Exact linearization of nonlinear systems with outputs

It is well known that the observed dynamicsẋ = f (x), y = h(x) can be put into the local observability canonical form provided that the Observability Rank Condition is satisfied. In this paper we investigate under what conditions we may obtain a linear observability canonical form when applying a properly chosen output coordinate change. Euqivalently, we solve the problem when a higher order differential equation in y variables may be transformed to a linear form by means of a change of y coordinates. For both single-output and multioutput observed dynamics necessary and sufficient conditions for the solvability of the above problems are derived.

International Journal of Systems Science, 2001

This paper deals with the exact feedback linearization of nonlinear plants using estimated states. Under appropriate hypotheses, exact linearization can be achieved through transformation of states and feedback. We assume that the states cannot be measured so that a nonlinear observer, with exponential convergence, is included in the loop. We establish su cient conditions to guarantee that the overall system trajectories asymptotically converge to those obtained with feedback linearization utilizing the true states. We apply our results to control an electrical drive using a permanent-magnet synchronous motor without mechanical and optical sensors. The behaviour of our control scheme is illustrated by simulations.

Proceedings of the Estonian Academy of Sciences

This paper presents necessary and sufficient linearizability conditions by state transformation for discrete-time multiinput nonlinear control system under the mild assumption on the surjectivity property and describes how to find the state transformation when it exists. The conditions are formulated in terms of backward shifts of vector fields, defined by the system dynamics. The conditions are compared with those that allow additionally the regular static state feedback. The theory is illustrated by two examples.

Automatica, 2001

Fostered by a growing interest in nonlinear control theory and catalyzed by the discovery in the early 1980s of the exact conditions under which a nonlinear plant can be linearized by static-state feedback and coordinate transformation, in the last decades there has been a rapid increase of interest in the search for approximate solutions to the problem of linearizing nonlinear systems by state or output feedback. Main reason for that is the limited applicability of the rigorous methods, and the complexity, sensitivity and design di$culties of the exact linearizing compensators, if any. In the present paper, the literature on the subject is reviewed and organized in what is believed to be a new and consistent perspective. Recent works, especially in the area of data-based techniques, are in fact described and related, whenever possible, to fundamental results previously obtained by model-based di!erential geometric methods; this is expected to bring modern system linearization methods closer to the needs of practicing control engineers and to stimulate further research eventually able to "ll visible gaps in this direction. : S 0 0 0 5 -1 0 9 8 ( 0 0 ) 0 0 1 1 7 -5

2015

Abstract:- This paper describes new software (NLSoft) developed for the design of nonlinear controllers based on feedback linearization technique. NLSoft is a software package containing several symbolic manipulation modules including differential geometric tools for the design and simulation of control systems. NLSoft presents a user-friendly graphical user interface (GUI) as well as a new and powerful module allowing the calculation time of linearizing control laws considering several Digital Signal Processors (DSPs) characteristics. These facilitate the real-time implementation of the control system. NLSoft is validated considering two illustrated examples. 1.

Rendiconti del Seminario Matematico e Fisico di Milano, 1996

The possibility of using feedback to achieve or to enhance system linearity is well known to control engineers since decades ago. A few major breakthroughs, made possible by the application of differential geometric tools to control theoretic issues, have revamped a new interest in all facets of the problem, including the search, the analysis and the computation of suitable approximate solutions. In the present paper, recent developments and new trends in the field are shortly reviewed, with special attention paid to some research issues currently addressed by the authors. Though primarily meant for learned mathematically oriented readers, the presentation focuses on ideas and concepts more than on their most general and mathematically rigorous formulations. On the other hand, it does not assume familiarity with advanced control theory nor modern control technology.

IEEE Transactions on Instrumentation and Measurement, 2004

In this paper we propose a method to linearize a nonlinear dynamic system: the nonlinear distortions are reduced, and the linear dynamics are corrected to a flat amplitude and linear phase in a user defined frequency band.

cdn.intechopen.com

Publisher InTech A trend of inverstigation of Nonlinear Control Systems has been present over the last few decades. As a result the methods for its analysis and design have improved rapidly. This book includes nonlinear design topics such as Feedback Linearization, Lyapunov Based Control, Adaptive Control, Optimal Control and Robust Control. All chapters discuss different applications that are basically independent of each other. The book will provide the reader with information on modern control techniques and results which cover a very wide application area. Each chapter attempts to demonstrate how one would apply these techniques to real-world systems through both simulations and experimental settings.

Proceedings of the Estonian Academy of Sciences, 2017

The algebraic approach known as functions' algebra is used to develop the necessary and sufficient conditions for the existence of state transformation and static state feedback that linearize the system equations. The advantage of this method is that it allows considering also non-smooth systems. The main object in functions' algebra is the set of vector functions, divided into equivalence classes, which form a lattice. Both discrete-and continuous-time cases are considered. The solutions to the feedback linearization problem are expressed in terms of a finite sequence of vector functions, which contain all the independent functions having certain relative degrees. The theoretical results are illustrated by numerous examples.

AIChE Journal, 1990

Many common processes such as distillation columns, chemical reactions, and pH neutralizations are inherently nonlinear. Until recently, model-based control strategies for nonlinear processes have been based on local linearization and linear controller design based on the linearized model. For highly nonlinear processes, linear feedback controllers must be detuned significantly to ensure their stability, which often severely degrades performance. In recent years, differential geometric methods have been developed that allow exact linearization of the nonlinear model that is independent of the operating point (Isidori, 1989). Linear controllers can then be designed for the equivalent linear system. Existing techniques are of two types: 1. those that linearize the input-state map (Jakubczyk and Respondek, 1980; Hunt et al., 1983) and 2. those that linearize the input-output map. Several design methods based on input-output linearization have recently been developed for nonlinear process control problems. Methods such as generic model control (Lee and Sullivan, 1988), reference system synthesis (Bartusiak et al., 1989), and internal decoupling (Balchen et al., 1988) are implicitly based on differential geometric concepts (Henson and Seborg, 1990). Although these methods are applicable to models in which the input variables may appear nonlinearly, they are restricted to models in which the rate of change of the output is directly coupled to the manipulated input. Such models are said to have a relative degree of one. Other techniques, such as globally linearizing control (Kravaris and Chung, 1987), are explicitly based on concepts from differential geometry. These techniques are not restricted to models of relative degree one but are only applicable to models which are linear in the input variables. In this paper, input-output linearization of a more general class of nonlinear processes is investigated. In particular, input variables may appear nonlinearly and the models are not required to have a relative degree of one. Two approaches are considered. The first approach is based on the original process model, while the second is based on an "extended" model that is