Optimization Based Weighting Matrices Design for Norm Optimal Iterative Learning Control

2016 ◽  
Author(s):  
Xinyi Ge ◽  
Jeffrey L. Stein ◽  
Tulga Ersal
Keyword(s):  
Steady State ◽  
Iterative Learning Control ◽  
Optimization Problems ◽  
Linear Time ◽  
Learning Control ◽  
Iterative Learning ◽  
Convergence Speed ◽  
Single Input Single Output ◽  
Modeling Uncertainties ◽  
State Error

This paper focuses on Norm-Optimal Iterative Learning Control (NO-ILC) framework for Single-Input-Single-Output (SISO) Linear Time Invariant (LTI) systems and considers the weighting matrices design problem. The ideal design of weighting matrices should ensure Robust Monotonic Convergence (RMC) against modeling uncertainties while maximizing the convergence speed and minimizing the steady state error. The state-of-art RMC design methodologies either lead to conservative performance or require manual tunings. This paper provides a methodology to systematically achieve an optimal balance between robustness, convergence speed and steady state error. To this end, optimization problems are formulated at each frequency to maximize the convergence speed and minimize the steady state error. Two optimization formulations are proposed: one for an optimal nominal performance and one for an optimal performance against uncertainties. Both formulations offer a systematic approach for designing the weighting matrices for NO-ILC, thereby eliminating the manual tuning process and avoiding an unnecessarily conservative design. A simulation example is given to confirm the analysis and demonstrate the utility of the developed methodologies to design the weighting matrices.

Optimality of Norm-Optimal Iterative Learning Control Among Linear Time Invariant Iterative Learning Control Laws in Terms of Balancing Robustness and Performance

2018 ◽  
Vol 141 (4) ◽  
Author(s):  
Xinyi Ge ◽  
Jeffrey L. Stein ◽  
Tulga Ersal
Keyword(s):  
Steady State ◽  
Iterative Learning Control ◽  
Linear Time ◽  
Learning Control ◽  
Frequency Domain Analysis ◽  
Iterative Learning ◽  
Convergence Speed ◽  
Linear Time Invariant ◽  
And Performance ◽  
State Error

This paper presents a frequency domain analysis toward the robustness, convergence speed, and steady-state error for general linear time invariant (LTI) iterative learning control (ILC) for single-input-single-output (SISO) LTI systems and demonstrates the optimality of norm-optimal iterative learning control (NO-ILC) in terms of balancing the tradeoff between robustness, convergence speed, and steady-state error. The key part of designing LTI ILC updating laws is to choose the Q-filter and learning gain to achieve the desired robustness and performance, i.e., convergence speed and steady-state error. An analytical equation that characterizes these three terms for NO-ILC has been previously presented in the literature. For general LTI ILC updating laws, however, this relationship is still unknown. Adopting a frequency domain analysis approach, this paper characterizes this relationship for LTI ILC updating laws and, subsequently, demonstrates the optimality of NO-ILC in terms of balancing the tradeoff between robustness, convergence speed, and steady-state error.

A Frequency-Dependent Filter Design Approach for Norm-Optimal Iterative Learning Control and Its Fundamental Trade-Off Between Robustness, Convergence Speed, and Steady-State Error

2017 ◽  
Vol 140 (2) ◽  
Author(s):  
Xinyi Ge ◽  
Jeffrey L. Stein ◽  
Tulga Ersal
Keyword(s):  
Steady State ◽  
Model Uncertainty ◽  
Iterative Learning Control ◽  
Filter Design ◽  
Learning Control ◽  
Iterative Learning ◽  
Convergence Speed ◽  
Frequency Dependent ◽  
Trade Off ◽  
State Error

This paper focuses on norm-optimal iterative learning control (NO-ILC) for single-input-single-output (SISO) linear time invariant (LTI) systems and presents an infinite time horizon approach for a frequency-dependent design of NO-ILC weighting filters. Because NO-ILC is a model-based learning algorithm, model uncertainty can degrade its performance; hence, ensuring robust monotonic convergence (RMC) against model uncertainty is important. This robustness, however, must be balanced against convergence speed (CS) and steady-state error (SSE). The weighting filter design approaches for NO-ILC in the literature provide limited design freedom to adjust this trade-off. Moreover, even though qualitative guidelines to adjust the trade-off exist, a quantitative characterization of the trade-off is not yet available. To address these two gaps, a frequency-dependent weighting filter design is proposed in this paper and the robustness, convergence speed, and steady-state error are analyzed in the frequency domain. An analytical expression characterizing the fundamental trade-off of NO-ILC with respect to robustness, convergence speed, and steady-state error at each frequency is presented. Compared to the state of the art, a frequency-dependent filter design gives increased freedom to adjust the trade-off between robustness, convergence speed, and steady-state error because it allows the design to meet different performance requirements at different frequencies. Simulation examples are given to confirm the analysis and demonstrate the utility of the developed filter design technique.

