PID Controllers Design and Evaluationn

Doctoral thesis, 2003

PID control has been the most widely spread form of feedback in industry for at least five or six decades. It has very old roots, but prior to the 1930s the development was driven by instrument companies, plant designers and plant operators. Today the interest among academics is large and increasing. When new controller types and new tuning rules are presented, they have to show their superiority over already accepted types and rules in one respect or another. A correct comparison requires an evaluation method that can guarantee that an improvement of one property has not been paid by a too bad deterioration of another. Such a method is presented in this thesis. It is based on four well defined criteria, related to vital performance and robustness system characteristics. According to the proposed evaluation method optimal PI and PID controllers have been investigated for a large number of plant models. Common features have been observed, resulting in almost optimal tuning rules for stable plants, including those with an oscillating mode, and for plants with integral action. Derivative action in the controller is recommended, since in most cases a PID controller increases the output performance significantly compared to a PI controller. This improvement is reached, with moderate enlargement of the control activity and the sensor noise sensitivity and without deterioration of the stability margin, only by including the low-pass filter on the derivative part in the design. An alternative to the traditional parameterization of the PID controller is introduced, which makes the same parameters well suited for formulation of all kinds of low order controllers. Furthermore, almost optimal zeros for the PID controller (specified by two of the new parameters) can well be found by help of a simple step response. The two remaining PID parameters, the high-frequency gain (or alternatively the filter factor) related to control activity and the integral gain related to performance, can then be manipulated sequentially by the user to tune the important trade-off between output performance, stability margins and sensitivity to sensor noise as well as high-frequency robustness. To further improve the high-frequency properties it is also shown how additional low-pass filtering can easily be added to the classical PID controller.