Prediction for control

5th IFAC Conference on System Structure and Control 1998 (SSC'98), Nantes, France, 8-10 JulyThis paper shows that "optimal" controllers based on "optimal" predictor structures are not "optimal" in their closed loop behaviour and that predictors should be designed taking into account closed-loop considerations. This is first illustrated with a first order plant with delay. The ISE index is computed for two typical optimal controllers (minimum variance controller and generalized predictive controller) when a stochastic disturbance is considered. The results are compared to those obtained by the use of a non optimal PI controller that uses a non optimal Smith predictor and performs better than the optimal controllers for the illustrative example. A general structure for predictors is proposed. In order to illustrate the results, some simulation examples are shown.Ce papier montre que des lois de commandes "optimales" basees sur des structures predictives "optimales" ne sont pas "optimales" dans leur comportement en boucle fermee et que la synthese de predicteurs devrait prendre en compte des considerations de boucle fermee. Cela est d'abord illustre avec un systeme du premier ordre a retard. l'index ISE est calcule pour deux lois de commandes optimales typiques (loi de commande a variance minim ale et loi de commande predictive generalisee), quand une perturbation stochastique est consideree. Les resultats sont compares a. ceux obtenus avec un regulateur PI non optimal base sur un predicteur de Smith non optimal et sont, pour l'exemple illustratif, meilleurs que ceux obtenus avec un regulateur optimal. Vne structure generale de predicteur est proposee. Pour illustrer les resultats, des exemples de simulations sont montres

Average-cost based robust structural control

A method is presented for the synthesis of robust controllers for linear time invariant structural systems with parameterized uncertainty. The method involves minimizing quantities related to the quadratic cost (H2-norm) averaged over a set of systems described by real parameters such as natural frequencies and modal residues. Bounded average cost is shown to imply stability over the set of systems. Approximations for the exact average are derived and proposed as cost functionals. The properties of these approximate average cost functionals are established. The exact average and approximate average cost functionals are used to derive dynamic controllers which can provide stability robustness. The robustness properties of these controllers are demonstrated in illustrative numerical examples and tested in a simple SISO experiment on the MIT multi-point alignment testbed

A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems

This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version

Sound and Automated Synthesis of Digital Stabilizing Controllers for Continuous Plants

Modern control is implemented with digital microcontrollers, embedded within a dynamical plant that represents physical components. We present a new algorithm based on counter-example guided inductive synthesis that automates the design of digital controllers that are correct by construction. The synthesis result is sound with respect to the complete range of approximations, including time discretization, quantization effects, and finite-precision arithmetic and its rounding errors. We have implemented our new algorithm in a tool called DSSynth, and are able to automatically generate stable controllers for a set of intricate plant models taken from the literature within minutes.Comment: 10 page

Stabilization of systems with asynchronous sensors and controllers

We study the stabilization of networked control systems with asynchronous sensors and controllers. Offsets between the sensor and controller clocks are unknown and modeled as parametric uncertainty. First we consider multi-input linear systems and provide a sufficient condition for the existence of linear time-invariant controllers that are capable of stabilizing the closed-loop system for every clock offset in a given range of admissible values. For first-order systems, we next obtain the maximum length of the offset range for which the system can be stabilized by a single controller. Finally, this bound is compared with the offset bounds that would be allowed if we restricted our attention to static output feedback controllers.Comment: 32 pages, 6 figures. This paper was partially presented at the 2015 American Control Conference, July 1-3, 2015, the US

Computational burden reduction in Min-Max MPC

Min–max model predictive control (MMMPC) is one of the strategies used to control plants subject to bounded uncertainties. The implementation of MMMPC suffers a large computational burden due to the complex numerical optimization problem that has to be solved at every sampling time. This paper shows how to overcome this by transforming the original problem into a reduced min–max problem whose solution is much simpler. In this way, the range of processes to which MMMPC can be applied is considerably broadened. Proofs based on the properties of the cost function and simulation examples are given in the paper