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Advantages and disadvantages of the different types of controllers

In the following the disturbance behaviour is investigated using the controllers introduced in section 8.1. Their parameters are tuned optimally according to the performance index from section 7.3.2. The plant is given by Eq. (8.12). Figure 8.5 shows for the different types of controller the responses to a step disturbance of the controlled variable , which is normalised by . These curves indicate that because the relation is valid.

For discussing these curves the term settling time according to section 7.3.1 is used, which is related to the steady state of the uncontrolled case

(8.14)

In addition, the different cases should be compared with respect to the normalised maximum overshoot .

The different cases are discussed below:

a)
The P controller shows a relatively high maximum overshoot , a long settling time as well as a steady-state error .

b)
The I controller has a higher maximum overshoot than the P controller due to the slowly starting I behaviour, but no steady-state error.

c)
The PI controller fuses the properties of the P and I controllers. It shows a maximum overshoot and settling time similar to the P controller but no steady-state error.

d)
The real PD controller according to Eq. (8.9) with has a smaller maximum overshoot due to the 'faster' D action compared with the controller types mentioned under a) to c). Also in this case a steady-state error is visible, which is smaller than in the case of the P controller. This is because the PD controller generally is tuned to have a larger gain due to the positive phase shift of the D action. For the results shown in Figure 8.5 the gain for the P controller is and for the PD controller . The plant has a gain of .

e)
The PID controller according to Eq. (8.6) with fuses the properties of a PI and PD controller. It shows a smaller maximum overshoot than the PD controller and has no steady state error due to the I action.

The qualitative concepts of this example are also relevant to other type of plants with delayed proportional behaviour. This discussion has given some first insights into the static and dynamic behaviour of control loops.

Figure 8.5: Behaviour of the normalised controlled variable for step disturbance at the input to the plant ; for different types of controllers



Next: Empirical tuning rules according Up: PID control and associated Previous: Optimal tuning of PID   Contents
Christian Schmid 2005-05-09