A high dynamic sliding mode predictive two-level control method based on error optimization strategy

Abstract

The present invention proposes a high-dynamic sliding mode predictive two-layer control method based on an error optimization strategy, and constructs a two-layer collaborative control architecture. The outer layer uses linearized model predictive control to generate an optimal reference trajectory that meets the performance index requirements in real time, thereby achieving the optimization of performance indicators while ensuring computational efficiency; the inner layer designs a discrete logarithmic sliding mode controller based on an accurate nonlinear model, proposes a rapidity improvement of the logarithmic sliding mode control, and designs a trajectory error optimization mechanism for the strong coupling characteristics of nonlinear systems such as the aircraft tether system. The error of the inner layer discrete logarithmic sliding mode control in tracking the optimal reference trajectory generated by the outer layer model predictive control is optimized, and the traditional planned trajectory tracking is converted into direct tracking of the expected trajectory, so as to achieve rapid and accurate tracking of the system output to the optimal reference signal.

Description

Technical Field

[0001] The present invention relates to the field of control technology, and in particular to a high dynamic sliding mode prediction double-layer control method based on an error optimization strategy. Background Art

[0002] In the field of tethered deployment control of aircraft, sliding mode control technology has become the mainstream method due to its strong robustness to parameter perturbations, external interference and model uncertainty. However, existing technologies have significant limitations: the classical linear sliding mode control converges slowly near the equilibrium point and is difficult to meet the needs of rapid response; although the terminal sliding mode control can achieve finite time convergence of the controlled system, the existence of singular terms in its controller limits its practical application; although the non-singular terminal sliding mode control solves the singularity problem, the global convergence speed still cannot meet the requirements of high-precision deployment tasks. In summary, traditional sliding mode control still has difficulties in realizing both constrained control and fast control of nonlinear systems, and it is difficult to take into account the optimality of the motion process when achieving system stabilization.

[0003] On the other hand, although model predictive control can explicitly handle the optimal control problem of input-output constrained systems by solving quadratic programming problems, when faced with the complex dynamic characteristics of multivariable, highly nonlinear, and strongly coupled aircraft tether systems, online solution of nonlinear programming problems will generate huge computational loads, seriously affecting real-time control performance and not conducive to the online deployment of model predictive control. More seriously, the existing model predictive control has a steady-state tracking deviation between the planned trajectory and the expected trajectory, that is, there is still a relative gap between the optimal planned trajectory generated by the model predictive control strategy and the expected trajectory after the tracking state is basically stable, which affects the real tracking error of the system, resulting in the actual control accuracy being difficult to meet the requirements of aircraft tether deployment, which is a serious constraint on aircraft deployment tasks that require precise control of tether tension and posture. Summary of the invention

[0004] In view of the problems existing in the prior art, the present invention proposes a high-dynamic sliding mode predictive two-layer control method based on logarithmic sliding mode control, model predictive control and error optimization, and constructs a two-layer collaborative control architecture. The outer layer adopts linearized model predictive control to generate the optimal reference trajectory that meets the performance index requirements in real time, and optimizes the performance index while ensuring computational efficiency; the inner layer designs a discrete logarithmic sliding mode controller based on an accurate nonlinear model, proposes a rapid improvement in the logarithmic sliding mode control, and designs a trajectory error optimization mechanism for the strong coupling characteristics of nonlinear systems such as the aircraft tether system. The error of the inner layer discrete logarithmic sliding mode control in tracking the optimal reference trajectory generated by the outer layer model predictive control is optimized, and the traditional planned trajectory tracking is converted into direct tracking of the expected trajectory, so as to achieve rapid and accurate tracking of the system output to the optimal reference signal.

