PID (Proportion Integration Differentiation) tracking control method fusing intelligent parameter adjustment

Abstract

The invention discloses a nonlinear PID control method based on intelligent element driving and a fault-tolerant control system thereof, and belongs to the technical field of intelligent control. According to the method, three behavior mapping mechanisms of punishment, memory and prediction are introduced, a traditional PID controller structure is expanded, a compound error signal is constructed, and a dual-channel control strategy of instinct response and learning response is designed. The controller provided by the invention has adaptive gain adjustment capability, a dynamic adjustment law is constructed in combination with a Lyapunov stability theory, and robust control without model information is realized. Meanwhile, a fault-tolerant mechanism is provided for correcting control signal input by considering the situation of performance degradation of an actual actuator, so that the stability and tracking precision of a control system under non-ideal conditions are improved. The control method is suitable for complex nonlinear object control scenes such as underwater robots, mobile robots and parallel Delta robots.

Description

Technical Field

[0001] This invention relates to the field of intelligent control and actuator fault-tolerant control technology, specifically a nonlinear PID fault-tolerant control method based on intelligent element-driven control. It is applicable to the control of nonlinear multiple-input multiple-output (MIMO) objects, and is particularly suitable for scenarios with high requirements for control accuracy and reliability, such as underwater robot systems, ground mobile robot systems, multi-agent control systems, and servo motor control. Background Technology

[0002] Traditional PID controllers are widely used in industrial process control due to their simple structure and high engineering feasibility. However, in real-world complex nonlinear systems, conventional PID controllers have the following shortcomings:

[0003] 1. Fixed gain, difficult to adjust: Fixed proportional-integral-derivative parameters are difficult to adapt to changes in the dynamic characteristics of the system, and traditional error signals fail to reflect intelligent behaviors such as "experience" and "trend" in human adjustment;

[0004] 2. Runaway due to strong nonlinearity: Linear PID controllers have difficulty handling and dealing with strong nonlinear characteristics, which may lead to system malfunctions when strong nonlinearity exists in the system.

[0005] 3. Integral saturation phenomenon: The integral term accumulates over time, eventually exceeding the actuator's execution threshold and causing saturation.

[0006] 4. Lack of fault tolerance mechanism and insufficient disturbance suppression capability: When the actuator degrades or external disturbances occur, the performance of PID control drops rapidly;

[0007] In recent years, although "intelligent PID" based on methods such as neural networks and fuzzy logic has achieved improvements in some performance indicators, it generally suffers from problems such as complex structure, strong training dependence, and difficulty in proving stability.

[0008] Therefore, there is an urgent need for a control method that has a clear structure, requires no training, and possesses intelligent adjustment capabilities and robustness to solve the above problems. Summary of the Invention

[0009] The purpose of this invention is to overcome the shortcomings and deficiencies of existing technologies, such as low control accuracy, strong model dependence, and insufficient fault tolerance. It provides a nonlinear PID control method with behavioral intelligence characteristics for complex nonlinear objects. This method, through composite error construction and dual-channel dynamic fusion control technology, can adapt to closed-loop regulation problems in multi-input multi-output systems under conditions of strong nonlinear coupling, structural uncertainty, actuator degradation, and disturbances. This method can ensure that the system output achieves stable convergence to the desired trajectory under model-free or weakly modeled conditions, thereby improving the accuracy, robustness, and intelligence of task execution.

[0010] The main innovative points of this invention are as follows:

[0011] 1. Intelligent control mechanism driven by composite error. A composite error signal construction method based on three intelligent behaviors of "punishment-memory-prediction" is proposed to realize dynamic amplification, saturation suppression and feedforward prediction of error at different stages. It has intelligent features and does not require training.

[0012] 2. Dual-channel behavior mapping control structure. A dual-channel PID regulation mechanism consisting of "instinctive response + learned response" is proposed. Combined with behavior-driven fusion weights, dynamic behavior switching is achieved, simulating human control logic and significantly improving the system's adaptability and flexibility.

[0013] 3. Adaptive Gain Adjustment Based on Lyapunov Stability. A simple yet provably stable adaptive gain law is introduced to achieve online real-time gain adjustment of the learning controller, ensuring asymptotic stability of the closed-loop system and compatibility with uncertain systems.

[0014] 4. Fault-tolerant actuator modeling module and anti-degradation control strategy. Construct an actuator modeling mechanism with efficiency factor and disturbance term to enhance the system's robustness to actuator degradation, external disturbances, and control error propagation, adapting to the actual deployment needs of engineering projects.

[0015] Compared with the prior art, the present invention has the following advantages:

[0016] 1. Strong Adaptability: This invention introduces a near-intelligent adjustment mechanism on the basis of the traditional PID control framework, which can dynamically correct the PID parameters according to the real-time error and the error change trend, so that the control system has good adaptability and is suitable for controlled objects with uncertain structure or strong dynamic changes in environment.

