On the design of Robust tube-based MPC for tracking

17th IFAC World Congress (IFAC'08)Seoul, Korea, July 6-11This paper deals with the design procedure of the recently presented robust MPC for tracking of constrained linear systems with additive disturbances. This controller is based on nominal predictions and it is capable to steer the nominal predicted trajectory to any target admissible steady state, that is retaining feasibility under any set point change. By means of the notion of tube of trajectories, robust stability and convergence is achieved. The controller formulation has some parameters which provides extra degrees of freedom to the design procedure of the predictive controller. These allow to deal with control objectives such as disturbance rejection, output offset prioritization or enlargement of the domain of attraction. In this paper, output prioritization method, LMI based design procedures and algorithms for the calculation of invariant sets are presented. The proposed enhanced design of the MPC is demonstrated by an illustrative example

Lateral fligh control design for a highly flexible aircraft using a nonsmooth method

This paper describes a nonsmooth optimization technique for designing a lateral flight control law for a highly flexible aircraft. Flexible modes and high-dimensional models pose a major challenge to modern control design tools. We show that the nonsmooth approach offers potent and flexible alternatives in this difficult context. More specifically, the proposed technique is used to achieve a mix of frequency domain as well as time domain requirements for a set of different flight conditions

Gain-scheduling through continuation of observer-based realizations-applications to H∞ and μ controllers

The dynamic behavior of gain scheduled controllers is highly depending on the state-space representations adopted for the family of lienar controllers designed on a set of operating conditions. In this paper, a technique for determining a set of consistent and physically motivated linear state-space transformations to be applied to the original set of linear controllers is proposed. After transformation, these controllers exhibits an-observer-based structure are therefore easily interpolted and implemented

Multi - objective sliding mode control of active magnetic bearing system

Active Magnetic Bearing (AMB) system is known to inherit many nonlinearity effects due to its rotor dynamic motion and the electromagnetic actuators which make the system highly nonlinear, coupled and open-loop unstable. The major nonlinearities that are associated with AMB system are gyroscopic effect, rotor mass imbalance and nonlinear electromagnetics in which the gyroscopics and imbalance are dependent to the rotational speed of the rotor. In order to provide satisfactory system performance for a wide range of system condition, active control is thus essential. The main concern of the thesis is the modeling of the nonlinear AMB system and synthesizing a robust control method based on Sliding Mode Control (SMC) technique such that the system can achieve robust performance under various system nonlinearities. The model of the AMB system is developed based on the integration of the rotor and electromagnetic dynamics which forms nonlinear time varying state equations that represent a reasonably close description of the actual system. Based on the known bound of the system parameters and state variables, the model is restructured to become a class of uncertain system by using a deterministic approach. In formulating the control algorithm to control the system, SMC theory is adapted which involves the formulation of the sliding surface and the control law such that the state trajectories are driven to the stable sliding manifold. The surface design involves the transformation of the system into a special canonical representation such that the sliding motion can be characterized by a convex representation of the desired system performances. Optimal Linear Quadratic (LQ) characteristics and regional pole-clustering of the closed-loop poles are designed to be the objectives to be fulfilled in the surface design where the formulation is represented as a set of Linear Matrix Inequality optimization problem. For the control law design, a new continuous SMC controller is proposed in which asymptotic convergence of the system’s state trajectories in finite time is guaranteed. This is achieved by adapting the equivalent control approach with the exponential decaying boundary layer technique. The newly designed sliding surface and control law form the complete Multi-objective SMC (MO-SMC) and the proposed algorithm is applied into the nonlinear AMB in which the results show that robust system performance is achieved for various system conditions. The findings also demonstrate that the MO-SMC gives better system response than the reported ideal SMC (I-SMC) and continuous SMC (C-SMC)

Investigation of practical applications of H infinity control theory to the design of control systems for large space structures

The applicability of H infinity control theory to the problems of large space structures (LSS) control was investigated. A complete evaluation to any technique as a candidate for large space structure control involves analytical evaluation, algorithmic evaluation, evaluation via simulation studies, and experimental evaluation. The results of analytical and algorithmic evaluations are documented. The analytical evaluation involves the determination of the appropriateness of the underlying assumptions inherent in the H infinity theory, the determination of the capability of the H infinity theory to achieve the design goals likely to be imposed on an LSS control design, and the identification of any LSS specific simplifications or complications of the theory. The resuls of the analytical evaluation are presented in the form of a tutorial on the subject of H infinity control theory with the LSS control designer in mind. The algorthmic evaluation of H infinity for LSS control pertains to the identification of general, high level algorithms for effecting the application of H infinity to LSS control problems, the identification of specific, numerically reliable algorithms necessary for a computer implementation of the general algorithms, the recommendation of a flexible software system for implementing the H infinity design steps, and ultimately the actual development of the necessary computer codes. Finally, the state of the art in H infinity applications is summarized with a brief outline of the most promising areas of current research

Advanced rotorcraft control using parameter optimization

A reliable algorithm for the evaluation of a quadratic performance index and its gradients with respect to the controller design parameters is presented. The algorithm is part of a design algorithm for an optimal linear dynamic output feedback controller that minimizes a finite time quadratic performance index. The numerical scheme is particularly robust when it is applied to the control law synthesis for systems with densely packed modes and where there is a high likelihood of encountering degeneracies in the closed loop eigensystem. This approach through the use of a accurate Pade series approximation does not require the closed loop system matrix to be diagonalizable. The algorithm has been included in a control design package for optimal robust low order controllers. Usefulness of the proposed numerical algorithm has been demonstrated using numerous practical design cases where degeneracies occur frequently in the closed loop system under an arbitrary controller design initialization and during the numerical search

Nonlinear control synthesis by convex optimization

A stability criterion for nonlinear systems, recently derived by the third author, can be viewed as a dual to Lyapunov's second theorem. The criterion is stated in terms of a function which can be interpreted as the stationary density of a substance that is generated all over the state-space and flows along the system trajectories toward the equilibrium. The new criterion has a remarkable convexity property, which in this note is used for controller synthesis via convex optimization. Recent numerical methods for verification of positivity of multivariate polynomials based on sum of squares decompositions are used