迭代学习控制理论及其在网络控制系统中的应用
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摘要
迭代学习控制(iterative learning control,简称ILC)策略适合于某种具有重复运动性质的被控对象。其控制的基本思想是：将控制系统历史的控制信号和误差信号相结合来修正当前控制信号,产生新的控制信号,实现在有限时间区间上的完全跟踪任务。本文先对迭代域变化的参考轨迹跟踪问题进行高阶内模迭代学习控制的研究,然后针对具有网络传输的控制系统中不同数据丢失和时延情况采用三种不同的迭代学习方法研究,并证明迭代学习律的收敛性。论文的主要研究内容包括如下几方面：
1.针对变参考轨迹跟踪问题,提出了高阶内模迭代学习控制。首先构造一个高阶内模(HOIM)描述变参考轨迹,然后将高阶内模嵌入到迭代学习律中,从而构造生成新型高阶内模迭代学习律。通过严格的数学分析和仿真实例,证明高阶内模算法能够保证跟踪误差沿迭代轴的渐近收敛性质。最后将高阶内模算法推广到非线性系统。
2.针对传感器至控制器通过网络连接的一类网络控制系统,存在Bernoulli分布的数据丢失和传输一步时延问题,应用经典迭代学习控制算法的前馈特性对网络控制系统进行有效补偿,确保系统的跟踪性能。
3.研究传感器至控制器通道存在随机数据丢失和传输时延行为的网络化控制系统。首先将随机数据丢失和传输时延行为建模为Markov链,然后提出了移动权重平均高阶迭代学习算法,最后证明新型算法对于网络控制系统的有效性。
4.针对控制器至执行器通道存在数据丢失的离散时变网络化控制系统问题。首先建立Bernoulli分布的数据丢失模型,其次提出了含平均迭代学习律的输入保持补偿算法,该方法的迭代学习控制器将所有的历史输入信号和所有误差信号叠加取平均,从而形成新的控制信号,而在执行器端采用零阶保持方法补偿丢失的控制信号,最后经理论分析和仿真实验,证明了该方法的有效性。
本文最后对全文进行了总结和展望。
Iterative learning control(ILC) is a technique which is applicable to systems or pro-cesses operating repetitively over a finite interval time. The present control input used the information such as the previous control input signals and tracking error signals after every trial until the desired trajectory is followed to a high precision. In this dissertation, First-ly, A high-order internal model (HOIM) ILC is presented for tracking problem of varying reference trajectories in iteration domain. Then there are three different ILC algorithms for discrete time networked control systems with various data dropouts and transmission delays and proved asymptotical convergence in iteration domain. The main contents are outlines as follows.
1. A HOIM-based ILC was proposed to deal with iteratively varying reference trajec-tories problems. Firstly, the varying reference trajectories in the iteration domain are described by a HOIM that can be formulated as a polynomials between two con-secutive iterations. Then, by incorporating HOIM into the ILC law, and designing appropriate learning control gains. Through both rigorous theoretical analysis and numerical simulations, the learning convergence of tracking error in the iteration do-main can be guaranteed for continuous-time linear time-varying system when the HOIM-based ILC is used. Finally, the HOIM-based ILC is applied to nonlinear cas-es.
2. An ILC is presented for a class discrete time networked control system which a net-work exists between the sensor and the controller. The packet dropouts and one-step delay subject to the Bernoulli distribution. Owing to the essence of feedforward-based control ILC can perform trajectory tracking tasks while both the packet dropout-s and the one-step delay phenomena are taken into consideration.
3. The discrete-time networked control systems are investigated where the sensor-to- controller channels experience both random packet dropouts and transmission de-lays. Firstly, random data dropouts and transmission delays of network communica-tion are modeled as a Markov chain process. Then, an ILC with moving weighted average is proposed for discrete time-varying linear system with network commu-nication channels. Finally, theoretical analysis validate the effectiveness of the ILC with moving weighted average for networked control system with both data dropouts and transmission delays.
4. The problem of ILC is considered for a class of discrete time-varying networked control systems with random packet dropouts. The packet dropout occurs during the packet transmission between the ILC controller and the actuator of plant. Firstly, the packet dropout is viewed as a binary switching sequence which subjects to the Bernoulli distribution. Then, the hold-input scheme with average ILC is proposed. The average ILC is consisted of averaging previous control signals and tracking er-ror signals, and the hold-input scheme is adopted to compensate the packet dropout at the actuator. Finally, theoretical analysis and numerical simulations validate the effectiveness of the hold-input scheme with average ILC for discrete time-varying linear system.
