A method for setting up a composite control system based on time-delay filter and PID controller

Abstract

The present invention relates to the field of vibration reduction control technology for flexible manipulators, and discloses a method for setting a composite control system based on a time-delay filter and a PID controller, including: establishing a dynamic mathematical model of the flexible manipulator; designing an optimal time-delay filter with minimum residual oscillation based on a traditional time-delay filter; establishing a mathematical model of a spiral dynamic algorithm based on opposite points, and solving PID controller parameters based on the spiral dynamic algorithm; designing an improved PID controller based on the PID controller parameters and the spiral dynamic algorithm based on opposite points; combining the optimal time-delay filter and the improved PID controller to design a composite control system for suppressing residual oscillation of the flexible manipulator. The present invention improves the traditional PID controller, introduces a spiral dynamic algorithm based on opposite points to dynamically adjust the parameters of the PID controller, and at the same time introduces the optimal time-delay filter to the front end of the controller in an external loop mode, so as to effectively suppress the residual vibration of the flexible manipulator.

Description

Technical Field

[0001] The invention relates to the technical field of vibration reduction control of a flexible mechanical arm, in particular to a method for setting a composite control system based on a time-delay filter and a PID controller. Background Art

[0002] Lightweight robotic arms are widely used in many high-performance industrial scenarios, such as flexible manufacturing and spacecraft. As a key mechanical control component, especially in intelligent robots, servo motors play a vital role. When the moving parts driven by the servo motor are made of elastic materials or the moving parts themselves are flexible robotic arm structures. The application of flexible robotic arms inevitably causes elastic vibrations during the operation of the robot, which has an adverse effect on the robot's motion accuracy. Not only that, the elastic vibrations will also cause serious fatigue damage to the structure of the robotic arm, shortening the service life of the robotic arm. Therefore, the vibration of the robotic arm must be suppressed.

[0003] When the vibration of the manipulator is suppressed, in addition to improving the hardware structure of the flexible system, it is also necessary to select a suitable closed-loop control system to suppress the residual oscillation of the tip of the manipulator when positioning. The time-delay filter can effectively suppress the residual oscillation of the high-precision positioning system and is a feedforward open-loop control method. However, the design of the filter requires the input and output values ​​of the step system, and the robustness is poor, and it cannot effectively suppress unpredictable external interference. The PID controller has a simple algorithm, good robustness, and high reliability. It adjusts the parameters and determines the appropriate parameters to match the controller characteristics with the controlled object, so that the controlled object can be controlled by vibration reduction. However, in the actual control system, the parameters will change, and the parameter determination is more complicated. The traditional PID often has poor parameter setting and poor performance, making it difficult for the system to achieve the best control effect.

[0004] Therefore, the present invention proposes a method for setting up a composite control system based on a time-delay filter and a PID controller to achieve accurate tracking of the robot arm trajectory, minimize the positioning time of the robot arm, and effectively suppress the residual vibration that occurs in the process of the end of the robot arm from high-speed operation to rapid deceleration and stop. Summary of the invention

[0005] The purpose of the present invention is to provide a method for setting a composite control system based on a time-delay filter and a PID controller to address the deficiencies in traditional vibration reduction control methods for robotic arms. Among them, the closed-loop positioning controller adopts an improved spiral dynamic algorithm PID control, which has a good control response and can achieve accurate and rapid control of the flexible robotic arm. The time-delay filter is located outside the closed-loop controller, which can shorten the positioning time and comprehensively consider the vibration mode of the system to eliminate the residual vibration of the robotic arm. The closed-loop positioning controller and the open-loop time-delay filter are combined to design a composite control system to achieve rapid vibration reduction positioning of the robotic arm.

[0006] The present invention is implemented by the following technical solution: A method for setting a composite control system based on a time-lag filter and a PID controller, comprising the following steps:

[0007] Establish the dynamic mathematical model of the flexible robotic arm;

[0008] Design an optimal time-delay filter with minimum residual oscillation based on the traditional time-delay filter;

[0009] Establish a mathematical model of the spiral dynamic algorithm based on the opposite point, and solve the PID controller parameters based on the spiral dynamic algorithm;

[0010] An improved PID controller is designed based on the PID controller parameters and the mathematical model of the spiral dynamic algorithm based on the opposite point;

[0011] By combining the optimal time-delay filter with the improved PID controller, a composite control system is designed to suppress the residual oscillation of the flexible manipulator.