[0005] The technical solution of the present invention is:

[0006] A high dynamic sliding mode predictive double-layer control method based on error optimization strategy comprises the following steps:

[0007] Step 1: Establish a nonlinear second-order system:

[0008]

[0009] in are the state variables of the nonlinear second-order system, yes The first derivative of yes The first-order derivative of and and their respective first-order and second-order derivatives can be measured; is the control signal of the nonlinear second-order system; is a known nonlinear second-order system dynamics function, are known input coefficients;

[0010] Step 2: Establish the discrete system equation of the nonlinear second-order system:

[0011]

[0012] in is the discrete system time mark, For the The discrete system state vector at each moment is , For the The discrete system state variables are for The first derivative of ; For the The discrete system state vector at each moment is ; For the Discrete system control signal at each moment; is the known discrete system state matrix, is the known discrete system coefficient matrix, is the compensation matrix of the known discrete system;

[0013] Step 3: Use the model predictive control method to plan the discrete system established in step 2 and obtain the optimal control signal based on the discrete system equation and predicted status ;

[0014] Step 4: According to the predicted status obtained in step 3 , establish a discrete sliding surface containing logarithmic terms:

[0015]

[0016] in is the designed discrete sliding surface containing logarithmic terms, is the natural logarithm function, , , All are set normal numbers; is a symbolic function; is the position tracking error of the discrete system, for The derivative of represents the velocity tracking error of the discrete system, where

[0017]

[0018] In the formula, is the command signal, The adjustment function is set as:

[0019]

[0020] For the moment set;

[0021] Step 5: Based on the discrete sliding mode surface containing logarithmic terms designed in step 4, a discrete logarithmic sliding mode control strategy is established:

[0022]

[0023] in is the discrete logarithmic sliding mode control output, are the known input coefficients of the discrete system, is a known dynamical function of the discrete system, is the sampling interval of the discrete system, yes The second-order derivative of For switching gain.

[0024] Furthermore, in step 3, the specific process of using the model predictive control method to plan the discrete system established in step 2 is:

[0025] Setting performance targets for discrete systems and command signals ; The model predictive control method is used to solve the optimization problem under the set constraints and obtain the first The optimal control signal based on the discrete system equation at each moment and predicted status .

[0026] Furthermore, in step 3, the performance index is a continuous, differentiable, positive definite function; the set constraints include state constraints and input constraints.

[0027] Further, in step 4, when at time 0, the adjustment function value is 1, and when at At time and later, the regulation function value is 0, driving the discrete system state Fast and accurate tracking of command signals .

[0028] Furthermore, in step 5, a differential solver based on a superhelical algorithm is used to solve Perform a derivative operation.

[0029] Beneficial effects:

[0030] The present invention proposes a high dynamic sliding mode predictive double-layer control method based on error optimization strategy, which combines the rapidity and optimality of linear model predictive control with the rapidity and robustness of logarithmic sliding mode control, and can realize rapid optimal control of nonlinear control systems. Specifically, it has the following effects:

[0031] The method includes a predictive planning step. The control planning step based on the model predictive control principle can ensure that the reference signal meets the input and output constraints of the controlled system and that the control process is optimal relative to the performance index.

[0032] Compared with traditional predictive tracking control, the error optimization strategy adopted in this method solves the steady-state error problem between the planned trajectory generated by the prediction and the desired trajectory, achieves faster tracking of the desired trajectory and improves the control accuracy of the nonlinear control system.

[0033] This method establishes a discrete sliding surface containing logarithmic terms, which can be used in discrete control systems. Linear terms are added to the discrete sliding surface, and the sliding surface has a global large slope on the phase plane, thereby significantly increasing the dynamic performance of the sliding surface far from the equilibrium point.

[0034] This method further adopts a differential solver based on the superhelix algorithm to achieve fast and accurate estimation of the error signal and its derivative in the sliding surface; in this method, the nonlinear term in the sliding surface suppresses high-frequency noise, and the integral term compensates for the signal derivative, thereby improving the finite time convergence and noise resistance capabilities, and is suitable for occasions with certain requirements on convergence time and high robustness.

