588 research outputs found
Piecewise Linear Control Systems
This thesis treats analysis and design of piecewise linear control systems. Piecewise linear systems capture many of the most common nonlinearities in engineering systems, and they can also be used for approximation of other nonlinear systems. Several aspects of linear systems with quadratic constraints are generalized to piecewise linear systems with piecewise quadratic constraints. It is shown how uncertainty models for linear systems can be extended to piecewise linear systems, and how these extensions give insight into the classical trade-offs between fidelity and complexity of a model. Stability of piecewise linear systems is investigated using piecewise quadratic Lyapunov functions. Piecewise quadratic Lyapunov functions are much more powerful than the commonly used quadratic Lyapunov functions. It is shown how piecewise quadratic Lyapunov functions can be computed via convex optimization in terms of linear matrix inequalities. The computations are based on a compact parameterization of continuous piecewise quadratic functions and conditional analysis using the S-procedure. A unifying framework for computation of a variety of Lyapunov functions via convex optimization is established based on this parameterization. Systems with attractive sliding modes and systems with bounded regions of attraction are also treated. Dissipativity analysis and optimal control problems with piecewise quadratic cost functions are solved via convex optimization. The basic results are extended to fuzzy systems, hybrid systems and smooth nonlinear systems. It is shown how Lyapunov functions with a discontinuous dependence on the discrete state can be computed via convex optimization. An automated procedure for increasing the flexibility of the Lyapunov function candidate is suggested based on linear programming duality. A Matlab toolbox that implements several of the results derived in the thesis is presented
Gain-scheduled H∞ control via parameter-dependent Lyapunov functions
Synthesising a gain-scheduled output feedback H∞ controller via parameter-dependent Lyapunov functions for linear parameter-varying (LPV) plant models involves solving an infinite number of linear matrix inequalities (LMIs). In practice, for affine LPV models, a finite number of LMIs can be achieved using convexifying techniques. This paper proposes an alternative approach to achieve a finite number of LMIs. By simple manipulations on the bounded real lemma inequality, a symmetric matrix polytope inequality can be formed. Hence, the LMIs need only to be evaluated at all vertices of such a symmetric matrix polytope. In addition, a construction technique of the intermediate controller variables is also proposed as an affine matrix-valued function in the polytopic coordinates of the scheduled parameters. Computational results on a numerical example using the approach were compared with those from a multi-convexity approach in order to demonstrate the impacts of the approach on parameter-dependent Lyapunov-based stability and performance analysis. Furthermore, numerical simulation results show the effectiveness of these proposed techniques
Model predictive control techniques for hybrid systems
This paper describes the main issues encountered when applying model predictive control to hybrid processes. Hybrid model predictive control (HMPC) is a research field non-fully developed with many open challenges. The paper describes some of the techniques proposed by the research community to overcome the main problems encountered. Issues related to the stability and the solution of the optimization problem are also discussed. The paper ends by describing the results of a benchmark exercise in which several HMPC schemes were applied to a solar air conditioning plant.Ministerio de Eduación y Ciencia DPI2007-66718-C04-01Ministerio de Eduación y Ciencia DPI2008-0581
Robust Multi-Criteria Optimal Fuzzy Control of Continuous-Time Nonlinear Systems
This paper presents a novel fuzzy control design of continuous-time nonlinear systems with multiple performance criteria. The purpose behind this work is to improve the traditional fuzzy controller performance to satisfy several performance criteria simultaneously to secure quadratic optimality with inherent stability property together with dissipativity type of disturbance reduction. The Takagi– Sugeno fuzzy model is used in our control system design. By solving the linear matrix inequality at each time step, the control solution can be found to satisfy the mixed performance criteria. The effectiveness of the proposed technique is demonstrated by simulation of the control of the inverted pendulum system
An integral sliding-mode parallel control approach for general nonlinear systems via piecewise affine linear models
The fundamental problem of stabilizing a general nonaffine continuous-time
nonlinear system is investigated via piecewise affine linear models (PALMs) in
this article. A novel integral sliding-mode parallel control (ISMPC) approach
is developed, where an uncertain piecewise affine system (PWA) is constructed
to model a nonaffine continuous-time nonlinear system equivalently on a compact
region containing the origin. A piecewise sliding-mode parallel controller is
designed to globally stabilize the PALM and, consequently, to semiglobally
stabilize the original nonlinear system. The proposed scheme enjoys three
favorable features: (i) some restrictions on the system input channel are
eliminated, thus the developed method is more relaxed compared with the
published approaches; (ii) it is convenient to be used to deal with both
matched and unmatched uncertainties of the system; and (iii) the proposed
piecewise parallel controller generates smooth control signals even around the
boundaries between different subspaces, which makes the developed control
strategy more implementable and reliable. Moreover, we provide discussions
about the universality analysis of the developed control strategy for two kinds
of typical nonlinear systems. Simulation results from two numerical examples
further demonstrate the performance of the developed control approach
Survey of Gain-Scheduling Analysis & Design
The gain-scheduling approach is perhaps one of the most popular nonlinear control design approaches which has
been widely and successfully applied in fields ranging from aerospace to process control. Despite the wide
application of gain-scheduling controllers and a diverse academic literature relating to gain-scheduling extending
back nearly thirty years, there is a notable lack of a formal review of the literature. Moreover, whilst much of
the classical gain-scheduling theory originates from the 1960s, there has recently been a considerable increase in
interest in gain-scheduling in the literature with many new results obtained. An extended review of the gainscheduling
literature therefore seems both timely and appropriate. The scope of this paper includes the main
theoretical results and design procedures relating to continuous gain-scheduling (in the sense of decomposition
of nonlinear design into linear sub-problems) control with the aim of providing both a critical overview and a
useful entry point into the relevant literature
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