A frequency domain approach for designing filters for Norm-Optimal Iterative Learning Control and its fundamental tradeoff between robustness, convergence speed and steady state error

2016 ◽  
Author(s):  
Xinyi Ge ◽  
Jeffrey L. Stein ◽  
Tulga Ersal
Keyword(s):  
Steady State ◽  
Frequency Domain ◽  
Iterative Learning Control ◽  
Learning Control ◽  
Iterative Learning ◽  
Convergence Speed ◽  
Frequency Domain Approach ◽  
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.

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.

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.

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