[0035] Additional aspects and advantages of the present invention will be given in part in the following description and in part will be obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] The above and / or additional aspects and advantages of the present invention will become apparent and easily understood from the description of the embodiments in conjunction with the following drawings, in which:

[0037] Figure 1 : The logical structure diagram of the high dynamic sliding mode prediction double-layer control method based on error optimization strategy proposed in the present invention;

[0038] Figure 2 : Phase plane comparison diagram of the traditional logarithmic sliding mode manifold and the logarithmic sliding mode manifold proposed by the present invention;

[0039] Figure 3 : The tracking error of the first joint desired signal output by the system in the embodiment;

[0040] Figure 4 : The tracking error of the desired signal of the second joint output by the system in the embodiment;

[0041] Figure 5 : The tracking error of the system output to the expected signal of the first joint in the traditional scheme;

[0042] Figure 6 : The tracking error of the system output to the desired signal of the second joint in the traditional scheme. DETAILED DESCRIPTION

[0043] Embodiments of the present invention are described in detail below. The embodiments are exemplary and intended to be used to explain the present invention, but should not be construed as limiting the present invention.

[0044] Embodiment 1:

[0045] The high dynamic sliding mode prediction double-layer control method based on the error optimization strategy proposed in this embodiment can not only ensure that the motion process of the controlled system is approximately optimal, but also improve the convergence speed of the logarithmic sliding mode controller, and generalize the logarithmic sliding mode control to the discrete time domain. At the same time, the error between the planned trajectory and the expected trajectory is reduced, so that the error finally becomes the difference between the current trajectory and the expected trajectory, rather than the difference between the current trajectory and the planned trajectory, thereby improving the tracking accuracy of the system; in the process of designing the controller, a tracking differentiator is introduced to solve the problem of fast and accurate estimation of unknown nonlinear quantities and their derivatives in the control process, and finally a reasonable compromise between optimization speed and control efficiency is achieved; specifically, the following steps are included:

[0046] Step 1: Establish a nonlinear second-order system, that is, the system equation of the controlled object. For the application of tethered deployment control of spacecraft, a typical nonlinear second-order system is a two-degree-of-freedom manipulator.

[0047] The nonlinear second-order system is expressed as:

[0048] (1)

[0049] in are the state variables of the nonlinear second-order system, yes The first derivative of yes The first-order derivative of and and their respective first-order and second-order derivatives can be measured; for a second-order system, Usually refers to information such as position and angle. Usually refers to information such as speed and angular velocity; is the control signal of the nonlinear second-order system; is a known nonlinear second-order system dynamics function, are known input coefficients;

[0050] Step 2: Establish the discrete system equation of the nonlinear second-order system:

[0051] (2)

[0052] in is the discrete system time mark, For the The discrete system state vector at each moment is , For the The discrete system state variables are for The first derivative of ; For the The discrete system state vector at each moment is ; For the Discrete system control signal at each moment; is the known discrete system state matrix, is the known discrete system coefficient matrix, is the compensation matrix of the known discrete system;

[0053] Step 3: Use the model predictive control method to plan the discrete system established in step 2, including the following process:

[0054] Setting performance targets for discrete systems and command signals , where performance indicators is a continuous, differentiable, positive definite function, and its common form is a quadratic function.

[0055] The command signal That is, the desired state variables of a discrete system, such as the joint angles of a two-degree-of-freedom robotic arm.

[0056] Using the traditional model predictive control method, we can solve the optimization problem under the set constraints to obtain the first At each moment, the optimal control signal based on the discrete system equation (2) is and predicted status The set constraints include state constraints and input constraints, such as the limit constraints of the joint angles of a two-degree-of-freedom manipulator and the limit constraints of the input joint torques.

