Automatic disturbance rejection using quasilinear control

Abstract

In control theory, when controllers are designed it is assumed that there exists a value of controller e ort than can stabilize the system and additionally, the reference can be tracked. If on the other hand, the plant model of the system is unstable, or if it has modeling errors, the controller e ort needs to be unbounded. Physically speaking every controller needs to be realized using analog hardware or using digital hardware. The output terminals of the controller cannot drive a signal having boundless magnitude. For instance, if the controllers are implemented using operational ampli er, the output of the ampli er is always bounded by the DC supply voltages. If the supply voltage is Vs volts, then the maximum signal that can be driven by the ampli er without getting into saturation would be in the range Lð€€€ L+. The solution of the issue is presented by quasilinear controller theory. To demonstrate the issue, three controllers for magnetic levitation system (MLS) are designed in this work. First controller is designed using loop-shaping methods. As the MLS is highly non-linear, so its linearized model can frequently and abruptly actuate saturation non-linearity. It is shown, the systems transient performance, steady state performance and the disturbance rejection is exactly what is required. But the controller e ort signal reaches a value of 50 plus units in tracking the unit step reference. Second controller has been designed using active disturbance rejection control (ADRC) theory. The ADRC controller performs better than loop-shaping controller, in terms of transient speci cations, steady state speci cations and disturbance rejection. Also, this controller does not need accurate plant model, so it does counteract modeling errors more e ectively than loop-shaping control. But this controller has exhibited huge controller e ort to do the perfect job. Third controller (which is the proposed solution) is designed using quasilinear control theory (QLC). It is shown that this controller not only satis es the performance speci cations, but the magnitude of controller e orts remains within the bounds. And it never actuates the saturation non-linearity.