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 L 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.