[0057] Step 4: The predicted state obtained by the model predictive control in step 3 , establish a discrete sliding surface containing logarithmic terms:

[0058] (3)

[0059] in is the designed discrete sliding surface containing logarithmic terms, is the natural logarithm function, , , All are set normal numbers; is a symbolic function; is the position tracking error of the discrete system, for The derivative of represents the velocity tracking error of the discrete system, where

[0060]

[0061] In the formula, is the command signal, The adjustment function is set as:

[0062]

[0063] is the set moment. Through this adjustment function, when it is at time 0, the adjustment function value is 1, and when it is at At time and later, the adjustment function value is 0, so and The error between is adjusted to 0, driving the discrete system state Fast and accurate tracking of command signals This function solves the problem of steady-state error between the planned trajectory generated by model predictive control and the given desired trajectory, and improves the tracking accuracy of the system.

[0064] Step 5: Based on the discrete sliding mode surface containing logarithmic terms designed in step 4, a discrete logarithmic sliding mode control strategy is established according to the equivalent control method:

[0065] (4)

[0066] in is the discrete logarithmic sliding mode control output, are the known input coefficients of the discrete system, is a known dynamical function of the discrete system, is the sampling interval of the discrete system, yes The second-order derivative of is the switching gain used to provide the desired robustness.

[0067] For the above control strategy, the following provides its stability proof:

[0068] First define , for a discrete system, if the discrete error satisfies the condition , which means that once the system reaches the sliding surface, it will always remain on the sliding surface, thus achieving global asymptotic convergence of the sliding variables. For the logarithmic sliding mode control strategy (4) proposed above, the next moment of the sliding surface (3) can be expressed as

[0069] (5)

[0070] For the above nonlinear second-order system (1), for the error , Define the error system as

[0071] (6)

[0072] Its discrete form is:

[0073] (7)

[0074] Substituting equation (1) and equation (7) into have to:

[0075] (8)

[0076] Finally, substituting (4) into (8) we get

[0077] Therefore, the stability of the controller is proved.

[0078] Furthermore, in the discrete logarithmic sliding mode control strategy of step 5, it is necessary to Perform a derivative operation, and , it is difficult to directly derive this term and there is a certain error. In order to avoid the reduction of system control accuracy due to derivative estimation error during the control process, this embodiment further adopts a differential solver based on a superhelical algorithm to process this term to ensure accurate convergence within a finite time in the absence of noise. The main steps are as follows:

[0079] Set the input signal is Defined function, input signal + Noise, is the base signal, and The first derivative of Satisfying the Lipschitz condition is , is the Lipschitz constant; the main goal of the algorithm is to design a differentiator to estimate in real time In and its derivatives , and must meet the following requirements:

[0080] Finite time convergence: When there is no noise, the estimate converges exactly, and the convergence time is mainly determined by the parameters and initial errors;

[0081] Robustness: In the presence of noise, the estimation error is correlated with the noise value and remains bounded.

[0082] Design support system ,in is the control input, for We define the error The main purpose is to make and When entering the sliding mode, we can get and , which means and The system can be written as

[0083] (9)

[0084] The function It may not be smooth, but its derivative exists, because it satisfies Lipschitz continuity, so we can get the system:

[0085] (10)

[0086] in as well as To set a constant.

[0087] Mainly through nonlinear terms and the integral term Achieve fast convergence. and is a constant, according to the Lipschitz constant Adjust to ensure limited time stability. and is bounded. The equation for the differentiator is

[0088] (11)

[0089] in It is the base signal Estimated value, is the derivative The estimated value of and can be regarded as the output of the differential solver; thus, in the subsequent controller design and application, a more accurate and .

[0090] Using this method, As ,Will As , an accurate solution can be achieved.

[0091] Embodiment 2:

[0092] This embodiment uses the double-layer control method proposed in the present invention to achieve high-precision trajectory tracking for the two-degree-of-freedom manipulator trajectory tracking control requirements during the tether deployment process of the spacecraft. The control target is that the end effector of the manipulator moves along the specified three-dimensional space trajectory, and the tracking error is required to be less than 0.1mm. The main challenges are that the dynamic model of the manipulator is nonlinear, coupled and uncertain. The sources of disturbance include friction, joint servo error and external interference (such as load change).