[0017] 2. High control precision and fast response speed: Through the error-driven parameter adjustment mechanism, the system response can quickly approach the expected value, significantly reducing overshoot and steady-state error, and improving tracking accuracy and system convergence speed.

[0018] 3. Simple structure and easy to implement: This invention retains the basic form of a PID controller, and the intelligent adjustment module is compactly designed, making it easy to embed into existing control platforms and suitable for practical engineering deployment.

[0019] 4. Strong anti-interference capability and good robustness: Since the controller parameters can be dynamically adjusted according to the error, the system can effectively suppress the adverse effects of external disturbances or modeling errors, and improve the overall robustness of the control system. Attached Figure Description

[0020] Figure 1 This is a structural diagram of an underwater robot;

[0021] Figure 2 This is a structural diagram of a mobile robot;

[0022] Figure 3 This is a structural diagram of a parallel Delta robot;

[0023] Figure 4 This is a diagram showing the tracking process of the joint positions of the robotic arm under the proposed method and the comparison method;

[0024] Figure 5 This is a comparison chart of the control inputs of the proposed method and the comparison method;

[0025] Figure 6 This is a comparison chart of virtual parameters.

[0026] Figure 4 This shows that asymptotic tracking can be achieved under the proposed control scheme, while adaptive linear PID can only ensure bounded tracking at all times. Figure 5 This indicates that the control input is continuous and bounded, and has a smaller amplitude compared to linear PID. Figure 6 The results show that, under the control algorithm, the virtual parameters are bounded, while those of the linear PID controller tend to increase. This further demonstrates the superiority of the proposed method. Detailed Implementation

[0027] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments.

[0028] Consider a multi-joint rigid-link robot manipulator with the following joint space dynamics. Its mathematical expression is:

[0029] (1)

[0030] in, and These represent joint position, velocity, and acceleration, respectively. The inertia matrix represents a symmetric and positive definite matrix. It is a centripetal and Coriolis matrix; Represents gravity; It is an interference vector. Through It affects the system's input signal.

[0031] To achieve the goal, the following assumptions are made:

[0032] Assumption 1: Some rough structure information can be used to allow the extraction of unknown constants. and known functions , making when ,in Bounded only if When it is bounded.

[0033] Based on the above system structure, we can conclude that:

[0034] (2)

[0035] Using the mean value theorem, we can derive the following: ,in:

[0036] (3)

[0037] Because unexpected actuator failures may occur during the long-term operation of a real system, the actual control input... and design input No longer the same, but in and There exists a relationship described by equation (13) in the power specification. Therefore, we can obtain:

[0038] (4)

[0039] in, It is a bounded time-varying diagonal matrix (with a bounded rate of change). Therefore, the relation is... = and Established. Set up. and As described, although the error is defined However, from (4), we can conclude that:

[0040] (5)

[0041] in:

[0042] (6)

[0043] Based on assumption 1, we can conclude that:

[0044] (7)

[0045] in, , and .

[0046] Right now:

[0047] (8)

[0048] in, , .

[0049] A PID-like tracking control for an IE-driven robot system (1) is proposed as follows:

[0050] (9)

[0051] in:

[0052] (10)

[0053] (11)

[0054] In the formula, The adaptive law is:

[0055] (12)

[0056] Theorem 1: If a control scheme 9 with an adaptive law (12) is applied, where the weighting factor is... If it is a freely chosen constant, then asymptotic tracking is achieved.

[0057] Proof: From (5) and (9), we can obtain:

[0058] (13)

[0059] in, It is symmetric positive definite. The candidate Lyapunov function is selected as follows:

[0060] (14)

[0061] The estimation error is defined as follows: ,in And c is a virtual parameter defined below (17). Taking the time derivative of (14) along (14), we get:

[0062] (15)

[0063] in, Similarly, there are:

[0064] (16)

[0065] in, ,and:

[0066] (17)

[0067] in, It is a computable scalar function. Therefore, we can conclude that:

[0068] (18)

[0069] Using the control scheme and update rule steps, we can obtain:

[0070] (19)

[0071] in, .when satisfy Then, by using a similar argument to that in the proof of Theorem 1, we can arrive at the conclusion that asymptotic joint tracking can be achieved.

[0072] experiment:

[0073] Consider a two-jointed rigid link robot with the following joint space dynamics.

[0074]

[0075] in, It is the generalized inertia matrix. Represents the Coriolis force and centrifugal force. Represents the gravitational vector. This indicates an unknown external disturbance. These represent the link position, velocity, and acceleration vectors, respectively. Through Affects the control input signal of the system, This represents a vector of unknown parameters. Specifically, the values ​​assigned to these variables are as follows:

[0076]

[0077]

[0078]

[0079]

[0080] and in .

[0081] The actuator efficiency factor matrix is ​​defined in the following form:

[0082]

[0083]

[0084] Among them, parameters , .

[0085] The desired trajectory is set as follows:

[0086]

[0087] The initial conditions are set as follows: , .

