The design of nonovershooting and nonundershooting multivariable state feedback tracking controllers

We consider the use of linear multivariable feedback control to achieve a nonovershooting and nonundershooting step response. Recently, Schmid and Ntogramatzidis (2010) [13] introduced a linear state feedback controller design method to avoid overshoot. In this paper, we describe conditions under which the design method may be modified to avoid undershoot. The method is applicable to square and nonsquare systems, minimum and nonminimum phase systems, and also strictly proper and bi-proper systems

Nonovershooting and nonundershooting exact output regulation

We consider the classic problem of exact output regulation for a linear time invariant plant. Under the assumption that either a state feedback or measurement feedback output regulator exists, we give design methods to obtain a regulator that avoids overshoot and undershoot in the transient response

Robust repeated pole placement

We consider the classic problem of pole placement by state feedback. Recently [1] offered an eigenstructure assignment algorithm to obtain a novel parametric form for the pole-placing gain matrix to deliver any set of desired closed-loop eigenvalues, with any desired multiplicities. In this paper we employ this parametric formula to introduce an unconstrained nonlinear optimisation algorithm to obtain a gain matrix that delivers any desired pole placement with optimal robustness

A Novel MIMO Control for Interleaved Buck Converters in EV DC Fast Charging Applications

This brief proposes a new multiple input multiple output (MIMO) control for off-board electric vehicle (EV) dc fast chargers. The proposed feedback matrix design avoids multiple tuning of controllers in multiple and interconnected loops while improving the performance of interleaved dc buck converters over classical PI/PID controls. The innovative features of the presented strategy are the reference current monotonic tracking from any initial state of charge with an arbitrarily fast settling time and the fast compensation of both load variations and imbalances among the legs. Numerical results validate the performance improvements of the proposed discrete-time MIMO algorithm for interleaved buck converters over classical PI/PID controls. Full-scale hardware-in-the-loop (HIL) and scaled-down prototype experimental results prove the feasibility and effectiveness of the proposal

About stabilization of non-minimum phase systems by output feedback

This thesis work has been motivated by an internal benchmark dealing with the output regulation problem of a nonlinear non-minimum phase system in the case of full-state feedback. The system under consideration structurally suffers from finite escape time, and this condition makes the output regulation problem very hard even for very simple steady-state evolution or exosystem dynamics, such as a simple integrator. This situation leads to studying the approaches developed for controlling Non-minimum phase systems and how they affect feedback performances. Despite a lot of frequency domain results, only a few works have been proposed for describing the performance limitations in a state space system representation. In particular, in our opinion, the most relevant research thread exploits the so-called Inner-Outer Decomposition. Such decomposition allows splitting the Non-minimum phase system under consideration into a cascade of two subsystems: a minimum phase system (the outer) that contains all poles of the original system and an all-pass Non-minimum phase system (the inner) that contains all the unavoidable pathologies of the unstable zero dynamics. Such a cascade decomposition was inspiring to start working on functional observers for linear and nonlinear systems. In particular, the idea of a functional observer is to exploit only the measured signals from the system to asymptotically reconstruct a certain function of the system states, without necessarily reconstructing the whole state vector. The feature of asymptotically reconstructing a certain state functional plays an important role in the design of a feedback controller able to stabilize the Non-minimum phase system

Control Systems: New Approaches to Analysis and Design

This dissertation deals with two open problems in control theory. The first problem concerns the synthesis of fixed structure controllers for Linear Time Invariant (LTI) systems. The problem of synthesizing fixed structure/order controllers has practical importance when simplicity, hardware limitations, or reliability in the implementation of a controller dictates a low order of stabilization. A new method is proposed to simplify the calculation of the set of fixed structure stabilizing controllers for any given plant. The method makes use of computational algebraic geometry techniques and sign-definite decomposition method. Although designing a stabilizing controller of a fixed structure is important, in many practical applications it is also desirable to control the transient response of the closed loop system. This dissertation proposes a novel approach to approximate the set of stabilizing Proportional-Integral-Derivative (PID) controllers guaranteeing transient response specifications. Such desirable set of PID controllers can be constructed upon an application of Widder's theorem and Markov-Lukacs representation of non-negative polynomials. The second problem explored in this dissertation handles the design and control of linear systems without requiring the knowledge of the mathematical model of the system and directly from a small set of measurements, processed appropriately. The traditional approach to deal with the analysis and control of complex systems has been to describe them mathematically with sets of algebraic or differential equations. The objective of the proposed approach is to determine the design variables directly from a small set of measurements. In particular, it will be shown that the functional dependency of any system variable on any set of system design parameters can be determined by a small number of measurements. Once the functional dependency is obtained, it can be used to extract the values of the design parameters