Sensitivity of MIQP-based design of MPC towards the uncertainty in backlash non-linearity gradient values

Actuator backlash, among other actuator nonlinearities,
has been known to cause serious degradation
in any control loop performance if not handled efficiently.
Current existing techniques in compensating
the backlash effect includes the utilization of backlash
nonlinear inverse, which is normally inserted prior to
the control valves such that the net effect is a pure
input/output gain. Though this technique proved efficient,
the main drawback is when the control valve
is operating near its saturation limits. As such, total
compensation is not possible and the backlash effect
may not be eliminated. The newly developed
Mixed-Integer Quadratic Programming (MIQP)-based
design within the framework of Model Predictive Control
(MPC) has been shown through extensive simulation
on industrial case studies to be able to handle
efficiently both actuator saturation and actuator backlash
nonlinearities simultaneously. In most cases, superior
performance is achieved by the MIQP-based MPC
in comparison to other existing backlash compensation
methods. The simulation studies so far, however,
are based on the assumption of unity backlash gradient.
This may not be necessarily true in real-life situations.
In this paper, the sensitivity of the MIQP-based
MPC design is evaluated against the uncertainty in
the backlash gradient values. Simulation results via an
industrial Fluidized Catalytic Cracking Unit (FCCU)
case study are presented to show the robustness of the
newly proposed method to the uncertainties in the gradient
values.