scholarly journals Optimal Gains of Iterative Learning Control with Forgetting Factor

2019 ◽  
Vol 37 (5) ◽  
pp. 1077-1084
Author(s):  
Baolin Dai ◽  
Jun Gong ◽  
Cuiming Li
Keyword(s):  
Optimal Control ◽  
Iterative Learning Control ◽  
Matrix Theory ◽  
Optimization Problems ◽  
Learning Control ◽  
Convergence Condition ◽  
Iterative Learning ◽  
Convergence Speed ◽  
Forgetting Factor ◽  
Control Gain

In order to solve the optimization problems of convergence characteristics of a class of single-input single-output (SISO) discrete linear time-varying systems (LTI) with time-iteration-varying disturbances, an optimal control gain design method of PID type iterative learning control (ILC) algorithm with forgetting factor was presented. The necessary and sufficient condition for the ILC system convergence was obtained based on iterative matrix theory. The convergence of the learning algorithm was proved based on operator theory. According to optimization theory and Toeplitz matrix characteristics, the monotonic convergence condition of the system was established. The accurate solution of the optimal control gain and the relationship equation between the forgetting factor and the optimal control gains were obtained according to the optimal theory which ensures the fastest system convergence speed, thereby reaching the end of the system convergence improvement. The convergence condition is weaker than the known results. The proposed method overcomes the shortcomings of traditional optimal control gain in ILC algorithm with forgetting factor, effectively accelerates the system convergence speed, suppresses the system output track error fluctuation, and provides a better solution for LTI system with time-iteration-varying disturbances. Simulation verifies the effectiveness of the control algorithm.

ILC-Based Internal Model Control of Superheater Steam Temperature

2013 ◽  
Vol 732-733 ◽  
pp. 864-869
Author(s):  
Wei Lu ◽  
Ming Chun Wang
Keyword(s):  
Iterative Learning Control ◽  
Internal Model ◽  
Handling Time ◽  
Learning Control ◽  
Internal Model Control ◽  
Iterative Learning ◽  
Steam Temperature ◽  
Periodic Disturbances ◽  
Modeling Uncertainties ◽  
Model Control

This paper proposes a novel Internal Model Control (IMC) method for the control of superheater steam temperature. The IMC is known for good robustness including handling of systems with time delays. While Iterative Learning Control (ILC) is a strategy for dealing with periodic disturbances. By using a combination of IMC and ILC, their individual advantages are used to increase the robustness against modeling uncertainties and handling time as well as decreasing the influence of the periodic disturbances affecting the superheater steam. Some simulation examples are shown to illustrate performance improvements that can be achieved by the new method over the conventional IMC and PID methods. Key Words: Superheater Steam Temperature; Internal Model Control; Iterative Learning Control

scholarly journals Robust Conditions for Iterative Learning Control in State Feedback and Output Injection Paradigm

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Muhammad A. Alsubaie ◽  
Mubarak KH. Alhajri ◽  
Tarek S. Altowaim ◽  
Salem H. Salamah
Keyword(s):  
Iterative Learning Control ◽  
State Feedback ◽  
Linear Time ◽  
Stability Margin ◽  
Learning Control ◽  
Iterative Learning ◽  
Delay Model ◽  
Linear Time Invariant ◽  
System Input ◽  
Linear Time Invariant Systems

A robust Iterative Learning Control (ILC) design that uses state feedback and output injection for linear time-invariant systems is reintroduced. ILC is a control tool that is used to overcome periodic disturbances in repetitive systems acting on the system input. The design basically depends on the small gain theorem, which suggests isolating a modeled disturbance system and finding the overall transfer function around the delay model. This assures disturbance accommodation if stability conditions are achieved. The reported design has a lack in terms of the uncertainty issue. This study considered the robustness issue by investigating and setting conditions to improve the system performance in the ILC design against a system’s unmodeled dynamics. The simulation results obtained for two different systems showed an improvement in the stability margin in the case of system perturbation.

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