几类系统的迭代学习控制
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摘要
对于具有重复运动性质的被控系统,迭代学习控制技术是一种简单有效的控制方法。迭代学习控制的基本思想是基于输出信号与给定目标轨迹的偏差不断修正不理想的控制输入信号,实现在有限时间区间的完全跟踪任务。
本文主要研究了几类系统在不同的初值条件下的收敛性和鲁棒性。针对不确定的线性、非线性的连续和离散系统,主要研究系统的特性、初值条件、外部扰动、学习控制律、不确定性以及时滞等对迭代学习控制过程和跟踪性能的影响等内容。本文得到了几种迭代学习控制收敛的充分条件,并提出了一系列迭代学习律的设计方法。为保证提出的学习律的有效性,对每种学习律,我们都进行了严格的理论分析和充分的仿真实验。
本文的主要成果如下:
(1)针对一类线性系统,主要考虑两类初始条件问题:一是系统具有固定的初值偏差;二是具有任意的初始偏差。我们提出了一种开闭环PID型学习律。分析了两类初始条件下学习算法的鲁棒性和收敛性,并给出了收敛条件。仿真结果表明开闭环PID型学习律的有效性,与开环PID型学习律相比拥有更快的收敛速度。
(2)针对一类具有扰动和噪声的非线性多时滞系统,提出了一种PD型学习算法,并借助λ范数,Bellman-Gronwall定理等得到了确保跟踪误差收敛的充分条件。同时考虑了初始无偏差条件,不确定性扰动和噪声对跟踪误差收敛的影响及系统中的多个时滞对迭代学习控制收敛性的影响。证明了当不存在初始误差、不确定扰动和噪声时,所给算法能实现对期望输出信号的完全跟踪,否则跟踪误差是一致有界并且这个界与扰动和噪声等因素的界有关。研究结果表明,系统状态的时滞对非线性系统的迭代学习控制没有明显的影响。仿真模拟验证了结果的有效性。
(3)针对一类线性离散多时滞系统,在初始条件未知的情况下,分别提出了高阶P型迭代学习律来提高系统的跟踪性能和高阶初始状态学习算法来放宽对初始条件的限制。同时,我们得到了保证学习算法渐近收敛的条件,分析了多时滞对迭代学习过程的影响。仿真结果表明给出的学习算法具有很好的跟踪性能,可使系统经过较少的迭代次数就可以实现对期望轨迹的跟踪。
(4)对本文所提出的各种迭代学习算法都做了仿真研究,验证了算法的可行性和有效性。
Iterative learning control is a simple, but effective control technique, which is applied to the system that operates repetitively over a fixed time interval and improves its transient response performance. The idea of ILC is to gradually revise imperfect control input using the error between system output and the desired trajectory and realize perfect tracking in a finite time interval.
In this dissertation, the convergence and robust issues of iterative learning control in response to different initial conditions for several plants are mainly studied。For uncertain linear and nonlinear continuous and discrete systems, the effects of the plant characteristics, disturbances and noises, initial conditions, time delays, uncertain modeling dynamic and learning algorithms on the convergence and performance of ILC are also investigated. A series of ILC laws and sufficient conditions guaranteeing the convergence of ILC are proposed, and the effectiveness of the proposed learning laws is ensured by the theoretical analysis and illustrated by the simulation examples.
The main contributions of this dissertation are summarized as follows:
(1) We study two cases of initial condition problems: 1). the initial states are the same but different from the desired initial states, 2). random initial states. For a class of linear systems, an open-closed-loop PID-type law is proposed. We analyze its robustness and convergence for two cases of initial conditions and present the convergence condition. The simulation results demonstrate Open-closed-loop PID-type algorithm is better than the Open-loop PID-type algorithm in terms of the convergent speed.
(2) We consider a class of nonlinear multiple time-delay dynamic systems with external disturbance and output noise, and present PD-type ILC learning algorithm. The convergence and robustness issues are addressed in the means ofλ? norm theory and Bellman-Gronwall lemma. Meanwhile, the effect of the external disturbances and measurement noises on the convergence of tracking error and the effect of multiple time delays on ILC convergence are considered when there is no initial error。We propose the sufficient conditions to guarantee the system outputs, states and control inputs to converge to desired trajectories with bounded tracking errors. In the case when the external disturbances and measurement noises decay to zero, the bounds of the tracking errors also decay to zero。It is shown that the multiple time delay in state variables do not affect the ILC convergence property significantly. The simulation example indicates the effectiveness of the proposed ILC laws。
(3) we design a high-order P-type iterative learning algorithm for improving the tracking performance and initial state learning scheme in order to relaxing the restriction on initial state for a class of linear discrete-time systems with multiple time delay whose initial condition is unknown at each iteration. At the same time, we derive the sufficient and necessary condition which guarantees asymptotic convergence of the actual output of system to the desired trajectory, and we also address the effect of multiple time delays on iterative learning process. The simulated results have shown that the proposed ILC scheme has a better tracking performance.
(4) Several simulations have been made according to the proposed algorithms in this dissertation. These simulation results illustrate the feasibility and effectiveness of the proposed iterative learning controller.