[0012] In order to better implement the present invention, further, the method for establishing a mathematical model of the spiral dynamic algorithm based on opposite points includes:

[0013] The opposite point learning algorithm and the dynamic spiral algorithm are combined to establish a spiral dynamic algorithm model based on opposite points.

[0014] In order to better implement the present invention, further, the method for designing an improved PID controller includes:

[0015] The mathematical model of the spiral dynamic algorithm based on the opposite point is introduced to dynamically adjust the parameters of the PID controller, and an improved PID controller with parameter adjustment based on the mathematical model of the spiral dynamic algorithm based on the opposite point is designed;

[0016] The PID controller parameters include proportional coefficient, integral coefficient and differential coefficient.

[0017] In order to better implement the present invention, further, the method of combining the optimal time-delay filter and the improved PID controller to design a composite control system for suppressing the residual oscillation of the flexible manipulator includes:

[0018] The optimal time-delay filter is convolved with the pulse sequence to filter out unnecessary frequency components in the input signal and eliminate residual oscillations of the flexible manipulator system.

[0019] After the optimal time-delay filter is initially filtered in the open loop, the PID controller improved by the mathematical model of the spiral dynamic algorithm based on the opposite point is used in the closed loop to effectively suppress the residual oscillation of the flexible manipulator for the second time.

[0020] The open-loop control based on the optimal time-delay filter and the closed-loop control of the PID controller improved by the mathematical model of the spiral dynamic algorithm based on the opposite point are coupled;

[0021] The optimal time-delay filter is introduced into the improved PID controller in an external loop mode, and a composite control system in an external loop mode is designed.

[0022] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0023] (1) The present invention introduces an optimal time-delay filter for open-loop control, which can effectively suppress the residual oscillation of the high-precision positioning system. At the same time, the traditional PID controller is improved, and the PID controller parameters are dynamically adjusted by a spiral dynamic algorithm based on opposite points to improve the control performance of the system. The optimal time-delay filter is introduced into the PID control system in an external loop mode, thereby effectively suppressing the residual vibration of the flexible manipulator. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] The present invention is further described in conjunction with the following drawings and embodiments, and all the concepts and innovations of the present invention should be regarded as the disclosed contents and the protection scope of the present invention.

[0025] Figure 1 A schematic diagram of a two-dimensional model of a flexible robotic arm in a method for setting a composite control system based on a time-lag filter and a PID controller provided by the present invention.

[0026] Figure 2 A closed-loop schematic diagram of a PID-controlled flexible manipulator based on a spiral dynamic algorithm of opposite points in a method for setting a composite control system based on a time-lag filter and a PID controller provided by the present invention.

[0027] Figure 3 A schematic diagram of the entire composite control in a method for setting a composite control system based on a time-lag filter and a PID controller provided by the present invention. DETAILED DESCRIPTION

[0028] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. It should be understood that the described embodiments are only part of the embodiments of the present invention, not all of the embodiments, and therefore should not be regarded as limiting the scope of protection. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technical personnel in this field without making creative work are within the scope of protection of the present invention.

[0029] Embodiment 1:

[0030] A method for setting a composite control system based on a time-lag filter and a PID controller in this embodiment includes the following steps:

[0031] Establish the dynamic mathematical model of the flexible robotic arm;

[0032] Design an optimal time-delay filter with minimum residual oscillation based on the traditional time-delay filter;

[0033] Establish a mathematical model of the spiral dynamic algorithm based on the opposite point, and solve the PID controller parameters based on the spiral dynamic algorithm;

[0034] An improved PID controller is designed based on the PID controller parameters and the mathematical model of the spiral dynamic algorithm based on the opposite point;

[0035] By combining the optimal time-delay filter with the improved PID controller, a composite control system is designed to suppress the residual oscillation of the flexible manipulator.

[0036] In this embodiment, .

[0037] Embodiment 2:

[0038] This embodiment is further optimized on the basis of the embodiment 1. In this embodiment, a dynamic mathematical model of a flexible robotic arm is established. Before establishing the dynamic equation of the flexible robotic arm, some necessary assumptions are made:

[0039] 1) The flexible manipulator is a uniform rectangular cross-section beam.

[0040] 2) The surface moment of inertia and mass per unit length are constant.

