Search

The control of an automotive suspension system by means of a hydraulic actuator is a complex nonlinear control problem. In this work, a linear parameter varying (LPV) model is proposed to reduce the complexity of the system while preserving the nonlinear behavior. In terms of control, a dual controller consisting of a model predictive control (MPC) and a Linear Quadratic Regulator (LQR) is implemented. To ensure stability, quadratic stability conditions are imposed in terms of Linear Matrix Inequalities (LMI). Simulation results for quarter-car model over several disturbances are tested in both frequency and time domain to show the effectiveness of the proposed algorithm.

U ovom radu opisan je algoritam modelski prediktivnog upravlja i njegova implementacija u FPGA sklopovlju. Budući da se algoritam upravljanja koristi za upravljanje iznosom struje na mrežnoj strani dvosmjernog mrežnog učinskog pretvarača, prikazan je njegov matematički model. Zbog neodređenosti u iznosu induktiviteta na mrežnoj strani, zapisan je kao linearni parametarski promjenjivi politopski model u prostoru stanja. Kako bi se izbjeglo računanje složenog minimizacijskog problema kojeg MPC rješava u svakom koraku, korištena je metoda brzog gradijenta s projekcijom. Prije izračuna upravljačkog signala određuje se najmanji elipsoidni skup koji opisuje trenutno stanje sustava, a na temelju njega trenutni invarijantni upravljački skup. FPGA sklopovlje omogućava paralelno pretraživanje skupa zbog čega je vrijeme izvođenja algoritma ubrzano. Problem numeričke složenosti u koraku projekcije kod metode brzog gradijenta riješen je korištenjem Quakeovog algoritma za brzi izračun inverza kvadratnog korijena. In this thesis, Model predictive control algorithm and its implementation in FGPA hardware is described. Since this control algorithm is used for current regulation on the grid side of a grid connected two level inverter, its mathematical model is presented. Beacause of uncertainty of grid side inductance value, model is shown as linear parameter-varying polytopic model in state space. In order to avoid complex minimisation problem calculation, which MPC solves in each step, fast gradient projection method is used. Before the input signal calculation, the smallest ellipsoidal set which describes system state needs to be determined. Based on that set current invariant control set is also determined. Numerical complexity problem in projection step in fast gradient projection method is solved using Quake's fast invese square root algorithm.

A LQR-Model Predictive Control (MPC) algorithm for Linear Parameter Varying (LPV) systems is developed herein. The proposed algorithm applies a MPC approach whenever the system is outside a terminal ellipsoid defined as a stability zone where a LPV-LQR feedback gain is implemented to reach the equilibrium point. In order to cope with the uncertainties of the future values of the scheduling parameters, a recursive least squares algorithm is performed before the prediction of future states is made in order to be suitable and feasible for a more simple online optimization problem. Quadratic stability is ensured by the means of working with the LPV system as an uncertain parametric system with the uncertainty being the error of the recursive least squares prediction and considering the discrete algebraic Riccati Equations in a Linear Matrix Inequality form. This method also includes terminal set attraction to steer the predictions of the states into the terminal ellipsoid. This thesis also includes two successful simulations of this technique in order to show the benefits and applications of the algorithm. Maestría en Ciencias de Ingeniería

International audience; In the context of state estimation of dynamical systems subject to bounded perturbations and measurement noises, this paper proposes an application of a guaranteed ellipsoidal-based set-membership state estimation technique to estimate the linear position of an octorotor used for radar applications. The size of the ellipsoidal set containing the real state is minimized at each sample time taking into account the measurements performed by the drone's sensors. Three case studies highlight the efficiency of the estimation technique in finding guaranteed bounds for the octoro-tor's linear position. The computed guaranteed bounds in the linear trajectory are exploited to find the maximum operating frequency of the radar, a necessary information in radar applications.

International audience; This paper presents a new online ellipsoidal guaranteed set-membership state estimation approach for Multi-Output linear systems with interval uncertainties, bounded perturbations and measurement noises. The ellipsoidal set containing the real state of the system is computed at each sample time. This approach consists in online minimizing the radius of the ellipsoidal state estimation set by solving a Linear Matrix Inequality optimization problem. Interval uncertainties are considered in both the evolution matrix and the observation matrix. An illustrative example is analyzed in order to show the advantages of the proposed approach.

International audience; This paper presents a comparison in terms of accuracy and complexity between two approaches used for state estimation of linear systems: a classic Kalman filter and a guaranteed set-membership state estimation technique. The main goal of this paper is to analyze the advantages of these techniques and to combine them in the future in a new accurate and simple extension that handles system uncertainties and chance constraints. Two academic examples illustrate the main differences between the compared techniques.

The 19th World Congress of the International Federation of Automatic Control 2014. Cape Town, Sudáfrica This paper proposes a new ellipsoid-based guaranteed state estimation approach for linear discrete-time systems with bounded perturbations and bounded measurement noise. This approach is based on the minimization of the radius of the ellipsoidal state estimation set. Firstly, the ellipsoidal state estimation is computed by off-line solving a Linear Matrix Inequality optimization problem. Secondly, a new online method is developed in order to improve the accuracy of the estimation but it leads to an increase of the online computation load. A new scaling technique is proposed to reduce the computation time, while keeping a good accuracy of the state estimation. An illustrative example is analyzed in order to show the advantages of the proposed approach.