[0093] The specific process is:

[0094] For a two-degree-of-freedom robotic arm dynamics system:

[0095] (12)

[0096] in, is the joint control torque, and is the matrix related to the system dynamics, is the state vector describing the joint angles of the robot arm.

[0097] (13)

[0098] (14)

[0099] (15)

[0100] in, are the masses of the two links of the robotic arm respectively; are the distances from the connection to the mass centers of the two connecting rods; are the lengths of the two connecting rods of the robotic arm; are the moments of inertia of the two links of the robotic arm; are the joint angles of the two links of the robotic arm.

[0101] Define the state vector , control variables , output variable , the state equation of the robot arm is:

[0102] (16)

[0103] (17)

[0104] For the robotic arm system, the above system can be linearized by finding the gradient matrix of the required working point, assuming that the expectation of the state variable is , whose derivative with respect to time is , the control variable is , the Jacobian matrix of the state variables is used to linearize the system, and the linearized system state variables are defined as , the linearized control variable is , so the formula is:

[0105] (18)

[0106] The constant term is Therefore, the final state space equation can be linearized and written as

[0107] (19)

[0108] in .

[0109] Next, we need to discretize the state space equation of the system, mainly by multiplying both sides of the equation by the matrix exponential The method is used for discretization. Assuming the sampling period is ,exist At this moment, discretization is performed to obtain:

[0110] (20)

[0111] The equation can be written as:

[0112] (twenty one)

[0113] Multiply both sides of the above equation by , the continuous linear kinetic model is obtained as

[0114] (twenty two)

[0115] Define the discrete time index as , in the above formula, use replace , then

[0116] (twenty three)

[0117] Therefore, the discrete-time linearized state space equation can finally be written as:

[0118] (twenty four)

[0119] in .

[0120] The outer layer of the control method adopts model predictive control, and the planning goal is based on a given trajectory point sequence (such as path key points and time constraints) to generate the expected reference trajectory of the robot arm joint angle. The performance indicators are:

[0121] (25)

[0122] in, For joint status, is the target state, is the control input (joint torque), and is the weight coefficient, is the number of trajectory points.

[0123] The constraints mainly include the range of joint angles. , joint speed limit , joint acceleration limit .

[0124] The inner layer of the control method is a discrete sliding mode control method containing logarithmic terms. The control goal is to achieve real-time tracking of joint trajectories while suppressing interference and model uncertainty. The design definition of the sliding surface is mainly a combination of logarithmic sliding mode and linear terms.

[0125] (26)

[0126] in is the designed discrete sliding surface containing logarithmic terms, is the natural logarithm function, , , All are set normal numbers; is a symbolic function; is the position tracking error, for The derivative of represents the velocity tracking error;

[0127]

[0128] In the formula, The adjustment function is set as:

[0129]

[0130] And estimate by tracking the differentiator The value of and its derivative.

[0131] The discrete logarithmic sliding mode control strategy is established according to the equivalent control method:

[0132] (27)

[0133] The collaborative mechanism of the inner and outer layers enables the two layers of data to interact. The reference trajectory generated by the outer model prediction is updated in real time, and the inner sliding mode controller performs tracking at a faster speed. The entire control process mainly relies on model predictive control to optimize the trajectory path. The sliding mode controller quickly performs trajectory tracking. If the actual state deviates too much from the reference trajectory, it will be fed back to the model predictive controller to adjust the trajectory planning.

[0134] In this embodiment, the load of the two-degree-of-freedom robotic arm is 2kg. They are 1m and 0.8m respectively. The trajectory task is to enable the end effector to track stably and accurately. First, the model is built to obtain the dynamic parameters of the robot arm; a nonlinear state space model is established for use in model predictive control, and then trajectory planning uses model predictive control to generate the expected trajectory of each joint of the robot arm. Next, trajectory tracking is performed, and the reference trajectory is passed to the sliding mode controller to adjust the input torque of the joint drive motor in real time to achieve trajectory tracking. Finally, data collection and analysis are performed to record the error between the actual trajectory of the end effector and the reference trajectory.