[0041] Under the above assumptions, the following differential equations and boundary conditions are derived according to Hamilton's principle:

[0042]

[0043] Where w is the elastic deflection of the flexible manipulator, L is the length of the flexible link, t is the center wheel axis, m is the mass of the load, and I h is the center wheel shaft inertia, θ(t) is the center wheel shaft angle, τ(t) is the center wheel shaft torque, and EI is the uniform bending stiffness of the connecting rod.

[0044] The flexible manipulator is usually a thin-walled link with a slender structure. Longitudinal vibration is ignored in the analysis. It is assumed that the flexible arm is only considered to be a transverse vibration Euler-Bernoulli model. Therefore, a simplified two-dimensional model of the flexible arm is as follows Figure 1 As shown, w(x, t) represents the elastic deflection of the flexible manipulator, EI represents the uniform bending stiffness of the link, L represents the length of the flexible link, ρ represents the uniform weight per unit length, and I h represents the inertia of the central wheel shaft, u represents the control torque, m t is the mass of the tip payload, θ(t) represents the angle of the central wheel axis, and w i represents the elastic deflection of the ith element under the xoy coordinate axis, Y i is the Y element of the arc approaching the right node position.

[0045] The other parts of this embodiment are the same as those of Embodiment 1, and thus will not be described in detail.

[0046] Embodiment 3:

[0047] This embodiment is further optimized on the basis of the above-mentioned embodiment 1 or 2. In this embodiment, a traditional time-delay filter is designed. The essence of the time-delay filter is to introduce a time-delay link. It contains a series of pulse sequences with different time delay times and amplitudes. By convolving the desired input pulse sequence, a shaped input is obtained to drive the system, thereby achieving the purpose of eliminating the residual oscillation of the flexible system. Its basic structure is:

[0048]

[0049] Among them, A i and t i is the amplitude of the pulse train and the corresponding time delay, n is the number of pulses contained, and F(s) is the basic structure of the time delay filter;

[0050] Using the time-delay filter feedforward control, the residual oscillation of the system can be described as a function of ω and ξ, where ω is the system model frequency and ξ is the damping ratio. The residual oscillation V(ω, ξ) of the system can be expressed as:

[0051] C(ω,ξ) is the sum of the sines of ω and ξ, ω is the system model frequency, ξ is the damping ratio, S(ω,ξ) is the sum of the cosines of ω and ξ, ω is the system model frequency, ξ is the damping ratio, t nis the time lag corresponding to the number of pulses, n is the number of pulses;

[0052] t i is the time delay corresponding to the pulse sequence, A i is the amplitude of the pulse train, ω is the system model frequency, ξ is the damping ratio;

[0053]

[0054] Formula (2) provides a method for designing a time-delay filter. At the system model frequency ω and damping ξ, the amplitude of the residual oscillation is 0, and the sum of all sines and the sum of all cosines must also be 0, that is:

[0055]

[0056]

[0057] In order for the final output value of the filtered and unfiltered input to be the same, the sum of the pulse amplitudes must satisfy the following gain constraint:

[0058] A i is the amplitude of the pulse train, n is the number of pulses included;

[0059] At the same time, the amplitude of the pulse is required to be positive, that is, A i ≥0;

[0060] When n=2, the time-delay filter includes 2 pulses and 4 unknowns,

[0061] K is the gain of the time-delay filter, T is the time lag of the time-delay filter, ω is the system model frequency, and ξ is the damping ratio.

[0062]

[0063] t1=0, t2=ΔT; where t1 and t2 are the lag time.

[0064] This two-pulse sequence is called a zero oscillation (ZV) time-delay filter. The form of the zero oscillation time-delay filter is F(s) is the basic structure of the zero oscillation time-delay filter, and A1 and A2 are the amplitudes when the pulse sequence is 1 and 2. According to the expression, the time delay t2 depends on the natural frequency and damping of the flexible manipulator. If the damping and natural frequency of the system cannot be accurately known, the time delay t2 is uncertain and the oscillation of the flexible manipulator cannot be effectively suppressed.

[0065] The other parts of this embodiment are the same as those of the above-mentioned embodiment 1 or 2, and thus will not be described in detail.

