Willem L. De Koning

State-space analysis and identification for a class of hysteretic systems

An identification technique is presented for certain non-linear state-space models describing systems under the influence of hysteresis

Brief Digital optimal reduced-order control of pulse-width-modulated switched linear systems

In this paper digital optimal control of pulse-width-modulated switched linear systems is considered. The equivalent discrete-time system and its deviation around a stationary solution plays an important role. An optimal linear discrete-time deviation controller is developed. The controller is chosen to be one-step-ahead predictive, which is a natural choice for control of digital pulse-modulated systems. The controller is optimal, i.e. a cost criterion is minimized. The theory is generally applicable and gives, in principle, a tool to design a digital optimal controller for an arbitrary pulse-width-modulated switched linear system. The theory is illustrated by examples from the field of switched electrical networks.

Stationary optimal control of stochastically sampled continuous-time systems

Abstract This paper solves the digital stationary optimal control problem in the case of linear stochastic continuous-time systems, long-term average integral criteria, complete state information and where the sampling periods are independent identically distributed stochastic variables, using the notions of mean-square stabilizability and mean-square detectability. It is shown that stochastic sampling may increase or restore stabilizability and may decrease or destroy stability if the presence of stochastic sampling is not taken into account in the determination of the optimal controller.

Physical Modeling of Piezoelectric Actuators for Control Purposes

Abstract The piezoelectric actuator is a well-known device for managing extremely small displacements in the range of 10 pm (1 pm = 10 –12 m) to 100 μ m. When developing a control system for a piezo-actuated positioning mechanism the actuator dynamics have to be taken into account. A piezo model, based on physical principles, is presented for the case of charge control as well as for the case of voltage control. In the latter model a first order differential equation is used to describe the hysteresis effect. Both models are suitable for control purposes.

Minimal representation of matrix valued white stochastic processes and U–D factorisation of algorithms for optimal control

Two different descriptions are used in the literature to formulate the optimal dynamic output feedback control problem for linear dynamical systems with white stochastic parameters and quadratic criteria, called the optimal compensation problem. One describes the matrix valued white stochastic processes involved, using a sum of deterministic matrices each one multiplied by a scalar stochastic process that is independent of the others. Another, that is more general and concise, uses Kronecker products instead. This article relates the statistics of both descriptions and shows their advantages and disadvantages. As to the first description, an important result that comes out is the minimum number of matrices multiplied by scalar, independent, stochastic processes needed to represent a certain matrix valued white stochastic process, together with an associated minimal representation. As to the second description, an important result concerns the generation of all Kronecker products that represent relevant st...Two different descriptions are used in the literature to formulate the optimal dynamic output feedback control problem for linear dynamical systems with white stochastic parameters and quadratic criteria, called the optimal compensation problem. One describes the matrix valued white stochastic processes involved, using a sum of deterministic matrices each one multiplied by a scalar stochastic process that is independent of the others. Another, that is more general and concise, uses Kronecker products instead. This article relates the statistics of both descriptions and shows their advantages and disadvantages. As to the first description, an important result that comes out is the minimum number of matrices multiplied by scalar, independent, stochastic processes needed to represent a certain matrix valued white stochastic process, together with an associated minimal representation. As to the second description, an important result concerns the generation of all Kronecker products that represent relevant statistics. Both results facilitate the specification of statistics of systems with white stochastic parameters. The second part of this article further exploits these results to perform an U–D factorisation of an algorithm to compute optimal dynamic output feedback controllers (optimal compensators) for linear discrete-time systems with white stochastic parameters and quadratic sum criteria. U–D factorisation of this type of algorithm is new. By solving several numerical examples, the U–D factored algorithm is compared with a conventional algorithm.

Stability aspects of a multifrequency model of a PWM converter

In this paper the stability of a multifrequency model of a PWM converter is investigated. A multifrequency model is a model based on Fourier series that contains as a special case the so-called state space average model. In contrast to a state space average model a multifrequency model may also include so-called higher order harmonics, where the zeroth order harmonic corresponds to the (moving) average. This paper focuses on a specific PWM converter, namely a ( uk converter, and it is proved that a multifrequency model of a ( uk converter with fixed duty ratio is asymptotically stable. This result generalizes the known corresponding result for a state space average model of a ( uk converter with fixed duty ratio. Taking all the harmonics into account the result also illustrates the well-known fact that a ( uk converter with a fixed duty ratio and a finite switching frequency is asymptotically stable in the following sense. If the signals in a ( uk converter do not correspond with a periodic behaviour, they will however do so in the limit, i.e. as time goes to infinity the signals will become periodic, and this limiting periodic behaviour is unique. Although the paper mainly deals with the stability issues for a ( uk converter, it is possible to use the ideas of the paper to derive similar results for other types of PWM converters.

Spectral Analysis of Stochastically Sampled Dynamic Systems

Abstract. In this paper a spectral analysis methodology is introduced for stochastically sampled linear, dynamic, and stochastic continuous-time systems. This particular problem is considered for the purpose of investigating the spectral analysis issues associated with turbulent velocity measurements. The properties of the equivalent linear discrete-time system allow for the determination of the covariance between observations as a function of the number of in-between measurements. Subsequently, this autocovariance function is analyzed in the frequency domain.

Digital control of Pritchard-Salamon systems

Abstract In this paper we are concerned with the digital approach to the LQ optimal control problem of Pritchard-Salamon systems. We show how the digital control problem can be converted into an equivalent discrete-time LQ control problem and the construction of the optimal control law is based on the solution of classical Riccati equations.

The influence of uncertainty on stability and compensatability

In this paper the influence of uncertainty of linear discrete-time systems modelled with white parameters on the properties of mean-square stability and compensatability is considered. A measure for the uncertainty in the system matrices is introduced. This measure is also a measure for the uncertainty in the system in the sense that stability and compensatability decreases if this system uncertainty increases. It is indicated how to calculate numerically the mean-square stability and compensatability. The results are illustrated with examples.

Temporal stabilizability and compensatability of time-varying linear discrete-time systems with white stochastic parameters

This paper reveals that apart from changes of system structure vital system properties such as stabilizability and compensatability may be lost temporarily due to the stochastic nature of system parameters. To that end new system properties called temporal mean-square stabilizability (tms-stabilizability) and temporal mean-square compensatability (tms-compensatability) for time-varying linear discrete-time systems with white stochastic parameters (multiplicative white noise) are developed. When controlling such systems by means of (optimal) state feedback, tms-stabilizability identifies intervals where mean-square stability (ms-stability) is lost temporarily. This is vital knowledge to both control engineers and system scientists. Similarly, tms-compensatability identifies intervals where ms-stability is lost temporarily in case of full-order (optimal) output feedback. Tests explicit in the system matrices are provided to determine each temporal system property. These tests compute measures of the associated temporal system properties. Relations among the new system properties as well as relations with associated existing system properties are investigated and established. Examples illustrating principal applications and practical importance are provided.