Synthesis and Analysis of Design Methods in Linear Repetitive, Iterative Learning and Model Predictive Control
Creators: Zhu, Jianzhong
Publisher: name: Columbia University
Year: 2018
Subjects: subject: Mechanical engineering
subject: FOS: Mechanical engineering
subject: Feedback control systems
subject: Automatic tracking
subject: Adaptive control systems

description: Repetitive Control (RC) seeks to converge to zero tracking error of a feedback control system performing periodic command as time progresses, or to cancel the influence of a periodic disturbance as time progresses, by observing the error in the previous period. Iterative Learning Control (ILC) is similar, it aims to converge to zero tracking error of system repeatedly performing the same task, and also adjusting the command to the feedback controller each repetition based on the error in the previous repetition. Compared to the conventional feedback control design methods, RC and ILC improve the performance over repetitions, and both aiming at zero tracking error in the real world instead of in a mathematical model. Linear Model Predictive Control (LMPC) normally does not aim for zero tracking error following a desired trajectory, but aims to minimize a quadratic cost function to the prediction horizon, and then apply the first control action. Then repeat the process each time step. The usual quadratic cost is a trade-off function between tracking accuracy and control effort and hence is not asking for zero error. It is also not specialized to periodic command or periodic disturbance as RC is, but does require that one knows the future desired command up to the prediction horizon.
      The objective of this dissertation is to present various design schemes of improving the tracking performance in a control system  based on ILC, RC and LMPC. The dissertation contains four major chapters. The first chapter studies the optimization of the design parameters, in particular as related to measurement noise, and the need of a cutoff filter when dealing with actuator limitations, robustness to model error. The results aim to guide the user in tuning the design parameters available when creating a repetitive control system. In the second chapter, we investigate how ILC laws can be converted for  use in RC to improve performance. And robustification by adding control penalty in cost function is compared to use a frequency cutoff filter. The third chapter develops a method to create desired trajectories with a zero tracking interval without involving an unstable inverse solution. An easily implementable feedback version is created to optimize the same cost every time step from the current measured position. An ILC algorithm is also created to iteratively learn to give local zero error in the real world while using an imperfect model. This approach also gives a method to apply ILC to endpoint problem without specifying an arbitrary trajectory to follow to reach the endpoint. This creates a method for ILC to apply to such problems without asking for accurate tracking of a somewhat arbitrary trajectory to accomplish learning to reach the desired endpoint. The last chapter outlines a set of uses for a stable inverse in control applications, including Linear Model Predictive Control (LMPC), and LMPC applied to Repetitive Control (RC-LMPC), and a generalized form of a one-step ahead control. An important characteristic is that this approach has the property of converging to zero tracking error in a small number of time steps, which is finite time convergence instead of asymptotic convergence as time tends to infinity.