[0066] Embodiment 4:

[0067] This embodiment is further optimized on the basis of any one of the above embodiments 1-3. In this embodiment, an optimal time-delay filter with minimum residual oscillation is designed. When designing the traditional two-pulse ZV (Zero Vibration), three-pulse ZVD (Zero Vibration Derivative) and extremely insensitive EI (Extensive Insensive) time-delay filters, in order to simplify the calculation, the distribution characteristics of the system parameter changes are ignored. If the probability characteristics of the system parameter changes are known, the system parameter changes and the system residual oscillation can be combined to obtain the minimum expected residual oscillation. Assume that f(o) is the probability density function of the system frequency or damping coefficient, and it obeys the average distribution U(p H ,p L ). Where p represents the system frequency ω or the damping coefficient ξ. H and L are region-limited, V(ω, ξ) is the impulse function of the system frequency ω or the damping coefficient ξ. If the system frequency ω or the damping coefficient ξ is considered at the same time, the two-dimensional probability density function can be expressed as:

[0068]

[0069] (1) Considering the system frequency error and when the system damping is small, the performance index J can be expressed as

[0070]

[0071] (2) When considering the system damping error, the performance index J can be expressed as

[0072]

[0073] (3) Considering the frequency error and damping error of the system, the performance index J can be expressed as

[0074]

[0075] Delay time and pulse amplitude is the variable that can be optimized in the time-delay filter. According to the constraint condition amplitude A i ≥0, the optimal solution of the objective function J can be obtained.

[0076] The other parts of this embodiment are the same as any one of the above embodiments 1-3, so they are not repeated here.

[0077] Embodiment 5:

[0078] This embodiment is further optimized on the basis of any one of the above embodiments 1-4. In this embodiment, a mathematical model based on the spiral dynamic algorithm (OSDA) based on the opposite point is established.

[0079] The traditional spiral dynamic optimization algorithm (SDA) is mainly used to explore the solution space of the model. In the early stage of spiral motion, particles move fully and explore all possible solution spaces, while in the later stage of spiral dynamic motion, particles move violently in a smaller search area and have a strong exploration ability. Compared with linear motion search, the movement strategy of this dynamic algorithm is more globally exploratory. However, the search strategy of this algorithm is relatively simple, the spiral trajectory is relatively fixed, and it is easy to fall into the local optimum. Therefore, adversarial learning is introduced to optimize the spiral dynamic algorithm to a certain extent.

[0080] The Opposition-based Spiral Dynamics Algorithm (OSDA) is a combination of the Opposition-based Learning Algorithm (OBL) and the Spiral Dynamics Algorithm (SDA). Applying OBL to SDA allows the algorithm to consider not only the usual solutions but also their corresponding opposite solutions, creating opportunities for the algorithm to find the optimal solution at the opposite position of the agent's current position. This strategy improves the distribution of the search agent in the predefined search space, thereby improving the development strategy of SDA. The OBL formula used is expressed as (13), which is a quasi-opposition variant of OBL.

[0081] v opp (i) = v mid (i)+(v o (i)-v mid (i))×rand (13);

[0082] Among them, v o (i) is defined as follows:

[0083] v o (i) = 2 × v mid (i)-v old (i) (14);

[0084] Among them, v mid The definition is as follows:

[0085]

[0086] Among them, v opp is the opposite position of the ith agent, rand is a generated random number, and v old is the old position of the ith agent, v max and v min are the upper and lower bounds of the ith agent. SDA is an agent-based algorithm that mainly uses the spiral equation to move the agent from one position to another. The spiral equation of SDA is defined as (16).

[0087] x i (t+1)=S(r,θ)x i (t)-(S(r,θ)-I)x * (t) (16);

[0088] Among them, x i (t+1) is the updated position of the i-th search agent in the t-th iteration, x i x(t) is the previous position of the i-th search agent in the t-th iteration, I represents the identity matrix, r represents the spiral radius, and θ represents the spiral angle. S(r,θ) represents the combination of the rotation matrix, which is defined by the radius r and the angle θ. * (t) represents the center point of the spiral form.

[0089] The Opposition-Based Spiral Dynamic Algorithm (OSDA) is a new algorithm that uses equations (13)-(16). The specific steps are as follows:

[0090] Step 1: Initialize the position X of the i-th agent i , the opposite position v of the i-th agent opp (i) and the maximum iteration T.

[0091] Step 2: Update the cost function f(X i ) and fitness function f(v opp (i)).

[0092] Step 3: Determine the best individual agent X fmin . With the cost function f min The agent with the lowest value is the best individual agent. The best individual agent is set to the destination location P dest .

