scholarly journals A Novel Method of Prescribed Constraint Control Without Initial Condition of Nonlinear Systems

2021 ◽  
Author(s):  
Hui Liu ◽  
Xiaohua Li ◽  
Xiaoping Liu
Keyword(s):  
Nonlinear Systems ◽  
Control Strategy ◽  
Control Method ◽  
Actuator Saturation ◽  
Initial Conditions ◽  
Setting Time ◽  
Tracking Error ◽  
Initial Condition ◽  
Constraint Control ◽  
Performance Constraint

Abstract A novel constraint control strategy without initial condition of constrained variables is investigated based on backstepping technique for nonlinear systems. In this paper, the novel constraint control strategy is presented for a class of strict-feedback nonlinear systems with actuator saturation and external disturbances by using a nonlinear mapping and a novel performance constraint function. In this control strategy, there are two prescribed constraint functions, the design of these functions is not related to the initial conditions of the constrained variables. Unlike the existing constraint control method without initial condition, the proposed method gives a new solution. It can guarantee that the constraint variable gets into a prescribed constraint region from any initial value no later than a setting time. And the setting time is a design parameter, it can be set arbitrarily. A prescribed performance constraint tracking controller is designed in this paper. It can make that the tracking error of the nonlinear system is constrained to a given region no later than the given setting time, and the transient and steady state performance of the system are ensured. Finally, the proposed method is compared with the existing method, the effectiveness and superiority of the proposed method are demonstrated by two practical examples.

scholarly journals Almost Disturbance Decoupling for a Class of Fractional-Order Nonlinear Systems with Zero Dynamics

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Xiaoping Liu ◽  
Yajing Zhao ◽  
Caiyun Wang ◽  
Huanqing Wang ◽  
Yucheng Zhou
Keyword(s):  
Nonlinear Systems ◽  
Fractional Order ◽  
Initial Conditions ◽  
Design Method ◽  
Tracking Error ◽  
Lyapunov Stability Theory ◽  
External Disturbances ◽  
Output Tracking ◽  
Almost Disturbance Decoupling ◽  
Disturbance Decoupling

The problem of almost disturbance decoupling is addressed for fractional-order nonlinear systems. A new definition for the norm is proposed to describe the effect of disturbances on the output tracking error for fractional-order systems. Based on the Lyapunov stability theory and the backstepping design method, a tracking controller is constructed to make the output tracking error converge to zero without external disturbances and to attenuate the effect of disturbances on the tracking error at zero initial conditions. In order to validate these theoretical results, a numerical example and two practical examples are given.

scholarly journals A hybrid control strategy for grinding and polishing robot based on adaptive impedance control

2021 ◽  
Vol 13 (3) ◽  
pp. 168781402110040
Author(s):  
Haibo Zhou ◽  
Shitai Ma ◽  
Guilian Wang ◽  
Yuxin Deng ◽  
Zhenzhong Liu
Keyword(s):  
Control Strategy ◽  
Control Method ◽  
Hybrid Control ◽  
Impedance Control ◽  
Tracking Error ◽  
Position Tracking ◽  
Robot System ◽  
Adaptive Impedance Control ◽  
The Impact ◽  
Grinding And Polishing

In order to realize the active and compliant motion of the robot, it is necessary to eliminate the impact caused by processing contact. A hybrid control strategy for grinding and polishing robot is proposed based on adaptive impedance control. Firstly, an electrically driven linear end effector is designed for the robot system. The macro and micro motions control model of the robot is established, by using impedance control method, which based on the contact model of the robot system and the environment. Secondly, the active compliance method is adopted to establish adaptive force control and position tracking control strategies under impact conditions. Finally, the algorithm is verified by Simulink simulation and experiment. The simulation results are as follows: The position tracking error does not exceed 0.009 m, and the steady-state error of the force is less than 1 N. The experimental results show that the motion curve coincides with the surface morphology of the workpiece, and the contact force is stable at 10 ± 3 N. The algorithm can realize more accurate position tracking and force tracking, and provide a reference for the grinding and polishing robot to realize surface processing.

