Predictive Second Order Sliding Control of Constrained Linear Systems with Application to Automotive Control Systems

Abstract

This paper presents a new predictive second order sliding controller (PSSC) formulation for setpoint tracking of constrained linear systems. The PSSC scheme is developed by combining the concepts of model predictive control (MPC) and second order discrete sliding mode control. In order to guarantee the feasibility of the PSSC during setpoint changes, a virtual reference variable is added to the PSSC cost function to calculate the closest admissible set point. The states of the system are then driven asymptotically to this admissible setpoint by the control action of the PSSC. The performance of the proposed PSSC is evaluated for an advanced automotive engine case study, where a high fidelity physics-based model of a reactivity controlled compression ignition (RCCI) engine is utilized to serve as the virtual test-bed for the simulations. Considering the hard physical constraints on the RCCI engine states and control inputs, simultaneous tracking of engine load and optimal combustion phasing is a challenging objective to achieve. The simulation results of testing the proposed PSSC on the high fidelity RCCI model show that the developed predictive controller is able to track desired engine load and combustion phasing setpoints, with minimum steady state error, and no overshoot. Moreover, the simulation results confirm the robust tracking performance of the PSSC during transient operations, in the presence of engine cyclic variability.

Constrained Nonlinear Discrete-Time Sliding Mode Control Based on a Receding Horizon Approach

“…Apart from the listed technical challenges, the main contribution of this work consists of defining a DSMC law for uncertain and possibly multi-input nonlinear systems, directly based on the nonlinear dynamics, that guarantees the satisfaction of both input and state constraints in a general form. Such a result, to the best of our knowledge, is not available in the literature, as the cited papers either deal with linear systems [8], [10], [11], [13]- [15] or linear systems approximations [9], or generate an overall control law that is not a DSMC law [12], or finally use a DSMC controller to enhance the robustness properties of a separate MPC controller [16]- [20]. Notice that, when the state constraints are defined directly on the components of the sliding variable, one could design a sliding mode controller without the need for receding-horizon approaches, so as to force the state to slide on the boundary of the admissible region (i.e., the region of the state space in which all state constraints are satisfied), whenever this boundary is reached, thus satisfying the imposed constraints (see, e.g., [24] for continuous-time SMC).…”

“…Also, [11] proposes an MPC law for single-input perturbed linear systems, which guarantees asymptotic convergence of the state to a boundary layer of S. Moreover, [12] presents single-input MPC laws for unperturbed linear and nonlinear systems, where S is used to define the terminal constraint of the MPC problem, while [13] proposes a DSMC law for linear multi-input systems based on the solution of a robust linear MPC problem: the resulting control law guarantees finite-time convergence of the state onto S (in case of vanishing disturbance) or into an apriori determined boundary layer of it (in case of persistent disturbance). DSMC for setpoint tracking in constrained linear systems was studied in [14] and [15]: [14] relies on a dualmode receding horizon DSMC law which exploits the flatness property of suitably defined sliding hyperplanes, while [15] proposes a second-order DSMC scheme to add virtual reference variables to the receding horizon law.…”

Adaptive Discrete Second-Order Sliding Mode Control With Application to Nonlinear Automotive Systems

“…Converting a high dimensional tracking control problem into a low dimensional stabilization control problem is the key feature of sliding mode control (SMC) [1,2]. SMC * Address all correspondence to this author.…”