Strategies for Feedback Linearisation

by Garces, Freddy; Becerra, Victor Manuel; Kambhampati, Chandrasekhar; Warwick, Kevin

• ISBN13: 9781852335014
• ISBN10: 1852335017
• eBook ISBN(s): 9781447100652
• Format: Hardcover
• Copyright: 2003-01-01
• Publisher: Springer Nature
• More Book Details
• Purchase Benefits

Summary

The last few decades have witnessed tremendous developments in nonlinear control theory. One of the most important of these is the model-based method of feedback linearisation in which a nonlinear system is transformed into a linear system by means of state feedback and nonlinear transformations. After feedback linearisation, a system can be dealt with by linear controller design. The extension of these techniques to include MIMO systems allows for the further simplification of controller design by decoupling the system. Strategies for Feedback Linearisation demonstrates this powerful technique in the light of research on neural networks which allow the identification of nonlinear models without the complicated and costly development of models based on physical laws. Dynamic or recurrent neural networks have inherent properties that allow them to approximate nonlinear dynamic systems. Strategies for the identification of nonlinear systems using such neural networks are presented in this monograph together with the use of such models for the design and application of input-output linearisation and decoupling methods. Strategies for Feedback Linearisation is written to serve academic and industrial researchers in non-linear control and system identification and practising control engineers interested in their application to real-world industrial systems. The reader will gain a balanced view of theoretical and practical issues: relevant mathematical proofs are provided as are case studies illustrating design and application issues.

Table of Contents

Introduction	1	(14)
The Need for Nonlinear Control in Industrial Processes	1	(1)
Nonlinear Control Strategies	1	(3)
Gain scheduling	2	(1)
Feedback linearisation	2	(2)
Feedback linearisation-decoupling	4	(1)
Nonlinear System Models: a Key Issue	4	(1)
Neural Networks	5	(3)
System Identification	8	(1)
Static Neural Networks for Identification and Control	9	(1)
Dynamic Neural Networks for Nonlinear Identification	10	(2)
Input--Output Linearisation-Decoupling and the Use of Dynamic Neural Networks	12	(1)
Potential applications	12	(3)
Fundamental Concepts	15	(12)
Elementary Concepts of Geometric Theory	15	(6)
Linear vector spaces	15	(1)
Euclidean space	15	(1)
Vector norms	16	(1)
Matrix norms	16	(1)
Sets	17	(1)
Vector fields	17	(1)
Differential operations	18	(2)
Distributions	20	(1)
Stability of Nonlinear Systems	21	(5)
Summary	26	(1)
Introduction to Feedback Linearisation	27	(34)
Nonlinear Control Affine Systems	27	(27)
Relative degree and characteristic matrix	30	(3)
Zero dynamics and normal form	33	(6)
Input--output linearisation	39	(7)
Input-output linearisation and decoupling	46	(2)
Stability of input--output linearised systems	48	(6)
Review of Other Linearisation Techniques	54	(3)
Exact linearisation	54	(1)
Linearisation by immersion	55	(1)
Volterra linearisation	56	(1)
General Nonlinear Systems	57	(1)
Lie derivative and relative degree	57	(1)
Approximate input--output linearisation	58	(1)
Symbolic Algebra Software	58	(1)
Remarks	58	(1)
Summary	59	(2)
Dynamic Neural Networks	61	(40)
Introduction	61	(1)
Origins of Neural Computation	62	(1)
Single Layer Neural Network Structure	62	(3)
Static Multilayer Feedforward Networks	65	(1)
Dynamic Neural Networks (DNNs)	66	(12)
Vector relative degree of a multi-input multi-output dynamic neural network	68	(1)
Stability of dynamic neural networks	69	(9)
Training Dynamic Neural Networks	78	(13)
Experiment design and input characterisation	78	(1)
Training as an optimisation problem	79	(3)
Initialising dynamic neural networks	82	(1)
Gradient based optimisation methods	82	(5)
Random search methods	87	(4)
Validating the Dynamic Neural Models	91	(3)
Overtraining and overfitting	91	(1)
Generalisation, bias and variance	92	(1)
Cross-validation and model structure selection	93	(1)
Regularisation	93	(1)
A Training Example	94	(1)
Summary	95	(6)
Nonlinear System Approximation Using Dynamic Neural Networks	101	(20)
The Universal Approximation Property of Static Multilayer Networks	101	(1)
Dynamic Neural Network Structure	102	(1)
Approximation Ability of Dynamic Neural Networks	103	(16)
Approximation of autonomous nonlinear systems	104	(5)
Approximation of non-autonomous nonlinear systems	109	(5)
Upper bound on the approximation error of general nonlinear systems	114	(5)
Summary	119	(2)
Feedback Linearisation Using Dynamic Neural Networks	121	(14)
Approximate Input--Output Linearisation of Control Affine Systems	122	(8)
Approximate input--output linearisation-decoupling and external control	125	(3)
Stability analysis	128	(2)
Approximate Input--Output Linearisation for General Nonlinear Systems	130	(1)
Related Work	131	(2)
Summary	133	(2)
Case Studies	135	(26)
The Pressure Pilot Plant	135	(3)
Description of the plant	135	(1)
Identification results	136	(1)
Globally linearising control experimental results	137	(1)
Single Link Manipulator	138	(3)
Evaporator System	141	(19)
Single loop control simulations on the evaporator	151	(2)
Approximate feedback linearisation-decoupling of the evaporator	153	(7)
Summary	160	(1)
References	161	(8)
Index	169