Backlash Compensation Using Receding Horizon Control

We present a receding horizon control algorithm for compensation ofbacklash at the input of a stable linear system under control rateconstraints. The problem is first posed as a receding horizonoptimal control problem by modelling backlash as a piecewise affinesystem having a state space partition with three regions.This optimal control problem involves solving, at each step, 3^N quadraticprogrammes, where N is the optimisation horizon. As analternative to solving the quadratic programmes, we propose astrategy based on a recently devised suboptimal receding horizoncontrol algorithm which utilises a singular value decomposition ofthe Hessian of the quadratic programme. This alternative strategyleads, at the cost of some performance degradation, to a much smallercomputational load since a feasible rather than optimal solution hasto be obtained at each step.