure hysteresis is mainly caused by the delay in data transmission and the response of liquid crystal molecules.

[0042] Step 2. Design a Smith predictor for time delay compensation: for the fractional transfer function model in Step 1 Existing time delay terms To address this, a Smith predictor is introduced. By introducing a predictor model in parallel with the controlled object model into the control loop, the time-delay term is moved out of the closed-loop characteristic equation, transforming the controlled object of the system into a time-delay-free equivalent model. This eliminates oscillations and overshoot caused by data transmission and liquid crystal response lag, thereby improving the system's response speed.

[0043] like Figure 1 As shown, Figure 1 The diagram illustrates the design of a Smith predictor, which separates the lag portion of the transfer function from the rational fractional portion. and These are the system's reference input and output signals, respectively; the fractional-order transfer function model is used as the controlled object model. The transfer function of the Smith predictor Designed as follows:

[0044] (4)

[0045] Combination Figure 2 As shown, Figure 2 This is a schematic diagram of a fractional-order internal model PID controller system based on the Smith predictor. For external disturbance terms; the controller has two degrees of freedom: tracking filter. Internal interference rejection filter used to optimize setpoint tracking performance Used to suppress external disturbances; the Smith predictor is connected in parallel after the controller, and after feedback compensation, the controlled object model of the closed-loop control system is obtained. Transform into a time-delay equivalent model :

[0046] (5)

[0047] This eliminates the impact of time delay terms on the stability of the control system.

[0048] Step 3. Design a two-DOF fractional-order internal model PID controller (2DOF-FOIMCPID): based on the time-delay-free equivalent model obtained in Step 2. Combining the principles of internal model control (IMC) and fractional calculus, a 2DOF-FOIMCPID controller is designed. This controller includes a feedback controller. and feedforward filter Two adjustable time constant parameters are introduced. and .in, Used to optimize setpoint tracking performance This is used to enhance the ability to suppress external interference, thereby achieving decoupled adjustment of target tracking and anti-interference performance.

[0049] The specific process is as follows:

[0050] Step 31. Internal mold structure design: such as Figure 3 The control system structure diagram of the 2DOF-FOIMCPID shown is illustrated. To ensure the physical realizability and robustness of the controller, a low-pass filter is introduced. and :

[0051] (6)

[0052] In the formula, the controlled object model , It is the inverse of its minimum phase portion. The low-pass filter is chosen as follows:

[0053] (7)

[0054] in, and These are the time parameters for the tracking filter and the internal disturbance rejection filter, respectively.

[0055] Step 32. Equivalent Feedback Structure Transformation: To facilitate engineering implementation, it is necessary to transform the equivalent feedback structure. Figure 3 The internal mold structure is converted into a standard feedback control structure, such as Figure 4 The block diagram of the equivalent two-degree-of-freedom fractional-order PID control system is shown. According to... Figure 3 and Figure 4 The equivalent relationship is used to derive the feedback controller. and feedforward filter The expression:

[0056] (8)

[0057] In this embodiment, the feedback controller Specific derivation: [The following is a continuation of the derivation process] Substitution From the formula, we obtain the transfer function form of the feedback controller:

[0058] (9)

[0059] Substituting formula (3) into the above equation, we can utilize the properties of fractional operations. The final feedback controller transfer function form is obtained as follows:

[0060] (10)

[0061] in, Used to generate feedback control quantities based on beam deflection angle errors.

[0062] Similarly, Substituting the values ​​into the feedforward filter, we obtain the transfer function form of the feedforward filter:

[0063] (11)

[0064] Step 4. Controller parameter tuning based on the Whale Optimization Algorithm (WOA): addressing unknown key time parameters in the controller. and A whale optimization algorithm is used for global optimization tuning. The integral time absolute error (ITAE) is selected as the objective function. In this embodiment, three behaviors during the humpback whale's hunting process are simulated to update the individual whale's position: updating the position of surrounding prey, updating the position of searching for prey, and updating the position of the spiral bubble net. The parameters are iteratively updated in the search space until the control parameters that optimize the overall performance of the system are obtained, and then applied to the LCOPA beam deflection control system.