The conclusions and perspectives are presented in the end of the dissertation.
1.针对变参考轨迹跟踪问题,提出了高阶内模迭代学习控制。首先构造一个高阶内模(HOIM)描述变参考轨迹,然后将高阶内模嵌入到迭代学习律中,从而构造生成新型高阶内模迭代学习律。通过严格的数学分析和仿真实例,证明高阶内模算法能够保证跟踪误差沿迭代轴的渐近收敛性质。最后将高阶内模算法推广到非线性系统。
2.针对传感器至控制器通过网络连接的一类网络控制系统,存在Bernoulli分布的数据丢失和传输一步时延问题,应用经典迭代学习控制算法的前馈特性对网络控制系统进行有效补偿,确保系统的跟踪性能。
3.研究传感器至控制器通道存在随机数据丢失和传输时延行为的网络化控制系统。首先将随机数据丢失和传输时延行为建模为Markov链,然后提出了移动权重平均高阶迭代学习算法,最后证明新型算法对于网络控制系统的有效性。
4.针对控制器至执行器通道存在数据丢失的离散时变网络化控制系统问题。首先建立Bernoulli分布的数据丢失模型,其次提出了含平均迭代学习律的输入保持补偿算法,该方法的迭代学习控制器将所有的历史输入信号和所有误差信号叠加取平均,从而形成新的控制信号,而在执行器端采用零阶保持方法补偿丢失的控制信号,最后经理论分析和仿真实验,证明了该方法的有效性。
本文最后对全文进行了总结和展望。
Iterative learning control(ILC) is a technique which is applicable to systems or pro-cesses operating repetitively over a finite interval time. The present control input used the information such as the previous control input signals and tracking error signals after every trial until the desired trajectory is followed to a high precision. In this dissertation, First-ly, A high-order internal model (HOIM) ILC is presented for tracking problem of varying reference trajectories in iteration domain. Then there are three different ILC algorithms for discrete time networked control systems with various data dropouts and transmission delays and proved asymptotical convergence in iteration domain. The main contents are outlines as follows.
1. A HOIM-based ILC was proposed to deal with iteratively varying reference trajec-tories problems. Firstly, the varying reference trajectories in the iteration domain are described by a HOIM that can be formulated as a polynomials between two con-secutive iterations. Then, by incorporating HOIM into the ILC law, and designing appropriate learning control gains. Through both rigorous theoretical analysis and numerical simulations, the learning convergence of tracking error in the iteration do-main can be guaranteed for continuous-time linear time-varying system when the HOIM-based ILC is used. Finally, the HOIM-based ILC is applied to nonlinear cas-es.
2. An ILC is presented for a class discrete time networked control system which a net-work exists between the sensor and the controller. The packet dropouts and one-step delay subject to the Bernoulli distribution. Owing to the essence of feedforward-based control ILC can perform trajectory tracking tasks while both the packet dropout-s and the one-step delay phenomena are taken into consideration.
3. The discrete-time networked control systems are investigated where the sensor-to- controller channels experience both random packet dropouts and transmission de-lays. Firstly, random data dropouts and transmission delays of network communica-tion are modeled as a Markov chain process. Then, an ILC with moving weighted average is proposed for discrete time-varying linear system with network commu-nication channels. Finally, theoretical analysis validate the effectiveness of the ILC with moving weighted average for networked control system with both data dropouts and transmission delays.
4. The problem of ILC is considered for a class of discrete time-varying networked control systems with random packet dropouts. The packet dropout occurs during the packet transmission between the ILC controller and the actuator of plant. Firstly, the packet dropout is viewed as a binary switching sequence which subjects to the Bernoulli distribution. Then, the hold-input scheme with average ILC is proposed. The average ILC is consisted of averaging previous control signals and tracking er-ror signals, and the hold-input scheme is adopted to compensate the packet dropout at the actuator. Finally, theoretical analysis and numerical simulations validate the effectiveness of the hold-input scheme with average ILC for discrete time-varying linear system.
The conclusions and perspectives are presented in the end of the dissertation.
引文
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