基于高阶内模的迭代学习控制及应用
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摘要
本论文以非线性系统为研究对象,着重研究了针对一些非严格重复问题的迭代学习控制设计方法,特别考虑了由一类高阶内模生成的不确定参数的非严格重复性,同时也考虑了参考轨迹、未知时变输入增益、输入输出扰动和迭代初态的非严格重复性。论文的主要工作及其创新点总结如下。
第一、针对一般连续时间非参数系统对非严格重复参考轨迹的跟踪问题,利用内模原理,提出了一种基于高阶内模的迭代学习控制器,理论上证明了当参考轨迹由一个高阶内模生成时系统跟踪误差的有界收敛性,并给出了相应的收敛条件。
第二、针对一类结构已知的连续时间非线性参数系统,考虑了一种由高阶内模生成的单参数非严格重复性,利用内模原理,提出了基于高阶内模的自适应迭代学习控制算法,特别说明了平行格式的学习更新律比高阶学习更新律具有更广的适用范围。通过严格的数学分析,证明了当参考轨迹可以任意迭代变化时,所提出的算法能够保证跟踪误差沿迭代轴的渐进收敛。还考虑了由混合高阶内模生成的多参数非严格重复性,并相应地将算法扩展为混合的平行自适应迭代学习控制以处理更加复杂多样的非严格重复性。
第三、针对一类含有非严格重复参数的连续时间非线性系统,及任意迭代变化的有界输入输出扰动和任意迭代变化的有界初始状态,提出了基于高阶内模的自适应迭代学习控制器的一种鲁棒设计方法,实现了跟踪误差沿迭代轴的有界收敛。
第四、针对一类结构已知的离散时间非线性参数系统,考虑了一种由高阶内模生成的参数非严格重复性,利用内模原理,分别提出了离散时间的基于最小二乘算法和基于投影算法的平行自适应迭代学习控制器,并分别证明了算法的有效性。
第五、将平行自适应迭代学习控制算法扩展到有限空间区间情形下,并分别应用于列车运行速度曲线跟踪控制和列车运行时间曲线跟踪控制,通过证明和仿真说明了所提出算法的有效性和在列车自动控制中的应用前景。
In the dissertation, new iterative learning control (ILC) design methods are studied to deal with several non-repetitiveness problems in nonlinear systems. Particularly, a class of non-repetitiveness in uncertain parameter is considered which is generated from a high-order internal model (HOIM). Meanwhile, non-repetitiveness phenomenons in reference trajectory, unknown time-varying input gain, input/output disturbance and initial state are also taken into consideration. Main works and contributions in the dissertation are summarized as follows.
1. In virtue of internal model principle, a HOIM-based iterative learning controller is proposed to deal with non-repetitive reference trajectory tracking problem for general continuous-time non-parametric systems. When the reference trajectory is generated from a HOIM, bounded convergence of the tracking error is proved theoretically, and the convergence condition is given correspondingly.
2. In virtue of internal model principle, a HOIM-based adaptive iterative learning control algorithm is proposed for a class of continuous-time nonlinear parametric systems to deal with non-repetitive parameter which is generated from a HOIM. It shows that the parallel updating scheme provides wider applicable scope comparing with the high-order updating scheme. Through rigorous analysis, asymptotical convergence of the tracking error in the iteration domain is guaranteed when proposed algorithm is used, even though the reference trajectory is arbitrarily iteration-varying. When mixed HOIMs in multiple parameters are considered, a mixed parallel adaptive iterative learning control algorithm is developed correspondingly to deal with more complicated non-repetitiveness.
3. A robust design approach for HOIM-based adaptive iterative learning control is proposed to deal with iteration-varying bounded input/output disturbance and iteration-varying bounded initial condition in a class of continuous-time nonlinear systems with non-repetitive parameters. Bounded convergence of the tracking error in the iteration domain is derived using proposed robust design.
4. In virtue of internal model principle, a Recursive-Least-Squares-based adaptive iterative learning control algorithm and a projection-based adaptive iterative learning control algorithm are proposed respectively for a class of discrete-time nonlinear parametric systems, to deal with non-repetitive parameter which is generated from a HOIM. The effectiveness of both algorithms is verified through rigorous analysis, respectively.
5. The parallel adaptive iterative learning control algorithm is extended into the spatial parallel adaptive iterative learning control algorithm when finite space interval is involved. The new control algorithm is applied to speed trajectory tracking problem and time trajectory tracking problem of a train operation, respectively. The effectiveness of proposed algorithm is verified by theoretical proof and experimental simulation. It is a promising application of the adaptive iterative learning control into the field of automatic train control.
