Iterative Learning Control Law Design Research Articles

Modified Newton method based iterative learning control design for discrete nonlinear systems with constraints

This paper considers the design of iterative learning control laws for classes of nonlinear dynamics. In particular, a new Newton method design is developed for discrete nonlinear systems in the presence of input constraints, where such constraints will arise in applications. The new design is based on the use of a penalty function and an iterative method for solving an unconstrained nonlinear optimization problem with an algorithm that has monotonic and super linear convergence characteristics. In this new algorithm the input inequality constraints are transformed into equality form by adding auxiliary variables. A cost function is then minimized to produce the new iterative learning control law design. Finally, a simulation based case study is given to illustrate the performance of the new design.

Higher-order Iterative Learning Control Law Design using Linear Repetitive Process Theory: Convergence and Robustness

Iterative learning control has been developed for processes or systems that complete the same finite duration task over and over again. The mode of operation is that after each execution is complete the system resets to the starting location, the next execution is completed and so on. Each execution is known as a trial and its duration is termed the trial length. Once each trial is complete the information generated is available for use in computing the control input for the next trial. This paper uses the repetitive process setting to develop new results on the design of higher-order ILC control laws for discrete dynamics. The new results include conditions that guarantee error convergence and design in the presence of model uncertainty.

Modeling and Iterative Learning Control of a Circular Deformable Mirror

An unconditionally stable finite difference scheme for systems whose dynamics are described by a fourth-order partial differential equation is developed using a regular hexagonal grid. The scheme is motivated by the well-known Crank-Nicolson discretization that was originally developed for second-order systems and it is used in this paper to develop a discrete in time and space model of a deformable mirror as a basis for control law design. As one example, the resulting model is used for iterative learning control law design and supporting numerical simulations are given.

Robust iterative learning control design for linear systems with time-varying delays and packet dropouts

This paper proposes the robust iterative learning control (ILC) design for uncertain linear systems with time-varying delays and random packet dropouts. The packet dropout is modeled by an arbitrary stochastic sequence satisfying the Bernoulli binary distribution, which renders the ILC system to be stochastic instead of a deterministic one. The main idea of this paper is to transform the ILC design into robust stability for a two-dimensional (2D) stochastic system described by the Roesser model with a delay varying in a range. A delay-dependent stability condition, which can guarantee mean-square asymptotic stability of such a 2D stochastic system, is derived in terms of linear matrix inequalities (LMIs), and formulas can be given for the ILC law design. An example for the injection molding is given to demonstrate the effectiveness of the proposed ILC method.

Vector Lyapunov functions for stability and stabilization of differential repetitive processes

Differential repetitive processes arise in the analysis and design of iterative learning control algorithms. They belong to a class of mathematical models whose dynamic properties are defined by two independent variables, such as a time and a spatial coordinate, also known as 2D systems in the literature. Moreover, standard stability analysis methods cannot be applied to such processes. This paper develops a vector Lyapunov function-based approach to the exponential stability analysis of differential repetitive processes and applies the resulting conditions to develop linear matrix inequality based iterative learning control law design algorithms in the presence of model uncertainty.

Experimentally verified generalized KYP Lemma based iterative learning control design

This paper considers iterative learning control law design for plants modeled by discrete linear dynamics using repetitive process stability theory. The resulting one step linear matrix inequality based design produces a stabilizing feedback controller in the time domain and a feedforward controller that guarantees convergence in the trial-to-trial domain. Additionally, application of the generalized Kalman–Yakubovich–Popov (KYP) lemma allows a direct treatment of differing finite frequency range performance specifications. The results are also extended to plants with relative degree greater than unity. To support the algorithm development, the results from an experimental implementation are given, where the performance requirements include specifications over various finite frequency ranges.

An iterative learning control design approach for networked control systems with data dropouts

SummaryIn network‐based iterative learning control (ILC) systems, data dropout often occurs during data packet transfers from the remote plant to the ILC controller. This paper considers the problem of controller design for such ILC processes. Packet missing is modeled by stochastic variables satisfying the Bernoulli random binary distribution, which renders such an ILC system to be a stochastic one. Then, the design of ILC law is transformed into the stabilization of a 2‐D stochastic system described by the Roesser model. A sufficient condition for mean‐square asymptotic stability is established by means of a linear matrix inequality technique, and formulas can be given for the control law design simultaneously. This result is further extended to more general cases where the system matrices also contain uncertain parameters. The effectiveness and merits of the proposed method are illustrated by a numerical example. Copyright © 2015 John Wiley & Sons, Ltd.

Robust finite frequency range iterative learning control design and experimental verification

Iterative learning control is an application for two-dimensional control systems analysis where it is possible to simultaneously address error convergence and transient response specifications but there is a requirement to enforce frequency attenuation of the error between the output and reference over the complete spectrum. In common with other control algorithm design methods, this can be a very difficult specification to meet but often the control of physical/industrial systems is only required over a finite frequency range. This paper uses the generalized Kalman–Yakubovich–Popov lemma to develop a two-dimensional systems based iterative learning control law design algorithm where frequency attenuation is only imposed over a finite frequency range to be determined from knowledge of the application and its operation. An extension to robust control law design in the presence of norm-bounded uncertainty is also given and its applicability relative to alternative settings for design discussed. The resulting designs are experimentally tested on a gantry robot used for the same purpose with other iterative learning control algorithms.

Output Information Based Iterative Learning Control Law Design With Experimental Verification

This paper considers iterative learning control law design using the theory of linear repetitive processes. This setting enables trial-to-trial error convergence and along-the-trial performance to be considered simultaneously in the design. It is also shown that this design extends naturally to include robustness to unmodeled plant dynamics. The results from experimental application of these laws to a gantry robot performing a pick and place operation are given, together with a discussion of the positioning of this approach relative to alternatives and possible further research.

Experimentally supported 2D systems based iterative learning control law design for error convergence and performance

This paper considers iterative learning control law design for both trial-to-trial error convergence and along the trial performance. It is shown how a class of control laws can be designed using the theory of linear repetitive processes for this problem where the computations are in terms of linear matrix inequalities (LMIs). It is also shown how this setting extends to allow the design of robust control laws in the presence of uncertainty in the dynamics produced along the trials. Results from the experimental application of these laws on a gantry robot performing a pick and place operation are also given.