Abstract
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.
Highlights
Control of nonlinear systems is gaining increasing attention in recent years due to its technical importance and its impact on various applications as well
We introduce a new concept of generalized quadratic linearization which seeks to remove the second-order nonlinearity in the system without introducing third- and higher-order nonlinearities in the process
Verification of quadratic linearization of PMSM through simulations is given in an earlier paper by the authors [18]
Summary
Control of nonlinear systems is gaining increasing attention in recent years due to its technical importance and its impact on various applications as well. Kang and Krener [6,7,8] extended the result for the approximate linearization of control affine systems and derived what are termed generalized homological equations. Applying quadratic linearization based on approximate linearization technique to this model introduces third- and higherorder terms into the model even though the machine does not possess nonlinearities of this order during normal operation. Application of generalized quadratic linearization to machine models helps to avoid the issue of singularity which is a drawback attributed to the existing exact linearization of machine models [2, 3]. This is the main contribution of the paper.
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