O.H. Bosgra

A generalized orthonormal basis for linear dynamical systems

In many areas of signal, system, and control theory, orthogonal functions play an important role in issues of analysis and design. In this paper, it is shown that there exist orthogonal functions that, in a natural way, are generated by stable linear dynamical systems and that compose an orthonormal basis for the signal space l/sub 2sup n/. To this end, use is made of balanced realizations of inner transfer functions. The orthogonal functions can be considered as generalizations of, for example, the pulse functions, Laguerre functions, and Kautz functions, and give rise to an alternative series expansion of rational transfer functions. It is shown how we can exploit these generalized basis functions to increase the speed of convergence in a series expansion, i.e., to obtain a good approximation by retaining only a finite number of expansion coefficients. Consequences for identification of expansion coefficients are analyzed, and a bound is formulated on the error that is made when approximating a system by a finite number of expansion coefficients. >

Multivariable feedback control design for high-precision wafer stage motion

Abstract Conventional PID-like SISO controllers are still the most common in industry, but with performance requirements becoming tighter there is a growing need for advanced controllers. For the positioning devices in IC-manufacturing, plant interaction is a major performance-limiting factor. MIMO control can be invoked to attack this problem. A practically feasible procedure is presented to design MIMO feedback controllers for electromechanical positioning devices, using H ∞ /μ techniques. Weighting filters are proposed to straightforwardly and effectively impose performance and uncertainty specifications. Experiments show that MIMO control can considerably improve upon the performance with multiloop SISO control. Some problems are highlighted that are important for industrial practice, but that lack a workable solution.

Synthesis of robust multivariable iterative learning controllers with application to a wafer stage motion system

Iterative Learning Control (ILC) is a powerful control concept that iteratively improves the transient behaviour of processes that are repetitive in nature. Although most of the published ILC schemes are heuristic in nature, some initial research has been performed on the formulation of the ILC problem in the H

Identification of Normalised Coprime Plant Factors from Closed-loop Experimental Data

Recently introduced methods of iterative identification and control design are directed towards the design of high performing and robust control systems. These methods show the necessity of identifying approximate models from closed loop plant experiments. In this paper a method is proposed to approximately identify normalized coprime plant factors from closed loop data. The fact that normalized plant factors are estimated gives specific advantages both from an identification and from a robust control design point of view. It will be shown that the proposed method leads to identified models that are specifically accurate around the bandwidth of the closed loop system. The identification procedure fits very naturally into a recently developed the iterative identification/control design scheme based on H∞ robustness optimization.

A conic reformulation of Model Predictive Control including bounded and stochastic disturbances under state and input constraints

Current state-of-the-art model predictive control does not provide means to handle stochastic disturbances in the presence of constraints. In this paper, we reformulate the MPC problem by bringing feed-back into the future prediction. This feedback is used to control the system response to bounded and stochastic disturbances. This eliminates the conservativeness of open-loop prediction-based dynamic optimization of uncertain stochastic systems in the presence of constraints. The resulting control framework alloys us to formulate the problem as a conic optimization. For conic problems numerically efficient algorithms exist, making on-line application of our strategy possible.

Design strategy for iterative learning control based on optimal control

This paper deals with the analysis and synthesis of iterative learning control (ILC) systems using a lifted representation of the plant. In this lifted representation the system dynamics are described by a static map whereas the learning dynamics are described by a difference equation. The properties of the lifted system and in particular the role of nonminimum phase zeros and system delays are investigated. Based on the internal model principle a general, integrating update law is suggested. Next, a new multiobjective design method is proposed for the design of the learning gain, based on optimal control theory. The convergence speed is optimized subject to a bound on the closed loop variance due to stochastic initial conditions, process disturbances and measurement noise. An efficient tailor-made solution to the design problem is presented, making optimal use of the specific and nice structure of the lifted system ILC representation. The potential of the design method is demonstrated on a realistic example.

Internal-model-based design of repetitive and iterative learning controllers for linear multivariable systems

Repetitive and iterative learning control are two modern control strategies for tracking systems in which the signals are periodic in nature. This paper discusses repetitive and iterative learning control from an internal model principle point of view. This allows the formulation of existence conditions for multivariable implementations of repetitive and learning control. It is shown that repetitive control can be realized by an implementation of a robust servomechanism controller that uses the appropriate internal model for periodic distrubances. The design of such controllers is discussed. Next it is shown that iterative learning control can be implemented in the format of a disturbance observer/compensator. It is shown that the resulting control structure is dual to the repetitive controller, and that both constitute an implementation of the internal model principle. Consequently, the analysis and design of repetitive and iterative learning control can be generalized to the powerful analysis and design procedure of the internal model framework, allowing to trade-off the convergence speed for periodic-disturbance cancellation versus other control objectives, such as stochastic disturbance suppression.

A full solution to the constrained stochastic closed-loop MPC problem via state and innovations feedback and its receding horizon implementation

In this paper we present a full solution to the closed-loop model predictive control problem intrinsically using an observer and innovations feedback, a structure that turns out to be crucial to find its receding horizon implementation. Closed-loop MPC is a strategy in which a reference feedforward trajectory and a linear time varying feedback map are optimized simultaneously using convex optimization techniques. In this formulation, future disturbances are suppressed in an unconservative way by taking future measurements into account. Due to the finite horizon formulation one is forced to use a receding horizon implementation (as in open-loop model predictive control) and we will reveal how to do so.

Extrapolation of optimal lifted system ILC solution, with application to a waferstage

The optimal solution from the lifted system design methods presented by Tousain (2001) has many advantages over classic iterative learning control (ILC) design methods, with one drawback: the ILC solution has to be recalculated for every trajectory of a different length. This paper shows that it is very well possible to avoid this by expressing the solution for the lifted system ILC as a finite time function of the plant parameters. This solution will be referred to as an extrapolated solution since the solution can be used for a trajectory of any length without recalculating the solution. This low order extrapolated solution has been compared to a high order lifted system optimal control (Q-)ILC solution in the application to an industrial grade wafer stage, showing the value of this extrapolated solution.

LMI-based closed-loop economic optimization of stochastic process operation under state and input constraints

In this paper we will solve a closed-loop steady-state economic optimization problem for process operation by means of convex optimization techniques. The objective is the simultaneous optimization of controller parameters and steady-state operating condition maximizing the economic profit of the plant. The main point is, given the economic objective of the plant, to replace back-off selection by back-off optimization together with optimal tuning of controller parameters.