scholarly journals Generalized Quadratic Linearization of Machine Models

2011 ◽  
Vol 2011 ◽  
pp. 1-10
Author(s):  
Parvathy Ayalur Krishnamoorthy ◽  
Kamaraj Vijayarajan ◽  
Devanathan Rajagopalan
Keyword(s):  
Nonlinear System ◽  
Taylor Series ◽  
State Feedback ◽  
Taylor Series Expansion ◽  
Higher Order ◽  
Exact Linearization ◽  
Linearization Technique ◽  
Practical Applications ◽  
Higher Order Terms ◽  
Approximate Linearization

In the exact linearization of involutive nonlinear system models, the issue of singularity needs to be addressed in practical applications. The approximate linearization technique due to Krener, based on Taylor series expansion, apart from being applicable to noninvolutive systems, allows the singularity issue to be circumvented. But approximate linearization, while removing terms up to certain order, also introduces terms of higher order than those removed into the system. To overcome this problem, in the case of quadratic linearization, a new concept called “generalized quadratic linearization” is introduced in this paper, which seeks to remove quadratic terms without introducing third- and higher-order terms into the system. Also, solution of generalized quadratic linearization of a class of control affine systems is derived. Two machine models are shown to belong to this class and are reduced to only linear terms through coordinate and state feedback. The result is applicable to other machine models as well.

scholarly journals Analysis of Exact Linearization and Aproximate Feedback Linearization Techniques

2011 ◽  
Vol 2011 ◽  
pp. 1-17 ◽  
Author(s):  
Gildeberto S. Cardoso ◽  
Leizer Schnitman
Keyword(s):  
Nonlinear System ◽  
Control Systems ◽  
Taylor Series ◽  
Feedback Linearization ◽  
Taylor Series Expansion ◽  
Linear Control ◽  
Linear Control Systems ◽  
Exact Linearization ◽  
Linear Controller ◽  
Linearization Techniques

This paper presents a study of linear control systems based on exact feedback linearization and approximate feedback linearization. As exact feedback linearization is applied, a linear controller can perform the control objectives. The approximate feedback linearization is required when a nonlinear system presents a noninvolutive property. It uses a Taylor series expansion in order to compute a nonlinear transformation of coordinates to satisfy the involutivity conditions.

Exact Linearization Algorithm of Tight Coupling Nonlinear System Based on Differential Manifold

2013 ◽  
Vol 380-384 ◽  
pp. 686-691
Author(s):  
Hua Ming Qian ◽  
Zhen Duo Fu ◽  
Liang Chen ◽  
Xiu Li Ning
Keyword(s):  
Control System ◽  
Nonlinear System ◽  
Attitude Control ◽  
Taylor Series Expansion ◽  
Expansion Method ◽  
Exact Linearization ◽  
Tight Coupling ◽  
Attitude Control System ◽  
Application Range ◽  
Differential Manifold

Dealt with the short precision the traditional Taylor series expansion induced and shortage that the system mechanics is hard to match with the exact linearization conditions, a novel exact linearization algorithm of tight coupling nonlinear system based on differential manifold to the missile attitude control system is proposed. A dimension expansion method is proposed, the method solves the problem that the input and output dimensions can not meet the exact linearization conditions; the algorithm application range is widened. Using the principle of the differential manifold, the missile velocity and height information are selected as the measure output, the exact linearization of the missile attitude system is derived based on the diffeomorphism transformations. The simulations are performed on the missile attitude control system. Simulation results show that the effectiveness of the algorithm proposed.

Efficient Propagation of Error Through System Models for Functions Common in Engineering

2012 ◽  
Vol 134 (1) ◽  
Author(s):  
Travis V. Anderson ◽  
Christopher A. Mattson ◽  
Brad J. Larson ◽  
David T. Fullwood
Keyword(s):  
Taylor Series ◽  
Error Propagation ◽  
Truncation Error ◽  
System Modeling ◽  
Kinematic Model ◽  
Computational Cost ◽  
Taylor Series Expansion ◽  
Design Decisions ◽  
First Order ◽  
Higher Order Terms

System modeling can help designers make and verify design decisions early in the design process if the model’s accuracy can be determined. The formula typically used to analytically propagate error is based on a first-order Taylor series expansion. Consequently, this formula can be wrong by one or more orders of magnitude for nonlinear systems. Clearly, adding higher-order terms increases the accuracy of the approximation but it also requires higher computational cost. This paper shows that truncation error can be reduced and accuracy increased without additional computational cost by applying a predictable correction factor to lower-order approximations. The efficiency of this method is demonstrated in the kinematic model of a flapping wing. While Taylor series error propagation is typically applicable only to closed-form equations, the procedure followed in this paper may be used with other types of models, provided that model outputs can be determined from model inputs, derivatives can be calculated, and truncation error is predictable.

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