A new class of nonlinear PID controllers are derived for nonlinear systems using a Nonlinear Generalised Predictive Control (NGPC) approach. First the disturbance decoupling ability of the nonlinear generalised predictive controller is discussed. For a nonlinear system where the disturbance cannot be decoupled, a nonlinear observer is designed to estimate the offset. By selecting the nonlinear gain function in the observer, it is shown that the closed-loop system under optimal generalised predictive control with the nonlinear observer is asymptotically stable.It is pointed out that this composite controller is equivalent to a nonlinear controller with integral action. As a special case, for a nonlinear system with a low relative degree, the proposed nonlinear controller reduces to a nonlinear PI or PID predictive controller, which consists of a nonlinear PI or PID controller and a prediction controller. The design method is illustrated by an example nonlinear mechanical system.

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A control law for a helicopter in low-speed flight is designed using the linear quadratic Gaussian/loop transfer recovery method. The specifications are adapted from a subset of the U.S. Army helicopter handling qualities requirements. The design model consists of the rigid-body dynamics linearized about the 30 kt forward flight condition, together with a simplified, low-order representation of actuator and rotor dynamics. Evaluation is performed using higher-order models, obtained by linearization about several different points in the flight envelope, covering the speed range from 10 to 50 kt. These models contain more accurate representations of the high-frequency actuator and rotor modes. The final selection of the numerical values of the linear quadratic parameters is made by numerical optimization of the loop shape. It is found that the specifications considered can be satisfied for all of the evaluation models without gain scheduling.