A study on the significance of backlash width values to the performance of the MIQP-based design of MPC

One of the main contributors to the serious degradation
in any control loop performance is the existence
of actuator backlash. Most 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,
one of the main disadvantages 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. An approach that
has been recently developed involved the integration of
the actuator backlash within the framework of Model
Predictive Control (MPC) controller algorithm itself.
This method, so-called the Mixed-Integer Quadratic
Programming (MIQP)-based design of MPC, has been
shown through extensive simulation on industrial case
studies to be able to handle efficiently 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, assumed that the actual value
of the backlash width is known exactly. In this paper,
the performance of the MIQP-based MPC design
is investigated against under- and over-estimation of
the backlash width values. Simulation results via an
industrial Fluidized Catalytic Cracking Unit (FCCU)
case study are presented to show the significance of
precise estimation of the backlash width in ensuring
successful implementation of the MIQP-based design
of MPC.