[0065] like Figure 5 As shown in this embodiment, Figure 5 This is a flowchart of the controller parameter tuning process based on the whale optimization algorithm. The specific steps are as follows:

[0066] Step 41. Initialize controller parameters and population; calculate the objective function;

[0067] In this embodiment, the population size is set. Maximum number of iterations The time parameter range is set to The integral time absolute error (ITAE) is chosen as the fitness function, i.e., the objective function is:

[0068] (12)

[0069] Step 42. Generate a random number P and calculate the coefficient vector. ; The error between the target angle input to the system and the actual output angle. For time.

[0070] Step 43. Determine whether the random number P is less than 0.5. If yes, proceed to step 44; otherwise, proceed to step 45.

[0071] Step 44. Determine the coefficient vector If the value is greater than or equal to 1, update the prey location and proceed to step 46; otherwise, update the surrounding prey location and proceed to step 46.

[0072] Step 45. Determine the coefficient vector If the value is less than 1, update the spiral bubble position and proceed to step 46; otherwise, return to step 42.

[0073] Step 46. Calculate the fitness value of each individual and update the controller parameters;

[0074] Step 47. Determine if the number of iterations is greater than 20. If so, output the optimal controller parameters; otherwise, return to step 42.

[0075] In this embodiment, the position surrounding the prey is updated, that is: when and At this time, individual whales move closer to the current best individual, and the update formula is:

[0076] (13)

[0077] In the formula, For the first The position of the individual whale in the next iteration. The current optimal individual position, and For the coefficient vector, This represents the distance vector between the current individual whale and the reference individual;

[0078] In this embodiment, the location of the prey is updated, that is: when and At that time, individual whales search around randomly selected individuals, and the update formula is:

[0079] (14)

[0080] In the formula, The location of a randomly selected individual whale in the population.

[0081] In this embodiment, the spiral bubble position is updated, that is: when At that time, individual whales update their positions around the current best individual using a spiral bubble net method, and the update formula is:

[0082] (15)

[0083] In the formula, The constant for the spiral shape. for Random numbers within the interval This is the distance vector between the current parameters and the current global best individual.

[0084] In this embodiment, the whale optimization algorithm can switch between global search and local optimization through the three position update methods described above, thereby obtaining the controller parameters that optimize the fitness function.

[0085] like Figure 6 As shown, Figure 6 The diagram shows the structure of a 2DOF-FOIMC-PID and Smith predictor compensation control system tuned based on the whale optimization algorithm. The control system of this invention includes a reference input module, a two-DOF FO-IMC-PID controller, and a liquid crystal optical phased array equivalent controlled object. (M The system includes a Smith predictor, a CCD detection module, and a whale optimization algorithm parameter tuning module. The 2DOF-FOIMCPID includes a feedforward filter. and feedback controller Reference input signal After feedforward filter The signal then enters the comparison stage, where it, together with the CCD feedback signal and the Smith prediction compensation signal, forms the control error signal; this control error signal is then processed by the feedback controller. The processed input forms a control input, which is then applied to the equivalent controlled object of the liquid crystal optical phased array. The output signal is obtained. The CCD detection module is used to acquire the deflection angle of the output beam of the liquid crystal optical phased array and feed the detection signal back to the control system. The Smith predictor is used to predict and compensate for system time delays, thereby improving the control performance degradation caused by the response lag of the liquid crystal material. The whale optimization algorithm is used to optimize the controller parameters to obtain the control parameters that best achieve the objective function.

[0086] like Figure 7 As shown, Figure 7 The ITAE variation curve shows that after 20 iterations, the ITAE value converges, yielding the optimal time parameter. .

