Digital Control

Basic concepts of digital control, schematic representation of a digital control system, quantisation of time, quantisation of the signal value.

Mathematical bases of discrete systems, sampled signals, z-transform, inverse z-transform, Parseval’s theorem, relations among different forms of Fourier transform, relation between z- and s-planes, transfer function, discrete convolution.

States of discrete systems, state-space representation and transfer function, relation between system response and system eigen-values and eigen-vectors, system response as a function of the system matrix, fundamental matrix, methods for determination of a state transition matrix, the response of non-homogenous linear systems, equilibrium states of the systems.

Frequency response of discrete systems.

Discrete equivalent of continuous systems, discrete equivalent of continuous transfer functions, discrete equivalent of continuous systems given by state-space representations, the relation between continuous and discrete representations, transformation of continuous PID controllers into discrete ones.

Controllability and observability of discrete systems, canonical forms.

Stability of discrete systems Stability criteria, stability of nonlinear systems, direct Lyapunov method.

State controller with a state observer. Basic state controller, optimal state controller, state observer, Kalman filter, duality principle.

• To present the area of discrete control systems, i.e. the systems, given in a form suitable for digital control
• To present complex methods of discrete systems analysis and design.
• To show the methods of conversion of continuous systems into discrete form.
• To present some modern control algorithms to be implemented in digital control.
• To introduce the problems of digital control robustness.

Lectures and laboratory work