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 the z-plane.
• Design a suitable digital controller in the z-plane.
• Implement the controller algorithm on a digital computer.
A discrete-time system can be in many different forms, depending on the type of input and the type of sensor used. Figure 9.1 shows a discrete-time system where the reference input is an analog signal, and the process output is also an analog signal. Analog-to-digital converters are then used to convert these signals into digital form so that they can be processed by a digital computer. A zero-order hold at the output of the digital controller approximates a D/A converter which produces an analog signal to drive the plant.
In Figure 9.2 the reference input is a digital signal, which is usually set using a keyboard or can be hard-coded into the controller algorithm. The feedback signal is also digital and the
error signal is formed by the computer after subtracting the feedback signal from the reference input. The digital controller then implements the control algorithm and derives the plant.