Control Design For Nonlinear Systems Research Articles

Design of nonlinear automatic flight control systems

A method for the synthesis of nonlinear automatic flight control systems is developed, and the performance of a control system synthesized by use of this method is compared to the performance of control system designed by use of linear quadratic optimal control theory. Comparisons are made on the basis of aircraft dynamic response at high angles of attack. It is found that the nonlinear controller reduces the altitude loss during stall and increases the magnitude of the angle of attack for which the aircraft can recover from stall.

On-Line Computer Control of Complex Nonlinear Systems

A design method which extends linear design techniques to nonlinear control systems design using an on-line digital computer is described. A linearization technique and a control design technique suitable for implementation on-line are described. The method is illustrated on a 10th order 2 input 2 output system. The method allows use of well-known classical design techniques such as series compensation while gaining the advantages of state variable feedback.

A three-stage design of non-linear control systems with time-delay

A new approach to the sub-optimal control of non-linear time-delay systems is presented in this paper. It consists of three stages. In the first stage the original time-delay system state equation is expanded about its nominal functions. The resulting linear time-varying system with delay is then reduced to a linear non-delay non-homogeneous system whose optimal control is the same. The third stage is the application of the maximum principle to the transformed system leading to the desired sub-optimal control. The method is applied to a non-linear system.

Design of Non-linear Multivariable Control Systems†

ABSTRACT Given a piece-wise single valued non-linear multivariable plant a design procedure is suggested to meet the desired specifications for step inputs. The system is first designed as a linear system satisfying the design specifications and its performance as a non-linear system is checked. The method may involve trial and error. An example is worked out Illustrating the procedure. Analogue computer results are also included.

The Design of Nonlinear Multivariable Control Systems From State Dependent Linear Models

A technique is presented for the design of a continuous nonlinear multivariable control algorithm from a set of simple, linear control models. The coefficients of the linear control models are dependent on the steady state operating point. The technique makes use of line integration and the method of least squares to bridge the gap between the sets of linear coefficients and the continuous nonlinear functions of the nonlinear algorithm. In general, the nonlinear control algorithm is nonunique. The method permits the extension of linear design procedures to the design of nonlinear control systems. It can be used to design a control system for a nonlinear process to maintain the dynamics of the entire system invariant with respect to changes in the operating point.

The Design of a Nonlinear Reactor Control System

The design procedure for a nonlinear reactor control system is described. The control system contains two nonlinearities, separated by a linear section: a dead-band, normally used to reduce the noise excitation of the control system, and a gear backlash, which in this case is particularly important, due to the fact that the control elements are cylinders with limited effective angular range. The type of electrical motors was also defined (Slo-Syn motors, which can operate as synchronous or stepping motors). The work has been developed using analog and analytical methods in parallel, and the final control scheme (a velocity servo with stepping motors) has been throughly tested on the analog computer with noisy inputs, and theoretically studied with a describing function method extended to the case of systems with multiple nonlinearities connected by linear sections.

Quasi-Linearization Design of Nonlinear Feedback Control Systems

This paper describes an application of the quasi-linearization principle and the use of off-line analog computers for the design of nonlinear feedback control systems. The design objective is to make the feedback system meet a set of transient as well as steady-state specifications under deterministic system inputs. According to the given specifications, the desired input to the nonlinear element is established. With the aid of an analog computer, the nonlinear element is tested by its desired input. Based on the test result, the nonlinear element is replaced by an equivalent linear element which has approximately the same input-output relationship as the nonlinear element. Linear system design techniques are then used to design the quasi-linearized systems, such that the actual input to the nonlinear element is indeed as desired. High-order feedback control systems in which the major nonlinearity, arises from the preamplifier and/or the error-measuring device are particularly amenable to this approach.

Quasi-linearization design of nonlinear feedback control systems

Quasi-linearization design of nonlinear feedback control systems

The design of nonlinear filters and control systems. Part 1

The objectives of this paper are to provide a systematic analytical approach to the synthesis of continuous nonlinear filters and to apply the results to a variety of problems, e.g., filtering of signals from noise, characterization of nonlinear systems, and the design of compensation networks for control systems. The problems are illustrated in Fig. 1. The work starts from the concept of a functional as the mathematical representative of a system. The optimum possible functional for any particular problem is approximated by a finite number of Volterra kernels. A typical question which the paper attempts to answer is: “Given an input (signal plus noise) which is a sample function from a stationary, ergodic, random process and using the mean-square error criterion, what is the optimum filter consisting of a finite number of Volterra kernels to filter the signal from the noise?” 1 1 A filter which consists of h 0 , h 1 , h 2 , h 3 , ···, h n is called a filter of degree n and sometimes will be denoted as < h 0 , h 1 , h 2 , ···, h n >. Every kernel h j is called a kernel of order j . Its corresponding filter is a filter of order j . This type of question leads to a set of simultaneous integral equations for which an iterative method of solution is provided. Examples and applications to filtering and control are discussed. Part II of the paper will describe an experimental application of the theory to the characterization of the servomechanism associated with the pupil of the human eye. A measure of the complexity of the experiment will be developed and the applicability of the method to real problems will be discussed from this point of view.

Physical and Mathematical Mechanisms of Instability in Nonlinear Automatic Control Systems

Abstract This paper is a critical examination of the stability problem in automatic control systems containing nonlinear elements. An attempt is made to classify and isolate essentially different phenomena, and to illustrate each type by means of simplified but representative examples. Particular attention is paid to the effects of system parameters and system inputs in provoking or destroying instability. The phenomena discussed are so diverse that they defy any over-all conclusions. Still, it is hoped that the tentative classification adopted here will be of help in recognizing important and unimportant aspects of problems in nonlinear control-system design.

Use of interpretation routines on a general-purpose digital computer for the design of linear and non-linear control systems

The behaviour of a linear servo-mechanism may be described by a set of linear first-order simultaneous differential equations. The programme applies, however, to other problems that can be described similarly and to partial differential equations which can be reduced to this form by finite-difference approximations.The digital differential analyser and similar analogue devices are considered, but a general-purpose machine is more versatile. A form of Runge-Kutta formula for the numerical integration of the equations is described.Each coefficient in the set of equations may be described by a code word which specifies both its magnitude and location. An interpretation routine examines these code words in turn and evaluates the derivatives required in the integration formula.The solution for any variable may be punched out or displayed on a cathode-ray tube, and parameters are easily varied when searching for an optimum design. By adding suitable sub-routines the general programme is easily adapted to handle non-linear systems.The technique is most useful for supplementing preliminary studies on a simple analogue computer and is more adaptable for non-linear systems.A simple worked example is used to illustrate the principles without assuming previous experience of either numerical analysis or computing machines.