[0135] By recording the experimental results, the trajectory tracking accuracy, disturbance suppression effect, control performance comparison, etc. are calculated. The tracking error of the system output to the desired signal after the control method of the present invention is as follows: Figure 3 and Figure 4As shown in Figure 2, the error after amplification is about 1e-4, while the tracking error of the system output to the desired signal under the traditional sliding mode predictive control scheme is as follows: Figure 5 and Figure 6 As shown, the error after amplification is about 1e-3. Obviously, the scheme of the present invention obtains a tracking error that is superior to the traditional scheme, which shows that the advantages of the error optimization strategy are mainly high-precision trajectory tracking, and the trajectory tracking accuracy of the robot arm is significantly improved through the rapid response and global optimization of the sliding mode control; in addition, the method of the present invention has strong anti-interference ability, and the inner sliding mode control is robust to external disturbances and parameter uncertainties; and it has good real-time performance, and the two-layer architecture has a clear division of labor, which reduces the computational complexity.

[0136] Although the embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and are not to be construed as limitations on the present invention. A person skilled in the art may change, modify, replace and modify the above embodiments within the scope of the present invention without departing from the principles and intent of the present invention.

Claims

1. A high dynamic sliding mode predictive double-layer control method based on error optimization strategy, characterized by: The following steps are involved: Step 1: Establish a nonlinear second-order system: in are the state variables of the nonlinear second-order system, yes The first derivative of yes The first-order derivative of and and their respective first-order and second-order derivatives can be measured; is the control signal of the nonlinear second-order system; is a known nonlinear second-order system dynamics function, are known input coefficients; Step 2: Establish the discrete system equation of the nonlinear second-order system: in is the discrete system time mark, For the The discrete system state vector at each moment is , For the The discrete system state variables are for The first derivative of ; For the The discrete system state vector at each moment is ; For the Discrete system control signal at each moment; is the known discrete system state matrix, is the known discrete system coefficient matrix, is the compensation matrix of the known discrete system; Step 3: Use the model predictive control method to plan the discrete system established in step 2 and obtain the optimal control signal based on the discrete system equation and predicted status ; Step 4: According to the predicted status obtained in step 3 , establish a discrete sliding surface containing logarithmic terms: in is the designed discrete sliding surface containing logarithmic terms, is the natural logarithm function, , , All are set normal numbers; is a symbolic function; is the position tracking error of the discrete system, for The derivative of represents the velocity tracking error of the discrete system, where In the formula, is the command signal, The adjustment function is set as: For the moment set; Step 5: Based on the discrete sliding mode surface containing logarithmic terms designed in step 4, a discrete logarithmic sliding mode control strategy is established: in is the discrete logarithmic sliding mode control output, are the known input coefficients of the discrete system, is a known dynamical function of the discrete system, is the sampling interval of the discrete system, yes The second-order derivative of For switching gain.

2. According to claim 1, a high dynamic sliding mode predictive double-layer control method based on error optimization strategy is characterized by: In step 3, the specific process of using the model predictive control method to plan the discrete system established in step 2 is: Setting performance targets for discrete systems and command signals ; The model predictive control method is used to solve the optimization problem under the set constraints and obtain the first The optimal control signal based on the discrete system equation at each moment and predicted status .

3. According to claim 2, a high dynamic sliding mode predictive double-layer control method based on error optimization strategy is characterized by: In step 3, the performance index is a continuous, differentiable, positive definite function; the set constraints include state constraints and input constraints.

4. According to claim 1, a high dynamic sliding mode predictive double-layer control method based on error optimization strategy is characterized by: In step 4, when it is at time 0, the adjustment function value is 1, and when it is at At time and later, the regulation function value is 0, driving the discrete system state Fast and accurate tracking of command signals .

5. According to claim 1, a high dynamic sliding mode predictive double-layer control method based on error optimization strategy is characterized by: In step 5, a differential solver based on the superhelical algorithm is used to solve Perform a derivative operation.

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