[0088] The numerical simulation results are shown in Figures 4 to 6.

[0089] Figure 4 This shows that asymptotic tracking can be achieved under the proposed control scheme, while adaptive linear PID can only ensure bounded tracking at all times. Figure 5 This indicates that the control input is continuous and bounded, and has a smaller amplitude compared to linear PID. Figure 6 The results show that, under the control algorithm, the virtual parameters are bounded, while those of the linear PID controller tend to increase. This further demonstrates the superiority of the proposed method.

Claims

1. A PID tracking control method of fusion type intelligent parameter adjustment, characterized in that, Comprising the following steps: Step one: Establishing a nonlinear system: (1)， where, is the system state; is the system output; represents an unknown and possibly time-varying parameter vector; is the actual input to the control system; is a smooth but unknown non-affine function vector; Considering actuator fault situation: (2)， wherein is a diagonal matrix; is a completely unadjustable controlled uncertainty partition; Step two: Designing filter signal: (3)， wherein to is a normal number such that the polynomial has a negative real part; is a reference trajectory; denotes the system tracking error; Step three: Constructing the compound error signal The compound error is composed of a penalty term, a memory term and a prediction term, defined as follows: (4) ， wherein, is a non-negative weighting factor; a penalty term is a penalizing action with certain limitations; a memory term is an experience-dependent element; a prediction term is the first derivative of the error, which is approximated by a first-order filter Step four: Designing adaptive weight: (5)， Parameter updating law: (6)， wherein, is a positive scalar function satisfying is a positive scalar function satisfying ; Step five: Generating final control quantity: (7)， wherein ; , , reflecting the controller weight distribution mechanism.

2. The fusion-based intelligent parameter-adjusted PID tracking control method according to claim 1, characterized in that, The penalty term function in Step three is Misbehavior penalty, allowing some restriction on the feedback signal z is chosen as: Considering actuator fault situation: (8)， such that the non-affine function is represented as (9)， wherein is an intermediate variable vector, is an unknown time-varying control gain matrix, the nonlinear system being represented as: (10)， Define the tracking error , which can be derived as where is the reference trajectory, we introduce a filtering variable z as follows (11)， wherein to is a positive constant such that the polynomial has a negative real part.

3. The fusion-based intelligent parameter-adjusted PID tracking control method according to claim 1, characterized in that, Constructing a composite error signal , which is composed of a penalty term, a memory term and a prediction term, defined as follows: (12)， where, is a non-negative weighting factor; the penalty term is a penalizing action with certain limitations; the memory term is an experience-dependent element; the prediction term is the first derivative of the error, which is approximated by a first-order filter.

4. The fusion-based intelligent parameter-adjusted PID tracking control method according to claim 1, characterized in that, Summarize / convert By properly weighting the IEs, a new signal is generated carrying the intelligent component ; using such signal , using as a control signal directly fed into the actuator, it is important to further process E by robust and adaptive weighting factors and , as well as trust / credit factors and to generate the final control action ; wherein: (13)。 5. The fusion-based intelligent parameter-adjusted PID tracking control method according to claim 1, characterized in that, The weighting factor in step five , satisfies: (14)， wherein, is a normal number, indicating the lower limit of the reliability of the response obtained, the selection regarding the trust factor is: (15)， wherein , is a selection constant.

6. The fusion-based intelligent parameter-adjusted PID tracking control method according to claim 1, wherein, Final control quantity in step five , the credibility of the weight and online update, to build the following embedded intelligent components of the PID control: (16)， Wherein, ， wherein, , are robust and adaptively adjusted weighting factors, respectively, in handling the varying nature of the dynamic system.

7. The fusion-based intelligent parameter-adjusted PID tracking control method according to claim 1, wherein, which in step three and represent forms of experiential accumulation and punishment for misbehavior, respectively; will be described below. and is represented by: (17)， Wherein: ， 。 8. The fusion-based intelligent parameter-adjusted PID tracking control method according to claim 1, wherein, The adaptive weight in step four satisfies the following form: (18)， The gain adaptive law satisfies: (19)， wherein, is a positive scalar function satisfying is a positive scalar function satisfying .

9. The fusion-based intelligent parameter-adjusted PID tracking control method according to claim 1, wherein, The adaptive law in step four is designed based on Lyapunov stability, and the target Lyapunov function is defined as: (20)， wherein, is a symmetric positive definite matrix; is a virtual parameter estimation error; The derivative with respect to time is: (21)， wherein ; the uncertain function can be expressed as: (22)， wherein , , is an unknown constant, and is a calculable scalar function; Therefore: (23)， That is: (24) The control law and the adaptive law together cause i.e. (25)， To ensure the boundedness of the closed-loop signal.

10. The fusion-based intelligent parameter-adjusted PID tracking control method according to claim 1, wherein, The actuator model that the control signal passes through in step five has a natural reaction and learning reaction structure, and finally: (26)， wherein ; , reflecting the controller weight distribution mechanism.

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