Multi-dimensional Taylor network-based adaptive control for nonlinear systems with unknown parameters

2020 ◽  
pp. 014233122095335
Author(s):  
Lei Chu ◽  
Yuqun Han ◽  
Shanliang Zhu ◽  
Mingxin Wang
Keyword(s):  
Nonlinear Systems ◽  
Tracking Control ◽  
Control Method ◽  
Controller Design ◽  
Tracking Error ◽  
Unknown Parameters ◽  
Nonlinear Characteristics ◽  
Control Approach ◽  
Closed Loop Systems ◽  
Adaptive Laws

This paper presents an adaptive multi-dimensional Taylor network (MTN) control approach for a class of nonlinear systems with unknown parameters. MTN is employed to identify unknown nonlinear characteristics existing in the system, and then a novel adaptive MTN tracking control method is proposed, via backstepping technique. In the controller design, double adaptive laws are designed and appropriate Lyapunov functions are chosen to overcome the difficulties caused by the unknown parameters. The designed controller can guarantee that all the variables in the closed-loop systems are bounded and the tracking error can be arbitrarily small. Finally, simulation results are presented to verify the effectiveness of the proposed approach.

Towards an Adaptive Control Concept for Unknown Nonlinear MIMO Systems

2018 ◽  
Author(s):  
Elmira Madadi ◽  
Dirk Söffker
Keyword(s):  
Adaptive Control ◽  
Nonlinear Systems ◽  
Control Method ◽  
Mimo Systems ◽  
Tracking Error ◽  
Underlying Structure ◽  
Unknown Parameters ◽  
Modified Model ◽  
Model Free ◽  
Model Free Control

The design of an accurate model often appears as the most challenging tasks for control engineers especially focusing to the control of nonlinear systems with unknown parameters or effects to be identified in parallel. For this reason, development of model-free control methods is of increasing importance. The class of model-free control approaches is defined by the non-use of any knowledge about the underlying structure and/or related parameters of the dynamical system. Therefore the major criteria to evaluate model-free control performance are aspects regarding robustness against unknown inputs and disturbances to achieve a suitable tracking performance including ensuring stability. Consequently it is assumed that the system plant model to be controlled is unknown, only the inputs and outputs are used as measurements. In this contribution a modified model-free adaptive approach is given as the extended version of existing model-free adaptive control to improve the performance according to the tracking error at each sample time. Using modified model-free adaptive controller, the control goal can be achieved efficiently without an individual control design process for different kinds unknown nonlinear systems. The main contribution of this paper is to extend the modified model-free adaptive control method to unknown nonlinear multi-input multi-output (MIMO) systems. A numerical example is shown to demonstrate the successful application and performance of this method.

scholarly journals A Robust Adaptive CMAC Neural Network-Based Multisliding Mode Control Method for Unmatched Uncertain Nonlinear Systems

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Honghui Wang ◽  
Xiaojun Yu ◽  
Shicheng Liang ◽  
Sheng Dong ◽  
Zeming Fan ◽  
...  
Keyword(s):  
Neural Network ◽  
Nonlinear Systems ◽  
Control Strategy ◽  
Control Method ◽  
Control Variable ◽  
Uncertain Nonlinear Systems ◽  
Cerebellar Model Articulation Controller ◽  
Mode Control ◽  
Cmac Neural Network ◽  
Robust Adaptive

This paper proposes a new robust adaptive cerebellar model articulation controller (CMAC) neural network-based multisliding mode control strategy for a class of unmatched uncertain nonlinear systems. Specifically, by employing a stepwise recursion-based multisliding mode method, such a proposed strategy is able to obtain the virtual variables and the actual control inputs of each order first, and then it reduces the conservativeness for controller parameter design by adopting the CMAC neural network to learn both system uncertainties and virtual control variable derivatives of each order online. Meanwhile, with the hyperbolic tangent function being chosen to replace the sign function in the variable structured control components, the proposed strategy is able to avoid the chattering effects caused by the discontinuous inputs. The stability analysis shows that the proposed control strategy ensures that both the system tracking errors and the sliding modes of each order could converge exponentially to any saturated layer being set. The control strategy was also applied onto a passive electrohydraulic servo loading system for verifications, and simulation results show that such a proposed control strategy is robust against all system nonlinearities and external disturbances with much higher control accuracy being achieved.

