A convexity approach to dynamic output feedback robust MPC for LPV systems with bounded disturbances

International audienceA convexity approach to dynamic output feedback robust model predictive control (OFRMPC) is proposed for linear parameter varying (LPV) systems with bounded disturbances. At each sampling time, the model parameters and disturbances are assumed to be unknown but bounded within pre-specified convex sets. Robust stability conditions on the augmented closed-loop system are derived using the techniques of robust positively invariant (RPI) set and the S-procedure. A convexity method reformulates the non-convex bilinear matrix inequalities (BMIs) problem as a convex optimization one such that the on-line computational burden is significantly reduced. The on-line optimized dynamic output feedback controller parameters steer the augmented states to converge within RPI sets and recursive feasibility of the optimization problem is guaranteed. Furthermore, bounds of the estimation error set are refreshed by updating the shape matrix of the future ellipsoidal estimation error set. The dynamic OFRMPC approach guarantees that the disturbance-free augmented closed-loop system (without consideration of disturbances) converges to the origin. In addition, when the system is subject to bounded disturbances, the augmented closed-loop system converges to a neighborhood of the origin. Two simulation examples are given to verify the effectiveness of the approach

Model Identification and Robust Nonlinear Model Predictive Control of a Twin Rotor MIMO System

PhDThis thesis presents an investigation into a number of model predictive control (MPC) paradigms for a nonlinear aerodynamics test rig, a twin rotor multi-input multi-output system (TRMS). To this end, the nonlinear dynamic model of the system is developed using various modelling techniques. A comprehensive study is made to compare these models and to select the best one to be used for control design purpose. On the basis of the selected model, a state-feedback multistep Newton-type MPC is developed and its stability is addressed using a terminal equality constraint approach. Moreover, the state-feedback control approach is combined with a nonlinear state observer to form an output-feedback MPC. Finally, a robust MPC technique is employed to address the uncertainties of the system. In the modelling stage, analytical models are developed by extracting the physical equations of the system using the Newtonian and Lagrangian approaches. In the case of the black-box modelling, artificial neural networks (ANNs) are utilised to model the TRMS. Finally, the grey-box model is used to enhance the performance of the white-box model developed earlier through the optimisation of parameters using a genetic algorithm (GA) based approach. Stability analysis of the autonomous TRMS is carried out before designing any control paradigms for the system. In the control design stage, an MPC method is proposed for constrained nonlinear systems, which is the improvement of the multistep Newton-type control strategy. The stability of the proposed state-feedback MPC is guaranteed using terminal equality constraints. Moreover, the formerly proposed MPC algorithm is combined with an unscented Kalman filter (UKF) to formulate an output-feedback MPC. An extended Kalman filter (EKF) based on a state-dependent model is also introduced, whose performance is found to be better compared to that of the UKF. Finally, a robust MPC is introduced and implemented on the TRMS based on a polytopic uncertainty that is cast into linear matrix inequalities (LMI)

Robust model predictive control for linear systems subject to norm-bounded model Uncertainties and Disturbances: An Implementation to industrial directional drilling system

