On-Line Analysis of a Non-Linear Control System Using Correlation Methods

1968 ◽  
Vol 1 (6) ◽  
pp. 222-225 ◽  
Author(s):  
R. E. Selway ◽  
D. Bell
Keyword(s):  
Optimal Control ◽  
Control System ◽  
Linear Control ◽  
Correlation Methods ◽  
Non Linear ◽  
On Line ◽  
Hybrid Computer ◽  
Non Linear System ◽  
M Sequences ◽  
Working Point

In non-linear control processes the application of optimal control generally leads to a solution which is difficult to implement. The problem is approached here by the use of a correlation method of continual tracking of the working point on the static and dynamic characteristics of the control system. A hybrid computer is utilised to compute the correlation functions and continually to identify and reoptimise about the working point using quasi-linearisation techniques. The non-linear system considered is a hyrdaulic servomotor of a type used in aircraft flight control systems. The three-level m-sequences used as test signals are injected into the system during normal operation and, since they are uncorrelated with any other signal, may have an extremely small amplitude compared with the normal working input signal. Optimal control in this instance is applied by the use of a phase compensation network with a variable bandwidth. The change of bandwidth required to satisfy the performance criterion is calculated on-line and used to optimise the system. A brief summary of correlation methods is presented together with the equation's governing identification and optimisation. The hybrid computer arrangement is described and a selection of typical results is shown and discussed. A note on the stability of the overall system as a system with time delays is included. In conclusion, the problems of time-variant dynamics on non-linear systems are considered. A proposed hybrid computer scheme is presented for this purpose in which the characteristics of the m-sequences are up-dated to match the identified time constants of the system.

Non-Linear Control of a Neutralisation Process

1971 ◽  
Vol 4 (9) ◽  
pp. T151-T157 ◽  
Author(s):  
P D Roberts
Keyword(s):  
Simulation Study ◽  
Digital Simulation ◽  
Linear Control ◽  
Attractive Alternative ◽  
Error Signal ◽  
Linear Controller ◽  
Linear Characteristic ◽  
Non Linear ◽  
On Line ◽  
Extra Parameter

The paper describes a digital simulation study of the application of a non-linear controller to the regulation of a single stage neutralisation process. In the controller, the proportional gain increases with amplitude of controller error signal. The performance of the non-linear controller is compared with that of a conventional linear controller and with the performance obtained by employing a linear controller with a linearisation network designed to compensate for the non-linear characteristic of the neutralisation curve. Although the performance of the non-linear controller is inferior to that obtained by employing a perfect linearisation network, its performance is still considerably superior to that obtained by using a conventional linear controller when operating at a symmetrical point on the neutralisation curve. In contrast to the linearisation network technique, the non-linear controller contains only one extra parameter and can be readily tuned on-line without prior knowledge of the neutralisation curve. Hence, it can be considered as an attractive alternative for the control of neutralisation processes.

A pole placement controller for non-linear dynamic plants

2002 ◽  
Vol 216 (6) ◽  
pp. 467-476 ◽  
Author(s):  
Q M Zhu ◽  
L Z Guo
Keyword(s):  
Control System ◽  
System Design ◽  
Discrete Time ◽  
Linear Control System ◽  
Linear Control ◽  
Pole Placement ◽  
Hammerstein Model ◽  
Control System Design ◽  
Non Linear ◽  
Pole Placement Controller

In this study a control-oriented model is proposed to represent a wide range of non-linear discrete-time dynamic plants. As a testimony to the efficiency of the model structure for control system design, a pole placement controller is designed for non-linear discrete-time plants. Mathematically the solution of the controller output is converted into resolving a polynomial equation in the current control term u( t), which significantly reduces the difficulties encountered in non-linear control system synthesis and computational complexities. The integrated procedure provides a straightforward methodology to use in linear control system design techniques when designing non-linear control systems. For a demonstration of the effectiveness of the proposed methodology used to deal with practical problems, pole placement controllers are designed for three non-linear plants, including the Hammerstein model, a laboratory-scale liquid level system and a continuous stirred tank reactor. The simulation results are presented with graphical illustrations.

Finite bang-bang controllability for certain non-linear systems

1977 ◽  
Vol 77 (1-2) ◽  
pp. 137-144 ◽  
Author(s):  
Gunnar Aronsson
Keyword(s):  
Control System ◽  
Sufficient Conditions ◽  
Linear Control ◽  
Usual Sense ◽  
Unperturbed System ◽  
Control Functions ◽  
Bounded Controls ◽  
Non Linear ◽  
Non Linear Systems ◽  
Image Position

SynopsisThis paper gives sufficient conditions ensuring that a non-linear control system of the formis controllable by means of control functions u(t), such that each ui(t) only takes two values, with a finite number of switches. It is assumed that the ‘unperturbed’ system ẋ = A(t)x + B(t)u is controllable in the usual sense, i.e. by measurable and bounded controls.

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