Eigenstructure Assignment for Semi-Proper Systems: Pseudo-State Feedback

Pomfret, Andrew; Ensor, Jonathan; Clarke, Tim

doi:10.3182/20050703-6-cz-1902.00627

Cited by 4 publications

(6 citation statements)

References 4 publications

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Section: Introductionmentioning

confidence: 99%

“…This is an open problem which has been widely discussed in the literature (Andry, Shapiro, & Chung, 1983;L. Chen & Clarke, 2009;Clarke & Griffin, 2004;Pomfret, Clarke, & Ensor, 2005;Roppenecker & O'Reilly, 1989;Srinathkumar, 1978;Zhao & Lam, 2016a, 2016b.Multirate control systems are those samplers and hold mechanisms that operate at more than one rate. Analysis and design methods for multirate control can be divided into two perspectives, the inferential control approach and the lifting approach (Tangirala, Li, Patwardhan, Shah, & Chen, August 10, 2016 International Journal of Control tCONguide 2001) which is the focus of this paper.…”

mentioning

confidence: 99%

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Increasing eigenstructure assignment design degree of freedom using lifting

Chen

Pomfret

Clarke

2016

International Journal of Control

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This paper presents the exposition of an output-lifting eigenstructure assignment (EA) design framework, wherein the available EA design degrees of freedom (DoF) is significantly increased, and the desired eigenstructure of a single-rate full state feedback solution can be achieved within an output feedback system. A structural mapping is introduced to release the output-lifting causality constraint. Additionally, the available design DoF can be further enlarged via involving the input-lifting into the output-lifting EA framework. The newly induced design DoF can be utilised to calculate a structurally-constrained, causal gain matrix which will maintain the same assignment capability. In this paper, the robustification of the output-lifting EA is also proposed, which allows a trade-off between performance and robustness in the presence of structured model uncertainties to be established. A lateral flight control benchmark in the EA literature and a numerical example are used to demonstrate the effectiveness of the design framework.Keywords: lifting; eigenstructure assignment; causality constraint IntroductionEigenstructure assignment (EA) is a mature technique for the design of control systems, especially for flight control system (Alireza & Batool, 2012;B. Chen & Nagarajaiah, 2007;Clake, Ensor, & Griffin, 2003;Farineau, 1989;Kshatriya, Annakkage, Hughes, & Gole, 2007;G. P. Liu & Patton, 1998;Y. Liu, Tan, Wang, & Wang, 2013;Moore, 1976;Ouyang, Richiedei, Trevisani, & Zanardo, 2012;Piou & Sobel, 1994, 1995Pomfret & Clarke, 2009;Shi & Patton, 2012;Wahrburg & Adamy, 2013;White, 1995;White, Bruyere, & Tsourdos, 2007). EA facilitates control system design by synthesizing a feedback gain matrix that exactly places the closed loop eigenvalues whilst matching the closed loop eigenvectors as closely as possible to a desired set. Some useful properties EA imbues on a system are: stability of response, appropriateness of transient response, decoupling of state or output response and disturbance rejection. Compared with many other competitive approaches exist to manipulate the eigenvalues of the closed-loop system and do not takes into account the role of the eigenvector, EA clearly exploits how system inputs affect mode dynamics and how these mode dynamics will be assigned to system states. Through defining a set of ideal closed-loop eigenstructure (e.g. eigenstructure which represents the realistic handling qualities of the flight control system), the realistic control effect will be guaranteed. In addition, the algorithm itself and the expression of the available design DoF can be highly visible. However, due to the lack of design DoF, e.g. the Kimura condition is not satisfied (Kimura, 1975), output feedback EA usually cannot fully assign the desired eigenstructure. This is an open problem which has been widely discussed in the literature (Andry, Shapiro, & Chung, 1983;L. Chen & Clarke, 2009;Clarke & Griffin, 2004;Pomfret, Clarke, & Ensor, 2005;Roppenecker & O'Reilly, 1989;Srinathkumar, 1978;Zhao & Lam, 2016a, 2016b.Mul...

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Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

Increasing eigenstructure assignment design degree of freedom using lifting

Chen

Pomfret

Clarke

2016

International Journal of Control

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“…Theorem 1: For a linear system with direct feedthrough (1) and (2), the solution of the linear quadratic regulation problem minimizing (3) using the output feedback (4) is given by the optimal control law 4 Then, the minimization of (3) by using the modified output feedback contr corresponds to the standard linear quadratic regulator with output feedback contr difference is that after determining the optimal output feedback gain d K , the gain K for the output feedback with direct feedthrough is obtained as follows:…”

Section: (9)mentioning

confidence: 99%

“…the input can be represented as (2) where x(t) is the n-dimensional state vector, u(t) is the m-dimensional input vector, and y(t) is the p-dimensional output vector. The p-by-m dimensional matrix D is called a direct feedthrough matrix.…”

Section: Linear-quadratic Output Feedback Regulatormentioning

confidence: 99%

“…In state-space representation, a multi-variable linear system possessing the semi-proper property is termed as having a direct feedthrough term in the output equation. Apart from strictly proper practical systems, semi-proper systems or systems with direct feedthrough have been studied for various reasons and situations in control system synthesis and analysis, e.g., inclusion of the measured acceleration of an aircraft in the system model, the proportional-integral-derivative controller, and the phase advance filter in various control systems [2]. In the process of model order reduction to eliminate highfrequency effects, direct feedthrough terms can be generated in the measurement equation [3,4] by using the concept of singular perturbations in control [5].…”

Section: Introductionmentioning

confidence: 99%

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Linear Quadratic Regulation and Tracking using Output Feedback with Direct Feedthrough

Kang¹,

Cha²,

Ko³

2016

International Journal of Aeronautical and Space Sciences

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This paper presents the development of linear quadratic regulation and output tracking algorithms using output feedback when both the measurement and performance output equations contain direct feedthrough terms. Although all physical systems can be modeled without direct feedthrough, there are still many situations where system models with direct feedthrough are important. For this situation, we modify previous work on the same topic for systems without direct feedthrough. It is shown that for the regulation problem, the optimal output feedback gain for a direct feedthrough case can be directly obtained, via a transformation, from the approach used for systems without direct feedthrough. However, for the tracking problem, a new set of coupled matrix equations for determining the optimal output feedback gain is derived from the necessary conditions for minimizing the cost function. The effectiveness of the developed algorithms is demonstrated using numerical examples

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Multistage output-lifting eigenstructure assignment: a multirate ball and plate example

Chen

Pomfret

Clarke

2018

International Journal of Control

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By exploiting both the left and the right allowable subspaces in consecutive stages, this paper extends a recently-developed output-lifting eigenstructure assignment approach into a multistage eigenstructure assignment scheme. In this scheme, design degrees of freedom, enlarged via output-lifting, are further exploited to improve eigenvector assignment. To mitigate the inherent conflicts between the theoretical development of eigenstructure assignment and inherent physical system characteristics, the paper also clearly demonstrates how to derive an ideal eigenstructure, particularly the desired eigenvectors, to distribute and decouple the natural modes among appropriate states or outputs, based upon an example: a novel multirate Ball and Plate system. The design and simulation results show the efficacy of the scheme.

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Eigenstructure Assignment for Semi-Proper Systems: Pseudo-State Feedback

Cited by 4 publications

References 4 publications

Increasing eigenstructure assignment design degree of freedom using lifting

Increasing eigenstructure assignment design degree of freedom using lifting

Linear Quadratic Regulation and Tracking using Output Feedback with Direct Feedthrough

Multistage output-lifting eigenstructure assignment: a multirate ball and plate example

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