PID controllers
PI variant

The disadvantage of nonzero steady state error can be eliminated by use of proportional-integral controller (PI). Transient response of system containing the PI controller is shown on the Figure, along with behavior of control variable u.

The response of the control system is different for different controller parameters (coefficients), as well as for different plant properties (structure, parameters). Often, plants, whose parameters vary a much, must be considered. One way to solve this problem is to use an adaptive controller, or a controller, which is able to perform some subset of system identification and to adjust its own coefficients (auto tuning). The other possibility is to use a robust control design methodology, which is able to assure stability for some range of varying plant parameters.

Fig. 8.21: Transient response for 3 different plants
Fig. 8.22: Trensient response - PID controler
Fig. 8.23: Tansient response for 3 different plants symetric
Fig. 8.24: Tansient response for 3 different plants symetric