[0093] Step 4, update the position of the i-th agent using the spiral equation (16).

[0094] Step 5: Determine the opposite position of the updated position of the i-th agent according to equations (13)-(16).

[0095] Step 6, check whether the algorithm has updated the positions of all agents. If it has, proceed to step 8. If it has not, repeat steps 4-7.

[0096] Step 7: Update the cost or fitness function f(X i ) and f(v opp (i)) value.

[0097] Step 8, determine the best proxy X fmin . This agent has the lowest cost function, fmin Is the best agent, P dest is specified as the target location.

[0098] Step 9, check whether the number of iterations reaches the maximum value T. If it has, stop the algorithm. If not, repeat steps 4 to 9.

[0099] The other parts of this embodiment are the same as any one of the above embodiments 1-4, so they are not repeated here.

[0100] Embodiment 6:

[0101] This embodiment is further optimized on the basis of any one of the above embodiments 1-5. In this embodiment, a PID controller based on OSDA is designed.

[0102] In the design of control systems, the most commonly used is the PID controller, which is a linear controller. PID control adjusts the controller parameters, that is, the proportional coefficient K P , integral coefficient K I and the differential coefficient K D By making adjustments, effective control effects can be achieved. The control equation of the PID controller consists of two parts: the initial given value i(t) and the actual output value o(t), that is, the control deviation: e(t) = i(t)-o(t);

[0103] The output equation u(t) after the PID controller is:

[0104] PID controller parameter tuning is the core content of control system design. The purpose of adjusting PID parameters is to make the characteristics of the controller and the controlled object match well to achieve the best vibration reduction effect. The traditional PID controller parameters cannot be changed after they are determined, that is, fixed parameters are used for control, and dynamic parameter adjustment cannot be achieved. Therefore, the spiral dynamic algorithm based on the opposite point is introduced to dynamically adjust the PID controller parameters, and the parameters are tuned based on the initial value parameters to improve the dynamic and static performance of the system.

[0105] The closed-loop block diagram of the PID control flexible manipulator based on OSDA is shown in the figure. Figure 2 shown.

[0106] Kp, ki and kd are defined as constants for the proportional, integral and derivative terms respectively. In this work, the output of interest is the angle of the center wheel shaft. Note the comparison of the center angle output response with the desired input. The difference between these signals is the error, which is applied to the SDA and the opposite point based spiral dynamics algorithm. Both optimization algorithms perform a search operation to minimize the error and thus determine a set of optimal parameters for PID control. The expressions for the SDA and OSDA cost functions are based on the error signal as shown in Equation (5). θdesired(i) and θ actual(i) are the expected input and center angle output responses of the flexible manipulator, respectively. N is the total number of sampled data of the error signal.

[0107]

[0108] The other parts of this embodiment are the same as any one of the above embodiments 1-5, so they are not repeated here.

[0109] Embodiment 7:

[0110] This embodiment is further optimized on the basis of any one of the above embodiments 1-6. In this embodiment, a composite control system is designed to suppress the residual vibration of the robot arm.

[0111] The optimal time-delay filter is used. The optimal time-delay filter can effectively filter out unnecessary frequency components in the input signal by convolution with the pulse sequence, thereby suppressing the residual vibration process of the flexible manipulator system for the first time outside the PID controller. In the closed-loop PID controller, the OSDA-based PID controller is used to suppress the residual vibration for the second time. OSDA solves the problem of dynamic changes in PID parameters, improves the vibration reduction performance, and has good robustness. The ways to couple the open-loop control based on the optimal time-delay filter and the PID closed-loop control based on OSDA are:

[0112] (1) Inner loop input filter: Introducing a time-delay filter into the feedback loop;

[0113] (2) External loop input filter: The time-delay filter is placed outside the feedback loop. If the internal loop is introduced, the originally stable closed-loop control system may become unstable. Therefore, an external loop composite control system is designed. The control structure diagram is as follows: Figure 3 shown.

[0114] The other parts of this embodiment are the same as any of the above embodiments 1-6, so they are not repeated here.

[0115] The above description is only a preferred embodiment of the present invention and does not limit the present invention in any form. Any simple modification or equivalent change made to the above embodiment based on the technical essence of the present invention shall fall within the protection scope of the present invention.

