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A general controller evaluation method is introduced, based on four performance and robustness criteria including both low-, mid-and high-frequency properties. According to this method, optimal PI and PID controllers are designed. In industrial applications derivative action is often omitted, due to noise sensitivity. In this paper is shown that when a low-pass filter is included in the design of a PID controller, the control activity as well as the noise sensitivity can be significantly reduced compared to common design rules. These benefits are reached without deterioration of stability margins or low frequency performance. Two sets of simple tuning rules for stable non-oscillating plants are proposed. One set is suitable for automatic tuning. The other one is based on a step response and leaves the operator with just one parameter to tune. This rule makes it in fact easier to tune a PID controller than a PI controller close to the optimum. Furthermore, it is pointed out that a well tuned PID controller with a second order filter often offers the same performance to the same price in form of control activity as a modern H 1 controller. For a delayed plant a Smith predictor can be introduced. However, when a PI controller is used, it is shown to be more profitable to provide the controller with derivative action than with a Smith predictor. On the other hand, together with a PID controller the Smith predictor may improve performance to some extent for plants with moderate delays.

In this paper PI and PID controllers augmented by a Smith predictor structure are compared to ordinary PI and PID controllers, for plants with medium and great time delays. The comparison is based an a systematic evaluation method, where both robustness and performance aspects in different frequency regions are taken into account.The results show that a Smith predictor increases performance somewhat for a PID controller when the time delay is moderate. For great time delays, however, the improvement is insignificant. An important remark is that it is necessary to include the predictor structure in the design to get acceptable robustness propertiea. For a PI controller the benefits from a predictor are mostly small or negligible independent of time delay.Most important is, however that a derivative part obviously will bring siflcantly greater improvement than a Smith predictor to a system with a PI controller. This result is somewhat surprising, since Smith predictors are normally used together with PI and not with PID controllers. Furthermore, it is sometime8 argued that it is no use to include derivative action for plants with significant time delay.

A procedure for fair comparison between different control structures and design parameters is suggested. Low, high and mid-frequency properties are then treated separately in the evaluation of closed loop performance and robustness. By this separation it is possible to investigate e.g. the tradeoff between low frequency performance and high frequency robustness, while pass band robustness (stability margins) is kept constant.More specifically we consider tuning of PID controllers, and find as a result of our design and evaluation procedure that low frequency performance and closed loop bandwidth can be improved significantly, without loosing high frequency robustness and mid-frequency stability margins.The key is to choose some parameters of a standard PID controller in a somewhat unconventional way.