Ole Jannerup

An Analysis Of Pole/zero Cancellation In LTR-based Feedback Design

The pole/zero cancellation in LTR-based feedback design will be analyzed for both full-order as well as minimal-order observers. The asymptotic behaviour of the sensitivity function from the LTR-procedure are given in explicit expressions in the case when a zero is not cancelled by an equivalent pole. It will be shown that the non-minimum phase case is included as a special case. The results are not based on any specific LTR-method.

Linear Control System Design

In this chapter a review of the design of multivariable feedback controllers for linear systems will be considered. This review treats mainly deterministic control objects with deterministic disturbances. After giving an overview of the type of linear systems to be treated, this chapter will handle the basic control system design method known as pole or eigenvalue placement. First systems where measurements of all the states are available will be treated. For cases when such complete state measurements are not available the concept of deterministic observers to estimate the states which are not measured directly will be introduced. It will also be shown that it is often possible to design reduced order observers where only the unmeasured states are estimated.

Numerically Controlled Bending of Metal Beams

The paper deals with the introduction of numerical control to a roll-bending process by which steel beams of any cross sections can be bent into desired arbitrarely plane curves.

Optimal Observers: Kalman Filters

This chapter has the purpose of reviewing the most important design aspects of Kalman filters as well as some of their most important properties. Heuristic derivations are given of the Kalman filter `equations for both continuous time and discrete time dynamic systems. It is shown that the state mean values propagate according to the same observer equations as given in Chap. 4. Moreover it is shown that the state noise propagates according to the time dependent Lyapunov equation derived in Chap. 6. When measurements are made on the system this equation has to be modified with a term which expresses the decrease of uncertainty which the measurements make possible. The combination of these two results yields the main stochastic design equation for Kalman filters: the Riccati equation. Solving this equation immediately gives the optimal observer gain for a Kalman filter. Combining a Kalman filter with optimal or LQR feedback results in a very robust controller design: the LQG or Linear Quadratic Gaussian regulator.

A Frequency Domain Design Method For Sampled-Data Compensators

A new approach to the design of a sampled-data compensator in the frequency domain is investigated. The starting point is a continuous-time compensator for the continuous-time system which satisfy specific design criteria. The new design method will graphically show how the discrete-time compensator and the sampling period should be selected so the sampled-data feedback system approximate the continuous-time feedback system as good as possible.

Noise in Dynamic Systems

The purpose of this chapter is to present a brief review of the salient points of the theory of stochastic processes which are relevant to the study of stochastic optimal control and observer systems. Starting with a brief review of the main properties of random variables, this chapter goes forward to a detailed description of the main random process which is used as a model for noise in technological systems: Gaussian white noise. Both time domain and frequency domain descriptions of this important noise model are given. The main result of these considerations is the time dependent Lyapunov equation which is a compact way to express how white noise propagates through linear dynamic systems. Both continuous time and discrete time versions of this equation are given.

State Space Modelling of Physical Systems

Modelling of state space models based on relevant physical laws is introduced. Linearization of nonlinear models is discussed and the connection between the transfer function model and the state space model is derived. Discrete time models are also introduced.

Analysis of State Space Models

In this chapter an overview of the properties of the state space models will be given. A basis for the investigation of these properties is the solution of the state equation given appropriate boundary conditions. The important notions of stability, controllability and observability will be introduced and the similarity transformation discussed. This makes possible the construction of state space models with a number of useful properties.