Constrained LQR Using Online Decomposition Techniques

This paper presents an algorithm to solve the infinite horizon constrained linear quadratic regulator (CLQR) problem using operator splitting methods. First, the CLQR problem is reformulated as a (finite-time) model predictive control (MPC) problem without terminal constraints. Second, the MPC problem is decomposed into smaller subproblems of fixed dimension independent of the horizon length. Third, using the fast alternating minimization algorithm to solve the subproblems, the horizon length is estimated online, by adding or removing subproblems based on a periodic check on the state of the last subproblem to determine whether it belongs to a given control invariant set. We show that the estimated horizon length is bounded and that the control sequence computed using the proposed algorithm is an optimal solution of the CLQR problem. Compared to state-of-the-art algorithms proposed to solve the CLQR problem, our design solves at each iteration only unconstrained least-squares problems and simple gradient calculations. Furthermore, our technique allows the horizon length to decrease online (a useful feature if the initial guess on the horizon is too conservative). Numerical results on a planar system show the potential of our algorithm.Comment: This technical report is an extended version of the paper titled "Constrained LQR Using Online Decomposition Techniques" submitted to the 2016 Conference on Decision and Contro

A comparative study of methods for estimating virtual flux at the point of common coupling in grid connected voltage source converters with LCL filter

Grid connected Voltage Source Converters (VSCs) with LCL filters usually have voltage measurements at the filter capacitors, while it can be important to control the active or reactive power injection at the grid-side of the LCL filter, for instance at a Point of Common Coupling (PCC). Synchronization to the PCC voltage can be obtained by Virtual Flux (VF) estimation, which can also allow for voltage sensor-less operation of VSCs. This paper is presenting a comparative evaluation of methods for estimating the VF at the PCC, considering a VSC connected to the grid through an LCL filter with a Proportional Resonant (PR) controller as the inner current control loop. The VF estimation is achieved by using frequency adaptive dual SOGI-QSGs (DSOGI-VF). The Frequency Locked Loop (FLL) is used in order to keep the positive and negative sequence (PNS) VF estimation inherently frequency adaptive. Three different methods are considered for obtaining the capacitor current needed for estimating the VF at the grid side of the LCL filter which are based on fully estimation by using the voltage sensor-less method, by estimating the capacitor current from the measured voltage or by using additional capacitor current sensors. The results have been compared and validated by simulation studies.Peer ReviewedPostprint (author's final draft

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

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.Comment: 6 pages, 5 figures, 2018 American Control Conferance (ACC), June 27-29, 2018, Milwaukee, WI, USA. [Accepted in Jan. 2018