scholarly journals Luenberger-Sliding Mode Observer Based Backstepping Control for the SCR System in a Diesel Engine

Energies ◽  
2019 ◽  
Vol 12 (22) ◽  
pp. 4270
Author(s):  
Zheng ◽  
Yang ◽  
Li ◽  
Ma
Keyword(s):  
Lyapunov Function ◽  
Control Method ◽  
Sliding Mode ◽  
Setting Time ◽  
Tracking Error ◽  
Backstepping Control ◽  
Sliding Mode Observer ◽  
Control Law ◽  
Virtual Control ◽  
Scr System

In order to keep the ammonia (NH3) slip of the downstream selective catalytic reduction (SCR) system at a low level and simultaneously achieve a high nitrogen oxide (NOX) conversion rate, a Luenberger-sliding mode observer based backstepping control method is proposed. Considering that the internal working condition of the catalyst cannot be measured by commercial sensors directly, a Luenberger-sliding mode observer is designed to estimate the ammonia concentration at the middle of the catalyst. In addition, based on the stepped distributed characteristic of the surface ammonia coverage ratio along the SCR axial direction, a backstepping control method is utilized for the SCR system, in which the SCR system is decomposed into two subsystems. Firstly, the Lyapunov function is designed to ensure the convergence of the downstream subsystem, and then the virtual control law is obtained. After that, taking the virtual control law as the tracking target of the upstream subsystem, the Lyapunov function of virtual control law is given. Finally, the actual control law of the whole closed loop system is acquired. Simulations under different conditions are conducted to investigate the effect of the proposed control method. In addition, comparisons with the traditional PID (Proportion Integration Differentiation) control are presented. Results show that the proposed method is much better than the PID control method in overshoot, setting time, and tracking error.

Constrained Tracking Control by Gain-Scheduled Feedback With Optimal State Resets: A General Servo Problem and an Online Optimization Method

2016 ◽  
Vol 138 (12) ◽  
Author(s):  
Nobutaka Wada ◽  
Hidekazu Miyahara ◽  
Masami Saeki
Keyword(s):  
Tracking Control ◽  
Control Algorithm ◽  
Optimization Problem ◽  
Control Method ◽  
Actuator Saturation ◽  
Tracking Error ◽  
Reference Signal ◽  
Optimal Solution ◽  
Optimization Method ◽  
Experimental Result

In this paper, a tracking control problem for discrete-time linear systems with actuator saturation is addressed. The reference signal is assumed to be generated by an external dynamics. First, a design condition of a controller parameterized by a single scheduling parameter is introduced. The controller includes a servo compensator to achieve zero steady-state error. Then, a control algorithm that guarantees closed-loop stability and makes the tracking error converge to zero is given. In the control algorithm, the controller state as well as the scheduling parameter is updated online so that the tracking control performance is improved. Then, it is shown that the decision problem of the scheduling parameter and the controller state can be transformed into a convex optimization problem with respect to a scalar parameter. Based on this fact, we propose a numerically efficient algorithm for solving the optimization problem. Further, we propose a method of modifying the control algorithm so that the asymptotic tracking property is ensured even when the numerical error exists in the optimal solution. A numerical example and an experimental result are provided to illustrate effectiveness of the proposed control method.

scholarly journals Adaptive Differentiator-Based Predefined-Time Control for Nonlinear Systems Subject to Pure-Feedback Form and Unknown Disturbance

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Man Yang ◽  
Qiang Zhang ◽  
Ke Xu ◽  
Ming Chen
Keyword(s):  
Nonlinear Systems ◽  
Control Method ◽  
Tracking Error ◽  
Nonlinear Function ◽  
Original System ◽  
Mean Value ◽  
Mean Value Theorem ◽  
Rbf Neural Networks ◽  
Feedback Form ◽  
Output Tracking Control

