Multirate sliding mode disturbance compensation for model predictive control

Abstract

SUMMARYIn this paper, a novel hierarchical multirate control scheme for nonlinear discrete-time systems is presented, consisting of a robust Nonlinear Model Predictive Controller (NMPC) and a Multirate Sliding Mode Disturbance Compensator (MSMDC). The proposed MSMDC acts at a faster rate than the NMPC in order to keep the system as close as possible to the nominal trajectory predicted by NMPC despite model uncertainties and external disturbances. The a-priori disturbance compensation turns out to be very useful in order to improve the robustness of the NMPC controller. A dynamic input allocation between MSMDC and NMPC allows to maximize the benefits of the proposed scheme that unites the advantages of sliding mode control (strong reduction of matched disturbances, low computational burden) to those of NMPC (optimality, constraints handling). Sufficient conditions required to guarantee Input-to-State Stability (ISS) and constraints satisfaction by the overall scheme are also provided.

Hierarchical Model Predictive/Sliding Mode Control of Nonlinear Constrained Uncertain Systems

“…In this case the equivalent disturbances visible by the MPC can be computed as a function of the maximal input allocated to SMC [Raimondo et al, 2014]. The choice of the upperbound for the ISM control and consequently for the MPC (see (18)) can be done dynamically.…”

“…The choice of the upperbound for the ISM control and consequently for the MPC (see (18)) can be done dynamically. For example in [Raimondo et al, 2014] the following strategy has been proposed: if the state is far from the origin, since the SMC cannot guarantee the robustness of the controlled system [Utkin, 1992], it is generated with the minimum actuation range in order to provide a large domain of attraction; if the state is closer to the origin more input is allocated to the SMC in order to provide a stronger disturbance rejection. Also for this scheme ISpS has been proved in [Raimondo et al, 2014].…”

“…In particular, the MPC has been used to update the parameters of the sliding manifold. A different idea to combine MPC and SMC was proposed in [Rubagotti et al, 2011a;Ferrara et al, 2013;Raimondo et al, 2014;Ferrara et al, 2014a], where a hierarchical control scheme composed by a high level MPC and a low level ISM is proposed (see Figure 1). The ISM component has the aim to reduce the difference between the dynamics of the nominal closed-loop system and the actual evolution of the state.…”

“…In order to provide a practical solution, a multirate discrete-time scheme is required [Raimondo et al, 2014]. In particular two different finite sampling times are used for the ISM (shorter) and for the MPC (longer).…”

“…Otherwise, if the state is closer to the origin and MPC requires less control amplitude, more amplitude is allocated to the ISM in order to provide a stronger disturbance rejection. ISpS has been proved also for this formulation [Raimondo et al, 2014]. A practical example of the MPC/ISM control strategy has been presented in [Ferrara et al, 2013], where a robust hierarchical multi-loop control scheme aimed at solving motion control problems for robot manipulators has been proposed.…”