本文主要研究了几类系统在不同的初值条件下的收敛性和鲁棒性。针对不确定的线性、非线性的连续和离散系统,主要研究系统的特性、初值条件、外部扰动、学习控制律、不确定性以及时滞等对迭代学习控制过程和跟踪性能的影响等内容。本文得到了几种迭代学习控制收敛的充分条件,并提出了一系列迭代学习律的设计方法。为保证提出的学习律的有效性,对每种学习律,我们都进行了严格的理论分析和充分的仿真实验。
本文的主要成果如下:
(1)针对一类线性系统,主要考虑两类初始条件问题:一是系统具有固定的初值偏差;二是具有任意的初始偏差。我们提出了一种开闭环PID型学习律。分析了两类初始条件下学习算法的鲁棒性和收敛性,并给出了收敛条件。仿真结果表明开闭环PID型学习律的有效性,与开环PID型学习律相比拥有更快的收敛速度。
(2)针对一类具有扰动和噪声的非线性多时滞系统,提出了一种PD型学习算法,并借助λ范数,Bellman-Gronwall定理等得到了确保跟踪误差收敛的充分条件。同时考虑了初始无偏差条件,不确定性扰动和噪声对跟踪误差收敛的影响及系统中的多个时滞对迭代学习控制收敛性的影响。证明了当不存在初始误差、不确定扰动和噪声时,所给算法能实现对期望输出信号的完全跟踪,否则跟踪误差是一致有界并且这个界与扰动和噪声等因素的界有关。研究结果表明,系统状态的时滞对非线性系统的迭代学习控制没有明显的影响。仿真模拟验证了结果的有效性。
(3)针对一类线性离散多时滞系统,在初始条件未知的情况下,分别提出了高阶P型迭代学习律来提高系统的跟踪性能和高阶初始状态学习算法来放宽对初始条件的限制。同时,我们得到了保证学习算法渐近收敛的条件,分析了多时滞对迭代学习过程的影响。仿真结果表明给出的学习算法具有很好的跟踪性能,可使系统经过较少的迭代次数就可以实现对期望轨迹的跟踪。
(4)对本文所提出的各种迭代学习算法都做了仿真研究,验证了算法的可行性和有效性。
Iterative learning control is a simple, but effective control technique, which is applied to the system that operates repetitively over a fixed time interval and improves its transient response performance. The idea of ILC is to gradually revise imperfect control input using the error between system output and the desired trajectory and realize perfect tracking in a finite time interval.
In this dissertation, the convergence and robust issues of iterative learning control in response to different initial conditions for several plants are mainly studied。For uncertain linear and nonlinear continuous and discrete systems, the effects of the plant characteristics, disturbances and noises, initial conditions, time delays, uncertain modeling dynamic and learning algorithms on the convergence and performance of ILC are also investigated. A series of ILC laws and sufficient conditions guaranteeing the convergence of ILC are proposed, and the effectiveness of the proposed learning laws is ensured by the theoretical analysis and illustrated by the simulation examples.
The main contributions of this dissertation are summarized as follows:
(1) We study two cases of initial condition problems: 1). the initial states are the same but different from the desired initial states, 2). random initial states. For a class of linear systems, an open-closed-loop PID-type law is proposed. We analyze its robustness and convergence for two cases of initial conditions and present the convergence condition. The simulation results demonstrate Open-closed-loop PID-type algorithm is better than the Open-loop PID-type algorithm in terms of the convergent speed.
(2) We consider a class of nonlinear multiple time-delay dynamic systems with external disturbance and output noise, and present PD-type ILC learning algorithm. The convergence and robustness issues are addressed in the means ofλ? norm theory and Bellman-Gronwall lemma. Meanwhile, the effect of the external disturbances and measurement noises on the convergence of tracking error and the effect of multiple time delays on ILC convergence are considered when there is no initial error。We propose the sufficient conditions to guarantee the system outputs, states and control inputs to converge to desired trajectories with bounded tracking errors. In the case when the external disturbances and measurement noises decay to zero, the bounds of the tracking errors also decay to zero。It is shown that the multiple time delay in state variables do not affect the ILC convergence property significantly. The simulation example indicates the effectiveness of the proposed ILC laws。
(3) we design a high-order P-type iterative learning algorithm for improving the tracking performance and initial state learning scheme in order to relaxing the restriction on initial state for a class of linear discrete-time systems with multiple time delay whose initial condition is unknown at each iteration. At the same time, we derive the sufficient and necessary condition which guarantees asymptotic convergence of the actual output of system to the desired trajectory, and we also address the effect of multiple time delays on iterative learning process. The simulated results have shown that the proposed ILC scheme has a better tracking performance.
(4) Several simulations have been made according to the proposed algorithms in this dissertation. These simulation results illustrate the feasibility and effectiveness of the proposed iterative learning controller.
引文
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[2] Arimoto S, Kawamura S and Miyazaki F. Bettering operation of robots by learning. Journal of Robotic Systems, 1984, 1(2):123-140.
[3] Arimoto S, Kawamura S and Miyazaki F and Tamaki S. Learning control theory for dynamical systems. In: Proceedings of the 24th IEEE Conference on Decision and control, Ft. Lauderdale, 1985, 3: 1375-1380.
[4] Arimoto S, Kawamura S and Miyazaki F. Bettering operation of robots by learning: Anew control theory for servomechanism and mechatronics Proceedings of the 23rd IEEE Conference on Decision and Control, Las Vegas, 1984, NV, 1064-1069.
[5]谢振东,刘永清.分布参数系统目标跟踪的二阶P-型学习算法.暨南大学学报, 1998, 19(1):60-64.
[6]谢胜利,谢振东,傅予力.连续非线性系统的迭代学习控制及其算法实现.控制理论与应用, 2002, 19(2) ,167-173.
[7] Tayebi A, and Zaremba MB. Iterative learning control for non-linear systems describedby ablended multiple model representation. International Journal of Control, 2002, 75(16):1376-1384.
[8]皮道映,孙优贤.开闭环迭代学习控制的研究进展与方向.机电工程, 1999, 5:165-166.
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