Resource-aware motion control:feedforward, learning, and feedback

Controllers with new sampling schemes improve motion systems’ performanc

Learning for Advanced Motion Control

Iterative Learning Control (ILC) can achieve perfect tracking performance for mechatronic systems. The aim of this paper is to present an ILC design tutorial for industrial mechatronic systems. First, a preliminary analysis reveals the potential performance improvement of ILC prior to its actual implementation. Second, a frequency domain approach is presented, where fast learning is achieved through noncausal model inversion, and safe and robust learning is achieved by employing a contraction mapping theorem in conjunction with nonparametric frequency response functions. The approach is demonstrated on a desktop printer. Finally, a detailed analysis of industrial motion systems leads to several shortcomings that obstruct the widespread implementation of ILC algorithms. An overview of recently developed algorithms, including extensions using machine learning algorithms, is outlined that are aimed to facilitate broad industrial deployment.Comment: 8 pages, 15 figures, IEEE 16th International Workshop on Advanced Motion Control, 202

Design and control of a multi-axis micro-electro-mechanical system array for coordinated micro-manipulation

Micro-electro-mechanical system design and implementation is a field that has received much attention over the past few decades. These robotic systems with features on the micro-scale have an unparalleled opportunity to change the way scientists interact with and understand micro and nano-scale phenomenon. Their capabilities allow experimentation that cannot be achieved with standard macro-scale equipment. Potential applications range from observing biological processes in living cells, to smart materials that automatically detect microcracks. So far, however, only a few truly successful applications have been realized. One of the most elusive goals in MEMS design is creating a system capable of coordinated motion tasks. This task requires an innovative approach to mechanism design and control. In this work a novel micro-positioning stage is presented that is intended to be implemented in a very large scale array. The stages are actuated by custom optimized electro-thermal-compliant micro-actuators intended for high force applications. These actuators, in combination with mechanical amplification, enable a high degree of mobility which allows a large work area. Furthermore the stage itself has a small foot print to allow a high density of actuators to interact in the common workspace. Control of the stages is realized using vision feedback with Kalman Filtering for high-speed intersample estimation. An iterative learning controller is then used for high precision tracking. This approach gives a high degree of accuracy that is nearly as good as the resolution of the measurement system, and at frequencies that approach the bandwidth of the system --Abstract, page iii

Eliminating the Internal Instability in Iterative Learning Control for Non-minimum Phase Systems

Iterative Learning Control (ILC) iterates with a real world control system repeatedly performing the same task. It adjusts the control action based on error history from the previous iteration, aiming to converge to zero tracking error. ILC has been widely used in various applications due to its high precision in trajectory tracking, e.g. semiconductor manufacturing sensors that repeatedly perform scanning maneuvers. Designing effective feedback controllers for non-minimum phase (NMP) systems can be challenging. Applying Iterative Learning Control (ILC) to NMP systems is particularly problematic. Asking for zero error at sample times usually involves inverting the control system. However, the inverse process is unstable when the system has NMP zeros. The control action will grow exponentially every time step, and the error between time steps also grows exponentially. If there are NMP zeros on the negative real axis, the control action will alternate its sign every time step. ILC must be digital to use previous run data to improve the tracking error in the current run. There are two kinds of NMP digital systems, ones having intrinsic NMP zeros as images of continuous time NMP zeros, and NMP sampling zeros introduced by discretization. Two ILC design methods have been investigated in this thesis to handle NMP sampling zeros, producing zero tracking error at addressed sample times: (1) One can simply start asking for zero error after a few initial time steps, like using multiple zero order holds for the first addressed time step only (2) Or increase the sample rate, ask for zero error at the original rate, making two or more zero order holds per addressed time step. The internal instability can be manifested by the singular value decomposition of the input-output matrix. Non-minimum phase systems have particularly small singular values which are related to the NMP zeros. The aim is to eliminate these anomalous singular values. However, when applying the second approach, there are cases that the original anomalous singular values are gone, but some new anomalous singular values appear in the system matrix that cause difficulties to the inverse problem. Not asking for zero error for a small number of initial addressed time steps is shown to eliminate all anomalous singular values. This suggests that a more accurate statement of the second approach is: using multiple zero order holds per addressed time step, and eliminating a few initial addressed time steps if there are new anomalous singular values. We also extend the use of these methods to systems having intrinsic NMP zeros. By modifying ILC laws to perform pole-zero cancellation inside the unit circle, we observe that all of the rules for sampling zeros are effective for intrinsic zeros. Hence, one can now achieve convergence to zero tracking error at addressed time steps in ILC of NMP systems with a well behaved control action. In addition, this thesis studies the robustness of the two approaches along with several other candidate approaches with respect to model parameter uncertainty. Three classes of ILC laws are used. Both approaches show great robustness. Quadratic cost ILC is seen to have substantially better robustness to parameter uncertainty than the other laws

Simultaneous Iterative Learning and Feedback Control Design

Iterative learning controllers aim to produce high precision tracking in operations where the same tracking maneuver is repeated over and over again. Model-based iterative learning control laws are designed from the system Markov parameters which could be inaccurate. Chapter 2 examines several important learning control laws and develops an understanding of how and when inaccuracy in knowledge of the Markov parameters results in instability of the learning process. While an iterative learning controller can compensate for unknown repeating errors and disturbances, it is not suited to handle non-repeating, stochastic errors and disturbances, which can be more effectively handled by a feedback controller. Chapter 3 explores feedback and iterative learning combination controllers, showing how a one-time step behind disturbance estimator and one-repetition behind disturbance estimator can be incorporated together in such a combination. Since learning control applications are finite-time by their very nature, frequency response based design techniques are not best suited for designing the feedback controller in this context. A finite-time feedback controller design approach is more appropriate given the overall aim of zero tracking error for the entire trajectory, even for shorter trajectories where the system response is still in its transient phase and has not yet reached steady state. Chapter 4 presents a combination of finite-time feedback and learning control as a natural solution for such a control objective, showing how a finite-time feedback controller and an iterative learning controller can be simultaneously synthesized during the learning process. Finally, Chapter 5 examines different configurations where a combination of a feedback controller and an iterative learning controller can be implemented. Numerical results are used to illustrate the feedback and iterative controller designs developed in this thesis

Synthesis and Analysis of Design Methods in Linear Repetitive, Iterative Learning and Model Predictive Control

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