[0087] Specific Implementation Method Two: Combination Figures 8 to 13This embodiment describes the performance verification and analysis of the liquid crystal optical phased array beam control method based on Smith prediction and a two-DOF fractional-order internal mode PID controller, as described in Embodiment 1. The optimal controller (2DOF-FOIMCPID) obtained in Embodiment 1 is applied to the LCOPA beam deflection control system and compared with traditional PID controllers and fractional-order PID controllers (FOPID). The control effect of the method is verified from three aspects: step response performance, fixed-point tracking performance, and disturbance rejection robustness.

[0088] The optimal controller designed above was applied to the LCOPA beam deflection control system, and step response, tracking square wave signal, and robustness tests were conducted on it, along with those of traditional PID and fractional-order PID (FOPID).

[0089] Step response test:

[0090] like Figure 8 and Figure 9 As shown, under the same step input conditions, the response time of the method of the present invention is only 7.68 ms, and the overshoot is 0, enabling it to quickly and smoothly reach the target output. The response time of FOPID is 28.685 ms, and the response time of PID is 38.916 ms, both exhibiting varying degrees of overshoot. Compared to FOPID, the response time of the method of the present invention is reduced by approximately 73.22%; compared to PID, the response time is reduced by approximately 80.27%. Furthermore, the absolute error curve of the step response shows that the method of the present invention exhibits the fastest error decay rate, with the steady-state error approaching 0. These results demonstrate that the method of the present invention can significantly improve the response speed of the LCOPA system, reduce overshoot and steady-state error, and possess better dynamic stability and control accuracy.

[0091] Tracking square wave signal test:

[0092] like Figure 10 and Figure 11 As shown, Figure 10 This is a diagram illustrating the control effect of the laser beam manipulation system tracking the square wave signal in this invention. Figure 11 This is a diagram showing the absolute error of the laser beam control system tracking the square wave signal in this invention. Figure 10 It can be seen that when the reference input (Step) is a square wave signal, the method of this invention can quickly follow the target angle change, with less tracking lag at the rising and falling edges of the square wave, and the output curve is closer to the target signal; while traditional PID and fractional-order PID methods have significant lag and oscillation during the tracking process. Figure 11It can be seen that all three methods will produce transient errors when the square wave signal changes abruptly. However, the error peak value of the method of the present invention is smaller and the error decay speed is faster, indicating that it has better dynamic tracking accuracy and error suppression capability.

[0093] Robustness testing:

[0094] like Figure 12 and Figure 13 As shown, Figure 12 This is a diagram illustrating the effect of the laser beam control system with a +0.2° disturbance in this invention. Figure 13 This diagram illustrates the effect of the laser beam manipulation system in this invention with a -0.2° disturbance control. Figure 12 and Figure 13 It can be seen that when external disturbances with amplitudes of +0.2° and -0.2° are applied to the system after it has stabilized, the method of the present invention can quickly suppress the influence of the disturbance and recover to a stable state in a short time. Compared with traditional PID and fractional-order PID methods, the method of the present invention has smaller fluctuation amplitude and shorter recovery time after disturbance, indicating that it has stronger robustness and stability under external disturbances.

[0095] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0096] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this invention patent should be determined by the appended claims.

Claims

1. A method for beam control of a liquid crystal optical phased array based on Smith's predicted two-degree-of-freedom fractional-order internal mode PID, characterized by: This method is implemented by the following steps: Step 1: Based on the beam control mechanism of liquid crystal optical phased arrays, construct a fractional transfer function model that includes a time delay term; Step 2: Introduce the Smith predictor into the fractional transfer function model containing time delay terms described in Step 1 to compensate for the time delay terms; obtain a time delay-free equivalent model. Step 3: Based on the time-delay-free equivalent model obtained in Step 2, and combined with the internal model control principle, design a two-degree-of-freedom fractional-order internal model PID controller. The PID controller includes a feedback controller and a feedforward filter. Both the feedback controller and the feedforward filter have two degrees of freedom, namely: a tracking filter and an internal anti-interference filter that further adjust the target tracking performance and anti-interference performance of the LCOPA beam deflection control system by adjusting the unknown time parameter of the PID controller. Step 4: Use the whale optimization algorithm to globally optimize and tune the unknown time parameters in the PID controller described in Step 3; use the integral time absolute error as the objective function, iteratively update the parameters by simulating the whale's behavior of surrounding prey, searching for prey, and attacking with a spiral bubble net, and finally output the optimal control parameters for beam control.