Model Predictive Control (MPC) refers to a class of receding horizon algorithms in which the current control action is computed by solving online, at each sampling instant, a constrained optimization problem. MPC has been widely implemented within the industry, due to its ability to deal with multivariable processes and to explicitly consider any physical constraints within the optimal control problem in a straightforward manner. However, the presence of uncertainty, whether in the form of additive disturbances, state estimation error or plant-model mismatch, and the robust constraints satisfaction and stability, remain an active area of research. The family of predictive control algorithms, which explicitly take account of process uncertainties/disturbances whilst guaranteeing robust constraint satisfaction and performance is referred to as Robust MPC (RMPC) schemes. In this thesis, RMPC algorithms based on Linear Matrix Inequality (LMI) optimization are investigated, with the overall aim of improving robustness and control performance, while maintaining conservativeness and computation burden at low levels. Typically, the constrained RMPC problem with state-feedback parameterizations is nonlinear (and nonconvex) with a prohibitively high computational burden for online implementation. To remedy this issue, a novel approach is proposed to linearize the state-feedback RMPC problem, with minimal conservatism, through the use of semidefinite relaxation techniques and the Elimination Lemma. The proposed algorithm computes the state-feedback gain and perturbation online by solving an LMI optimization that, in comparison to other schemes in the literature is shown to have a substantially reduced computational burden without adversely affecting the tracking performance of the controller. In the case that only (noisy) output measurements are available, an output-feedback RMPC algorithm is also derived for norm-bounded uncertain systems. The novelty lies in the fact that, instead of using an offline estimation scheme or a fixed linear observer, the past input/output data is used within a Robust Moving Horizon Estimation (RMHE) scheme to compute (tight) bounds on the current state. These current state bounds are then used within the RMPC control algorithm. To reduce conservatism, the output-feedback control gain and control perturbation are both explicitly considered as decision variables in the online LMI optimization. Finally, the aforementioned robust control strategies are applied in an industrial directional drilling configuration and their performance is illustrated by simulations. A rotary steerable system (RSS) is a drilling technology that has been extensively studied over the last 20 years in hydrocarbon exploration and is used to drill complex curved borehole trajectories. RSSs are commonly treated as dynamic robotic actuator systems, driven by a reference signal and typically controlled by using a feedback loop control law. However, due to spatial delays, parametric uncertainties, and the presence of disturbances in such an unpredictable working environment, designing such control laws is not a straightforward process. Furthermore, due to their inherent delayed feedback, described by delay differential equations (DDE), directional drilling systems have the potential to become unstable given the requisite conditions. To address this problem, a simplified model described by ordinary differential equations (ODE) is first proposed, and then taking into account disturbances and system uncertainties that arise from design approximations, the proposed RMPC algorithm is used to automate the directional drilling system.Open Acces

Robust feedback model predictive control of norm-bounded uncertain systems

This thesis is concerned with the Robust Model Predictive Control (RMPC) of linear discrete-time systems subject to norm-bounded model-uncertainty, additive disturbances and hard constraints on the input and state. The aim is to design tractable, feedback RMPC algorithms that are based on linear matrix inequality (LMI) optimizations. The notion of feedback is very important in the RMPC control parameterization since it enables effective disturbance/uncertainty rejection and robust constraint satisfaction. However, treating the state-feedback gain as an optimization variable leads to non-convexity and nonlinearity in the RMPC scheme for norm-bounded uncertain systems. To address this problem, we propose three distinct state-feedback RMPC algorithms which are all based on (convex) LMI optimizations. In the first scheme, the aforementioned non-convexity is avoided by adopting a sequential approach based on the principles of Dynamic Programming. In particular, the feedback RMPC controller minimizes an upper-bound on the cost-to-go at each prediction step and incorporates the state/input constraints in a non-conservative manner. In the second RMPC algorithm, new results, based on slack variables, are proposed which help to obtain convexity at the expense of only minor conservatism. In the third and final approach, convexity is achieved by re-parameterizing, online, the norm-bounded uncertainty as a polytopic (additive) disturbance. All three RMPC schemes drive the uncertain-system state to a terminal invariant set which helps to establish Lyapunov stability and recursive feasibility. Low-complexity robust control invariant (LC-RCI) sets, when used as target sets, yield computational advantages for the associated RMPC schemes. A convex algorithm for the simultaneous computation of LC-RCI sets and the corresponding controller for norm-bounded uncertain systems is also presented. In this regard, two novel results to separate bilinear terms without conservatism are proposed. The results being general in nature also have application in other control areas. The computed LC-RCI sets are shown to have substantially improved volume as compared to other schemes in the literature. Finally, an output-feedback RMPC algorithm is also derived for norm-bounded uncertain systems. The proposed formulation uses a moving window of the past input/output data to generate (tight) bounds on the current state. These bounds are then used to compute an output-feedback RMPC control law using LMI optimizations. An output-feedback LC-RCI set is also designed, and serves as the terminal set in the algorithm.Open Acces

