Comparative study between PI-AW and MPC controllers with Gaussian noise in feedback loop

Abstract

The present work proposes a comparative study between the classical PI controller with Antiwindup structure (PI-AW) and aModel Predictive Control (MPC), then the control to be applied is GPC-T. These two control techniques are applied to different plants considering the following situations: Presence of saturation on the control signal, which is related to the real limitations of actuators and the Gaussian noise presence in the feedback loop. Finally, as it is well known in the process control, actuators commonly operate close to their saturation limits, e.g., speed control of an electric motor is always under the influence of the load as consequence the control signal leads the actuators close to their limits. Therefore, loss of reference may happen leading to a steady-state error, which is undesirable in the control processes. This phenomenon is called Noise Induced Tracking Error NITE. Although predictive controller GPC has shown poorer performance compared to the PI-AW one, incorporation of the T-polynomial, i.e., the well-known GPC-T controller considerably improved both disturbance rejection and noise attenuation, when saturation is included in the optimization process with constraint, i.e, decreases the NITE phenomenon. In order to verify the aforementioned analysis experimentally, it has been chosen the speed control loop of a variable reluctance motor (SRM). Such plant has been shown to be suitable for the analysis as it has intrinsic mechanical oscillations and measurement noise. Therefore, by properly choosing a reference speed, one may take the machine to operate very close to the actuators limits, emphasizing the disturbances effect and noises in the overall operation. Then the NITE phenomenon is verified and its decrease by the GPC-T controller with analytic optimization, to decrease the computational effort in the DSP.