Linear Reduced Order Model Predictive Control

Model predictive controllers leverage system dynamics models to solve constrained optimal control problems. However, computational requirements for real-time control have limited their use to systems with low-dimensional models. Nevertheless many systems naturally produce high-dimensional models, such as those modeled by partial differential equations that when discretized can result in models with thousands to millions of dimensions. In such cases the use of reduced order models (ROMs) can significantly reduce computational requirements, but model approximation error must be considered to guarantee controller performance. In this work a reduced order model predictive control (ROMPC) scheme is proposed to solve robust, output feedback, constrained optimal control problems for high-dimensional linear systems. Computational efficiency is obtained by leveraging ROMs obtained via projection-based techniques, and guarantees on robust constraint satisfaction and stability are provided. Performance of the approach is demonstrated in simulation for several examples, including an aircraft control problem leveraging an inviscid computational fluid dynamics model with dimension 998,930.Comment: This work has been submitted to the IEEE Transactions on Automatic Control for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

Robust constrained model predictive control based on parameter-dependent Lyapunov functions

The problem of robust constrained model predictive control (MPC) of systems with polytopic uncertainties is considered in this paper. New sufficient conditions for the existence of parameter-dependent Lyapunov functions are proposed in terms of linear matrix inequalities (LMIs), which will reduce the conservativeness resulting from using a single Lyapunov function. At each sampling instant, the corresponding parameter-dependent Lyapunov function is an upper bound for a worst-case objective function, which can be minimized using the LMI convex optimization approach. Based on the solution of optimization at each sampling instant, the corresponding state feedback controller is designed, which can guarantee that the resulting closed-loop system is robustly asymptotically stable. In addition, the feedback controller will meet the specifications for systems with input or output constraints, for all admissible time-varying parameter uncertainties. Numerical examples are presented to demonstrate the effectiveness of the proposed techniques

Robust Output Feedback MPC: An Interval-Observer Approach

International audienceIn this work, we address the problem of output-feedback Model Predictive Control (MPC) of constrained, linear, discrete-time systems corrupted by additive perturbations on both state and output. The use of estimated variables in MPC is challenging and computationally expensive due to constraint satisfaction. To overcome this issue, the proposed approach incorporates interval observers on the MPC scheme to cope with uncertainty, leading to a novel, simple and very intuitive methodology providing robust constraint satisfaction with reduced computational complexity

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

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 output feedback MPC for LPV systems using interval observers

This work addresses the problem of robust output feedback model predictive control for discrete-time, constrained, linear parameter-varying systems subject to (bounded) state and measurement disturbances. The vector of scheduling parameters is assumed to be an unmeasurable signal taking values in a given compact set. The proposed controller incorporates an interval observer, that uses the available measurement to update the setmembership estimation of the states, and an interval predictor, used in the prediction step of the MPC algorithm. The resulting MPC scheme offers guarantees on recursive feasibility, constraint satisfaction, and input-to-state stability in the terminal set. Furthermore, this novel algorithm shows low computation complexity and ease of implementation (similar to conventional MPC schemes)

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