Robust Control of Synchronous Reluctance Motor Based on Automatic Disturbance Rejection

This article proposes the theoretical development and experimental application of the active disturbance rejection control (ADRC) to synchronous reluctance motor (SynRM) drives. The ADRC is a robust adaptive extension of the input-output feedback linearization control (FLC). It performs the exact linearization of the SynRM model by a suitable nonlinear transformation of the state based on the online estimation of the corrective term by the so-called extended state observers (ESO). Consequently, any unmodeled dynamics or uncertainty of the parameters are properly addressed. The control strategy has been verified successfully both in numerical simulations and experimentally on a suitably developed test set-up that provides the ADRC robustness versus parameters variations which cannot be obtained with other model-based nonlinear control techniques (e.g., FLC). Simulation results show the capability of the ADRC to maintain its dynamic performance, even in the presence of quick variations of the SynRM dynamic inductances. Experimental results confirm the robustness of the ADRC versus any model parameter uncertainty. The proposed ADRC has been experimentally compared with a previously developed FLC, in both a tuned and detuned working configuration, with the classic rotor oriented control, and with a finite state model predictive control (MPC), where speed control is integrated into the MPC. Experimental results show far better robustness versus any parameter variation

Hierarchical Motion Planning and Offline Robust Model Predictive Control for Autonomous Vehicles

Driving vehicles in complex scenarios under harsh conditions is the biggest challenge for autonomous vehicles (AVs). To address this issue, we propose hierarchical motion planning and robust control strategy using the front-active steering system in complex scenarios with various slippery road adhesion coefficients while considering vehicle uncertain parameters. Behaviors of human vehicles (HVs) are considered and modeled in the form of a car-following model via the Intelligent Driver Model (IDM). Then, in the upper layer, the motion planner first generates an optimal trajectory by using the artificial potential field (APF) algorithm to formulate any surrounding objects, e.g., road marks, boundaries, and static/dynamic obstacles. To track the generated optimal trajectory, in the lower layer, an offline-constrained output feedback robust model predictive control (RMPC) is employed for the linear parameter varying (LPV) system by applying linear matrix inequality (LMI) optimization method that ensures the robustness against the model parameter uncertainties. Furthermore, by augmenting the system model, our proposed approach, called offline RMPC, achieves outstanding efficiency compared to three existing RMPC approaches, e.g., offset-offline RMPC, online RMPC, and offline RMPC without an augmented model (offline RMPC w/o AM), in both improving computing time and reducing input vibrations.Comment: 6 pages, 9 illustrations, Accepted for publication in American Control Conference (ACC) 202

Predictive feedback control using a multiple model approach

A new method of designing predictive controllers for SISO systems is presented. The controller selects the model used in the design of the control law from a given set of models according to a switching rule based on output prediction errors. The goal is to design, at each sample instant, a feedback control law that ensures robust stability of the closed–loop system and gives better performance for the current operating point. The overall multiple model predictive control scheme quickly identifies the closest linear model to the dynamics of the current operating point, and carries out an automatic reconfiguration of the control system to achieve a better performance. The results are illustrated with simulations of a continuous stirred tank reactor

Robust predictive feedback control for constrained systems

A new method for the design of predictive controllers for SISO systems is presented. The proposed technique allows uncertainties and constraints to be concluded in the design of the control law. The goal is to design, at each sample instant, a predictive feedback control law that minimizes a performance measure and guarantees of constraints are satisfied for a set of models that describes the system to be controlled. The predictive controller consists of a finite horizon parametric-optimization problem with an additional constraint over the manipulated variable behavior. This is an end-constraint based approach that ensures the exponential stability of the closed-loop system. The inclusion of this additional constraint, in the on-line optimization algorithm, enables robust stability properties to be demonstrated for the closed-loop system. This is the case even though constraints and disturbances are present. Finally, simulation results are presented using a nonlinear continuous stirred tank reactor model