On robust and optimal control : with real time aspects

Abstract: This thesis deals with several issues in realistic design of control systems, both from a practical and a theoretical point of view. This is done in three papers which are preceded by an introduction and a short discussion on future research on time-varying delays. The first paper discusses the importance of reliable sensors in control systems. This is illustrated with an application from the paper industry, namely headbox control, where the problem is to control the outlet jet velocity. The velocity is found from computations based on the measured pressure in the headbox and the geometric appearance of the outlet. These computations are known to be inaccurate and it is also known that the pressure gauge is affected by aging, leading to an undetermined bias in the measured pressure. The presented solution uses a laser based velocity meter to correct the pressure gauge and also to detect aging. This solution has been chosen since continuous sensor information can not be guaranteed from the laser. The second paper investigates some widely used signal spaces for the purpose of extending standard $H_{\infty}$ theory to deal with persistent signals. The investigation is based on classical works by Wiener, Beurling and Marcinkiewicz. It is shown that a wide range of persistent signals can be used in for $H_{\infty}$ based control and modelling, in both continuous and discrete time. The third paper concerns constraints of the controller structure and sample-data aspects in $H_{2}$ optimal control. It is shown how the continuous $H_{2}$ criterion of the closed-loop system can be recast into a discrete parametric optimization problem from which a fixed structure controller can be found that minimizes the continuous criteria. The method accounts for intersample behaviour and it also makes use of an averaging sampler in order to circumvent the difficulty of sampling continuous white noise.