Microcontroller Based Applied Digital Control

9

Discrete Controller Design

The design of a digital control system begins with an accurate model of the process to be controlled. Then a control algorithm is developed that will give the required system response. The loop is closed by using a digital computer as the controller. The computer implements the control algorithm in order to achieve the required response.

Several methods can be used for the design of a digital controller:

• A system transfer function is modelled and obtained in the s-plane. The transfer function is then transformed into the z-plane and the controller is designed in the z-plane.
• System transfer function is modelled as a digital system and the controller is directly designed in the z-plane.
• The continuous system transfer function is transformed into the w-plane. A suitable controller is then designed in the w-plane using the well-established time response (e.g. root locus) or frequency response (e.g. Bode diagram) techniques. The final design is transformed into the z-plane and the algorithm is implemented on the digital computer.

In this chapter we are mainly interested in the design of a digital controller using the first method, i.e. the controller is designed directly in the z-plane.

The procedure for designing the controller in the z-plane can be outlined as follows:

• Derive the transfer function of the system either by using a mathematical approach or by performing a frequency or a time response analysis.
• Transform the system transfer function into ...