Fixed parameter feedback control action

As indicated previously, the control action of the controller seeks to alter the position of the final control element in such a way as to minimise the error in the least possible time with the minimum disturbance to the system. The control action selected depends largely upon the dynamic behaviour of the other components in the control system. 

The simplest type of control which is commonly experienced is that of having an on-off or two-position action (often called bang-bang control). A typical example is the thermostatically controlled domestic immersion heater. Depending on the temperature of the water in the tank, the power supply is either connected to, or disconnected from, the heater. The relationship between controller input and output might appear as in Fig. 7.4. Such a system is simple and inexpensive. However, the oscillatory nature of the control makes it suitable only for those purposes where close control is not essential and/or where its non-linear action can be taken into account. This is considered in more detail in Section 7.16.2. 

There are three principal types or modes of control action which are more generally employed, viz. proportional (P), integral (I), and derivative (D). In the first the controller produces an output signal J which is proportional to the error, i.e.  

with proportional control, the greater the magnitude of the error the larger is the corrective action applied. 

It is generally assumed when considering control system dynamics that at t 0 the control system is at a steady state and that e is zero. Hence, it is necessary to 

---