In this article, by utilizing the predefined-time stability theory, the predefined-time output tracking control problem for perturbed uncertain nonlinear systems with pure-feedback structure is addressed. The nonaffine structure of the original system is simplified as an affine form via the property of the mean value theorem. Furthermore, the design difficulty from the uncertain nonlinear function is overcome by the excellent approximation performance of RBF neural networks (NNs). An adaptive predefined-time controller is designed by introducing the finite-time differentiator which is used to decrease the computational complexity problem appeared in the traditional backstepping control. It is proved that the proposed control method guarantees all signals in the closed-loop system remain bound and the tracking error converges to zero within the predefined time. Based on the controller designed in this paper, the expected results can be obtained in predefined time, which can be illustrated by the simulation results.

PD-PD Type Learning Control for Uncertain Nonlinear Systems

2009 ◽  
Author(s):  
P. R. Ouyang
Keyword(s):  
Feedback Control ◽  
Nonlinear Systems ◽  
Iterative Learning Control ◽  
Control Method ◽  
Tracking Error ◽  
Learning Control ◽  
Iterative Learning ◽  
Learning Gains ◽  
Tracking Errors ◽  
Initial Errors

In this paper, a new learning control, called PD-PD type learning control, is proposed for trajectory tracking of nonlinear systems with uncertainty and disturbance. In the developed control scheme, a PD feedback control with the current tracking errors and a PD type iterative learning control using the previous tracking errors are combined in the updating law. Explicit expressions have been developed for choosing the feedback control gains and the iterative learning gains, and an initial updating scheme is proposed to reduce and eliminate initial errors from iteration to iteration. It is proven that the final tracking error is guaranteed to converge toward the desired trajectory in the presence of varying uncertainty, disturbance, and initial errors. Comparing with the traditional iterative learning control, the new algorithm has potential benefits that include: fast convergence rate, more flexible choices of the learning gains, and monotonic convergence of the tracking error. The effectiveness of the proposed learning control method is demonstrated by simulation experiments. Due to the straightforward implementation and very good trajectory performance of the proposed control algorithm, it should be highly applicable to industrial systems.

Design of variable curvature lane changing control system based on inverse system decoupling

2020 ◽  
pp. 095440702095462
Author(s):  
Xiutian Liang ◽  
Linfeng Zhao ◽  
Qidong Wang ◽  
Wuwei Chen ◽  
Guang Xia ◽  
...  
Keyword(s):  
Obstacle Avoidance ◽  
Control Strategy ◽  
Control Method ◽  
Single Point ◽  
Tracking Error ◽  
Path Tracking ◽  
Inverse System ◽  
Slip Angle ◽  
Lane Changing ◽  
Variable Curvature

At present, the lane changing technology for a single driving environment has been relatively mature, but the actual situations are much more complicated, such as the changing curvature and the changes in road conditions. In this paper, a new lane changing obstacle avoidance control strategy for the variable curvature road was proposed. It has two stages including path planning for variable curvature lane changing and inverse system decoupling (ISD) control for path tracking. The first stage established the lane changing path models for the variable curvature road. A longitudinal-lateral safe distance model was proposed to constrain the safe boundary of the lane changing path. The second stage proposed a dynamic decoupling method for longitudinal and lateral motion based on the inverse system decoupling, a direct yaw moment and active front wheel steering coordinated control method was designed. The inverse system decoupling algorithm can correct the single point preview (SPP) method to improve the stability and the path tracking accuracy in the lane changing obstacle avoidance process. The strategy was simulated by CarSim/Simulink co-simulation, and the experiments were carried out on the hardware-in-the-loop platform. The results show that the proposed control strategy can effectively avoid obstacles when the vehicle is driving on the variable curvature road. Besides, for the different road conditions and the strong non-linearity generated during the lane changing process, the control strategy can reduce the tracking error by a maximum of 32.7%, both the yaw rate and side slip angle can be controlled in a smaller range.

Sign in / Sign up

Export Citation Format

Share Document