2. The method for beam control of a liquid crystal optical phased array based on Smith-predicted two-degree-of-freedom fractional-order internal mode PID as described in claim 1, characterized in that: In step two, a Smith predictor is introduced in parallel with the controlled object model, transforming the controlled object of the system into a time-delay equivalent model. ; Transfer function of Smith predictor for: ; In the formula, For a time-delay equivalent model, This is a time-delay term.

3. The method for beam control of a liquid crystal optical phased array based on Smith-predicted two-degree-of-freedom fractional-order internal mode PID as described in claim 2, characterized in that: The specific process of step three is as follows: Step 31: Design the internal model structure; Introducing a low-pass filter and ; ； In the formula, the controlled object model , It is the inverse of the minimum phase part of the controlled object model; For tracking filters, For internal interference rejection; The low-pass filter is in the form of: ； In the formula, and These are the unknown time parameters for the tracking filter and the anti-interference filter, respectively; Step 3.2: Equivalent Feedback Structure Transformation; The internal model structure designed in step 31 is converted into a feedback control structure to obtain a feedback controller. and feedforward filter The expression; 。 4. The method for beam control of a liquid crystal optical phased array based on Smith-predicted two-degree-of-freedom fractional-order internal mode PID as described in claim 3, characterized in that: Internal interference rejection filter and tracking filter Introduced into the feedback controller and feedforward filter The final transfer function forms are as follows: ； In the formula, , These are the viscosity coefficients for unfolding and bending, respectively. , These are the elastic moduli for unfolding and bending, respectively. , For fractional derivatives, For the Laplace operator, This is the system gain coefficient.

5. The method for beam control of a liquid crystal optical phased array based on a two-degree-of-freedom fractional-order internal mode PID predicted by Smith, as described in claim 4, is characterized in that: In step four, the objective function of the whale optimization algorithm is... Set as: ； In the formula, The error between the target angle input to the system and the actual output angle. For time.

6. The method for beam control of a liquid crystal optical phased array based on Smith-predicted two-degree-of-freedom fractional-order internal mode PID according to claim 5, characterized in that: In step four, the parameters are iteratively updated by simulating the whale's behavior of surrounding prey, searching for prey, and spiral bubble web attack. The specific process is as follows: Step 41. Initialize controller parameters and population; calculate the objective function; Step 42. Generate a random number P and calculate the coefficient vector. ; Step 43. Determine whether the random number P is less than 0.

5. If so, proceed to step 44. Otherwise, proceed to step 45; Step 44. Determine the coefficient vector If the value is greater than or equal to 1, update the prey location and proceed to step 46; otherwise, update the surrounding prey location and proceed to step 46. Step 45. Determine the coefficient vector Is it less than 1? If so, update the spiral bubble position and proceed to step 46. Otherwise, return to step 42; Step 46. Calculate the fitness value of each individual and update the controller parameters; Step 47. Determine if the number of iterations is greater than 20. If so, output the optimal controller parameters; otherwise, return to step 42.

7. The method for beam control of a liquid crystal optical phased array based on Smith-predicted two-degree-of-freedom fractional-order internal mode PID according to claim 6, characterized in that: The prey surrounding position is updated using the following formula: ； In the formula, For the first The position of the individual whale in the next iteration. The current optimal individual position, and For the coefficient vector, This is the distance vector between the current whale individual and the reference individual; The prey location search and update formula is as follows: ； In the formula, The location of a randomly selected individual whale in the population; The spiral bubble position is updated using the following formula: ； In the formula, The constant for the spiral shape. for Random numbers within the interval This is the distance vector between the current parameters and the current global best individual.

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