Parametric Control to a Type of Quasi-Linear Descriptor Systems via Proportional Plus Derivative Feedback

IET Control Theory & Appl

2020

This study investigates a parametric method to design a dynamic compensator for descriptor high-order quasi-linear (DHQ) systems. Utilising the solution to generalised high-order Sylvester equations, a more unified parametric form of the dynamic compensator is developed to improve the control effects. Meanwhile, normalisation design by using the dynamic compensator is also considered for DHQ systems such that the closed-loop regularity can be maintained easily and effectively. Whether the closed-loop form is singular or not, it has an expected eigenstructure. Finally, an example is provided to verify the parametric method is feasible and reliable.

“…The Genesio–Tesi system can be represented by the following equation:

\begin{matrix} right left right left right left right left right left right left0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em3pt \\ \overset{⃛}{α} + 0.45 \ddot{α} + 1.1 \dot{α} + α - α^{2} = 0, \end{matrix}

and the Coullet system

\begin{matrix} right left right left right left right left right left right left0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em3pt \\ \overset{⃛}{β} + 0.45 \ddot{β} + 1.1 \dot{β} - 0.8 β + β^{3} = 0 \end{matrix}

based on the existing result in [20], the synchronisation problem of Genesio–Tesi and Coullet systems can be modelled as the following DHQ system:

A_{3} false(θ, y false) \overset{⃛}{q} + A_{2} false(θ, y false) \ddot{q} + A_{1} false(θ, y false) \dot{q} + A_{0} false(θ, y false) q = u,

where

q = {[\begin{matrix} center center1em4pt \\ β & e \end{matrix}]}^{T}

e = α - β

is the tracking error, and

\begin{matrix} right left right left right left right left right left right left0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em3pt \\ A_{3} (θ, y) & = [\begin{matrix} center center1em4pt \\ 0 & 1 \\ 0 & 0 \end{matrix}], A_{2} (θ, y) = [\begin{matrix} center center1em4pt \\ 0 & 0.45 \\ 0 & 0 \end{matrix}], \\ A_{1} (θ, y) & = [\begin{matrix} ... \end{matrix}] \end{matrix}

…”

Section: Examplementioning

confidence: 99%

Section: System Descriptionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Parametric method to design dynamic compensator for descriptor high‐order quasi‐linear systems

IET Control Theory & Appl

2020

“…Quasi-linear systems are commonly used for the modeling of spacecraft rendezvous [18], chaotic systems synchronization [19], spacecraft attitude control [20,21], circuit systems [22,23], and so on, which have a wide range of engineering applications. Meanwhile, quasi-linear systems maintain strong coupling and highly nonlinear characteristics but in a linear format, which can be regarded as the bridge and link between linear systems and nonlinear systems.…”

Section: Introductionmentioning

confidence: 99%

Controllability results for quasi‐linear systems: Standard and descriptor cases

Asian Journal of Control

2021

Self Cite

This paper investigates the controllability of quasi‐linear systems in standard and descriptor cases. Two extended PBH criteria depending on the coefficient matrices, as sufficient conditions, are proposed to test the controllability of quasi‐linear systems for standard and descriptor cases. Finally, two practical examples are provided to verify the effectiveness of the proposed criteria. The proposed method naturally extends the controllability conclusions to existing results and practically enlightens the study of nonlinear systems.

“…The parametric approach, creatively proposed by Duan (2014b, 2014c), solved the basic control problem and realized the performance optimization, which opens up the whole new field of research. Further, Gu et al developed its applications in various systems, such as linear time-varying systems (Gu et al 2019a; Gu and Zhang 2020a) and quasi-linear systems (Gu et al 2019b, 2019c; Gu and Zhang 2020b, 2020c, 2020d). The major benefits of the parametric approach are summarized in the following aspects.…”

Section: Introductionmentioning

confidence: 99%

Parametric control to permanent magnet synchronous motor via proportional plus integral feedback

Transactions of the Institute of Measurement and Control

2020

Self Cite

This study investigates a parametric approach to design the proportional-integral (PI) controller for a permanent magnet synchronous motor (PMSM). Based on the solutions of the generalized Sylvester equation, the generally parametric expressions of PI controller and right eigenvector matrix are obtained. By using the parametric approach, the closed-loop system is converted into a linear time-invariant system with an expected eigenstructure. Further, a numerical example is put forward to illustrate the effectiveness and feasibility of the proposed parametric approach.