第一、针对一般连续时间非参数系统对非严格重复参考轨迹的跟踪问题,利用内模原理,提出了一种基于高阶内模的迭代学习控制器,理论上证明了当参考轨迹由一个高阶内模生成时系统跟踪误差的有界收敛性,并给出了相应的收敛条件。
第二、针对一类结构已知的连续时间非线性参数系统,考虑了一种由高阶内模生成的单参数非严格重复性,利用内模原理,提出了基于高阶内模的自适应迭代学习控制算法,特别说明了平行格式的学习更新律比高阶学习更新律具有更广的适用范围。通过严格的数学分析,证明了当参考轨迹可以任意迭代变化时,所提出的算法能够保证跟踪误差沿迭代轴的渐进收敛。还考虑了由混合高阶内模生成的多参数非严格重复性,并相应地将算法扩展为混合的平行自适应迭代学习控制以处理更加复杂多样的非严格重复性。
第三、针对一类含有非严格重复参数的连续时间非线性系统,及任意迭代变化的有界输入输出扰动和任意迭代变化的有界初始状态,提出了基于高阶内模的自适应迭代学习控制器的一种鲁棒设计方法,实现了跟踪误差沿迭代轴的有界收敛。
第四、针对一类结构已知的离散时间非线性参数系统,考虑了一种由高阶内模生成的参数非严格重复性,利用内模原理,分别提出了离散时间的基于最小二乘算法和基于投影算法的平行自适应迭代学习控制器,并分别证明了算法的有效性。
第五、将平行自适应迭代学习控制算法扩展到有限空间区间情形下,并分别应用于列车运行速度曲线跟踪控制和列车运行时间曲线跟踪控制,通过证明和仿真说明了所提出算法的有效性和在列车自动控制中的应用前景。
In the dissertation, new iterative learning control (ILC) design methods are studied to deal with several non-repetitiveness problems in nonlinear systems. Particularly, a class of non-repetitiveness in uncertain parameter is considered which is generated from a high-order internal model (HOIM). Meanwhile, non-repetitiveness phenomenons in reference trajectory, unknown time-varying input gain, input/output disturbance and initial state are also taken into consideration. Main works and contributions in the dissertation are summarized as follows.
1. In virtue of internal model principle, a HOIM-based iterative learning controller is proposed to deal with non-repetitive reference trajectory tracking problem for general continuous-time non-parametric systems. When the reference trajectory is generated from a HOIM, bounded convergence of the tracking error is proved theoretically, and the convergence condition is given correspondingly.
2. In virtue of internal model principle, a HOIM-based adaptive iterative learning control algorithm is proposed for a class of continuous-time nonlinear parametric systems to deal with non-repetitive parameter which is generated from a HOIM. It shows that the parallel updating scheme provides wider applicable scope comparing with the high-order updating scheme. Through rigorous analysis, asymptotical convergence of the tracking error in the iteration domain is guaranteed when proposed algorithm is used, even though the reference trajectory is arbitrarily iteration-varying. When mixed HOIMs in multiple parameters are considered, a mixed parallel adaptive iterative learning control algorithm is developed correspondingly to deal with more complicated non-repetitiveness.
3. A robust design approach for HOIM-based adaptive iterative learning control is proposed to deal with iteration-varying bounded input/output disturbance and iteration-varying bounded initial condition in a class of continuous-time nonlinear systems with non-repetitive parameters. Bounded convergence of the tracking error in the iteration domain is derived using proposed robust design.
4. In virtue of internal model principle, a Recursive-Least-Squares-based adaptive iterative learning control algorithm and a projection-based adaptive iterative learning control algorithm are proposed respectively for a class of discrete-time nonlinear parametric systems, to deal with non-repetitive parameter which is generated from a HOIM. The effectiveness of both algorithms is verified through rigorous analysis, respectively.
5. The parallel adaptive iterative learning control algorithm is extended into the spatial parallel adaptive iterative learning control algorithm when finite space interval is involved. The new control algorithm is applied to speed trajectory tracking problem and time trajectory tracking problem of a train operation, respectively. The effectiveness of proposed algorithm is verified by theoretical proof and experimental simulation. It is a promising application of the adaptive iterative learning control into the field of automatic train control.
引文
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