Extended Quadratic Controller Normal Form and Dynamic State Feedback Linearization of Nonlinear Systems

“…Model (8) has to be first reduced to Brunovsky form [15, 16] of (2) before quadratic linearization of (3) and (4) Using the linear transformations (9) and (10), (8) can be reduced to Brunovsky form for two inputs (11) as below (where…”

Section: Quadratic Linearization Of Pmsm a Machine Modelmentioning

confidence: 99%

“…In order to cancel the quadratic term of the system, change of coordinate and feedback of the following form is considered, as given in [10,11] Applying the transformations (3) and (4), (1) can be derived by solving (6) and (7).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Analysis and Application of Quadratic Linearization to the Control of Permanent Magnet Synchronous Motor

Parvathy¹,

Devanathan²,

Kamaraj³

2014

ijeei

View full text Add to dashboard Cite

Abstract:The introduction of state equation model of the electrical machine based on direct and quadrature axes variables has paved the way for powerful control theories to be brought to bear on the problem of control of electric machines. Exact linearization has been applied to the control of permanent magnet synchronous motor (PMSM). In this paper, application of approximate linearization is proposed for the control of PMSM. Since the PMSM model is essentially quadratic, quadratic linearization is considered for the application. Conditions on the coordinate transformation and state feedback are derived for the linearization of a four dimensional permanent magnet (PM) machine model. The proposed linearization technique does not introduce singularities in the system as in the case of exact linearization. Also, to account for higher order nonlinearities including unmodelled dynamics, the linear zing transformations are adaptively tuned. Simulation studies verify the theoretical results presented. Hardware/software implementation is carried out to verify the effectiveness of the linearization technique proposed. The linearization technique proposed can also be applied to other types of electrical motors.

show abstract

“…is n -1, there exists a linear change of coordinates and feedback independent of , p transforming the system (1) into (6) 51 = X I , i 2 = 2 2 + 7 1 p , ... 5" = 2, + T n -l P , a = 21 + TnP, which transforms system (5) into (7). For the reason of simplicity, we still use ( 2 , x ) and U to represent the state variables and control input for the new system.…”

Section: Normal Forms and Invariantsmentioning

confidence: 99%

Bifurcation and topology of equilbrium sets

Kang¹

Proceedings of 35th IEEE Conference on Decision and Control

View full text Add to dashboard Cite

show abstract

Extended Quadratic Controller Normal Form and Dynamic State Feedback Linearization of Nonlinear Systems

Cited by 166 publications

References 6 publications

On the Convergence and Behavior of Three Dimensional Normal Forms

On the Convergence and Behavior of Three Dimensional Normal Forms

Analysis and Application of Quadratic Linearization to the Control of Permanent Magnet Synchronous Motor

Bifurcation and topology of equilbrium sets

Contact Info

Product

Resources

About