Claims

1. A method for setting a composite control system based on a time-delay filter and a PID controller, characterized in that: The following steps are involved: Establish the dynamic mathematical model of the flexible robotic arm; Design an optimal time-delay filter with minimum residual oscillation based on the traditional time-delay filter; Establish a mathematical model of the spiral dynamic algorithm based on the opposite point, and solve the PID controller parameters based on the spiral dynamic algorithm; An improved PID controller is designed based on the PID controller parameters and the mathematical model of the spiral dynamic algorithm based on the opposite point; By combining the optimal time-delay filter with the improved PID controller, a composite control system is designed to suppress the residual oscillation of the flexible manipulator. The method for establishing a mathematical model of a spiral dynamic algorithm based on opposite points comprises: The opposite point learning algorithm and the dynamic spiral algorithm are combined to establish a spiral dynamic algorithm model based on opposite points. The opposite point learning algorithm used is expressed as: v opp (i)=v mid (i)+(v o (i)-v mid (i))×rand (13); Among them, v o (i) is defined as follows: v o (i)=2×v mid (i)-v old (i) (14); Among them, v mid The definition is as follows: Among them, v opp is the opposite position of the ith agent, rand is a generated random number, and v old is the old position of the ith agent, v max and v min are the upper and lower bounds of the ith agent; SDA is an agent-based algorithm that mainly uses the spiral equation to move the agent from one position to another in a spiral; The spiral equation of the spiral dynamic algorithm used is: x i (t+1)=S(r,θ)x i (t)-(S(r,θ)-I)x * (t) (16); Among them, x i (t+1) is the updated position of the i-th search agent in the t-th iteration, x i (t) is the previous position of the i-th search agent in the t-th iteration, I represents the identity matrix, r represents the spiral radius, θ represents the spiral angle, and S(r,θ) represents the combination of the rotation matrix, which is defined by the radius r and the angle θ. * (t) represents the center point of the spiral form; The Opposition-Based Spiral Dynamic Algorithm (OSDA) is a new algorithm that uses equations (13)-(16); the specific steps are as follows: Step 1: Initialize the position X of the i-th agent i , the opposite position v of the i-th agent opp (i) and maximum iteration T; Step 2: Update the cost function f(X i ) and fitness function f(v opp (i)); Step 3: Determine the best individual agent X fmin ; With the minimum cost function f min The value is the best individual agent; the best individual agent is set to the target position P dest ; Step 4, update the position of the i-th agent using the spiral equation (16); Step 5, determine the opposite position of the updated position of the i-th agent according to equations (13)-(16); Step 6, check whether the algorithm has updated the positions of all agents; if so, proceed to step 8; if not, repeat steps 4-7; Step 7: Update the cost or fitness function f(X i ) and f(v opp (i)) value; Step 8, determine the best proxy X fmin , the agent has the lowest cost function, f min Is the best agent, P dest is designated as a target location; Step 9, check whether the number of iterations reaches the maximum value T; if it has, stop the algorithm; if not, repeat steps 4 to 9.

2. A method for setting a composite control system based on a time-delay filter and a PID controller according to claim 1, characterized in that: The method for designing an improved PID controller comprises: The mathematical model of the spiral dynamic algorithm based on the opposite point is introduced to dynamically adjust the parameters of the PID controller, and an improved PID controller with parameter adjustment based on the mathematical model of the spiral dynamic algorithm based on the opposite point is designed; The PID controller parameters include proportional coefficient, integral coefficient and differential coefficient.

3. A method for setting a composite control system based on a time-delay filter and a PID controller according to claim 1, characterized in that: The method of combining the optimal time-delay filter and the improved PID controller to design a composite control system for suppressing residual oscillation of the flexible manipulator comprises: The optimal time-delay filter is convolved with the pulse sequence to filter out unnecessary frequency components in the input signal and eliminate residual oscillations of the flexible manipulator system. After the optimal time-delay filter is initially filtered in the open loop, the PID controller improved by the mathematical model of the spiral dynamic algorithm based on the opposite point is used in the closed loop to effectively suppress the residual oscillation of the flexible manipulator for the second time. The open-loop control based on the optimal time-delay filter and the closed-loop control of the PID controller improved by the mathematical model of the spiral dynamic algorithm based on the opposite point are coupled; The optimal time-delay filter is introduced into the improved PID controller in an external loop mode, and a composite control system in an external loop mode is designed.

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