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Guang Ren Duan,Ya-Jun Gao 제어·로봇·시스템학회 2020 International Journal of Control, Automation, and Vol.18 No.8
In this paper, based on the inverse of block companion matrix pencils associated with matrix polynomials, a first-order state-space realization in descriptor system form for a general high-order linear system is derived. An important feature of the proposed realization is that it allows the high-order linear system to be singular. While in the case that the high-order system is nonsingular, two realizations in normal state-space system forms are directly deduced. With the help of the proposed realization, a generalized Popov Belevitch Hautus (PBH) criterion for highorder systems is then established in terms of the original system matrix polynomials. Examples are studied which well demonstrate the proposed theories.
Parametric Control of Quasi-linear Systems via State Feedback
Guang-Ren Duan 제어로봇시스템학회 2014 제어로봇시스템학회 국제학술대회 논문집 Vol.2014 No.10
In the last decade, a complete parametric approach for multi-input linear systems has been proposed, which gives general parametrization of the state feedback gain, and at the same time, produces a complete parametric expression for the eigenvector matrices. In this paper, it is shown that such an approach can be generalized to a type of quasilinear systems with coefficient matrices containing the state variables and also a time-varying parameter vector. General complete parametrization of a quasi-linear state feedback controller is proposed based on the solution to a type parametervarying generalized Sylvester matrix equations, which gives a linear closed-loop system with desired eigenstructure. What is more, in such a realization the linear closed-loop system can often be made constant. The approach also provides all the degrees of freedom which may be further utilized to improve the system performance. An example demonstrates the proposed parametric approach.
Quaternion-based Satellite Attitude Control-A Direct Parametric Approach
Guang-Ren Duan 제어로봇시스템학회 2014 제어로봇시스템학회 국제학술대회 논문집 Vol.2014 No.10
In this paper, the dynamical model in a matrix second-order nonlinear form with respect to the quaternion coordinates is firstly established for the attitude system of a satellite, which is complete in the sense that no approximation is taken. Then, with the help of a recently proposed general parametric design approach for general fully-actuated second-order nonlinear systems, a direct parametric approach for satellite attitude control via proportional plus derivative quaternion feedback is proposed, which gives a complete parametrization of the pair of feedback gains. The approach possesses two important features. Firstly, with the proposed controller parametrization, the satellite attitude system, though highly nonlinear, can be turned into a constant linear system with desire eigenstructure. Secondly, in such a design there are still degrees of freedom which may be further utilized to improve the system performance. An example is considered to demonstrate the use of the proposed approach.
Guang-Ren Duan,Qin Zhao,Tianyi Zhao 제어·로봇·시스템학회 2024 International Journal of Control, Automation, and Vol.22 No.1
The high-order fully actuated system (HOFAS) approach has recently been proposed, aiming at establishing a unified architecture for control of general nonlinear systems. Its core idea is to firstly obtain a HOFAS model for a dynamical system, and then to cancel the nonlinearity using the full-actuation property. Based on this, the control problem of both linear and many types of nonlinear systems is finally turned into a specific eigenstructure assignment problem of a particular matrix pair. Because of this, the specific eigenstructure assignment problem is considered as the fundamental problem of the HOFAS approach, and is investigated in detail in this paper. A general parametric solution is established in an iterative form with all the degrees of freedom provided, and special solutions for some commonly used cases are also given. These form a database for various design problems and provide some ready-to-use results. Finally, illustrative examples demonstrate the usage of the database.
Feng Zhang,Guang Ren Duan 제어·로봇·시스템학회 2018 International Journal of Control, Automation, and Vol.16 No.5
This paper tackles the problem of integrated translation and rotation stabilization of the spacecraft in proximity operations by proposing a novel manipulator actuation strategy. To do so, by theoretically integrating the attitude/position motion of the spacecraft and the joint motion of the manipulator, a coupled translational and rotational kinematics of the spacecraft with a single space manipulator mounted is formulated, where system unknown parameters and residual system momentum are taken into account and analyzed. Taking the joint motion as the control input, a projection-based adaptive control scheme is then developed such that the translation and rotation of the spacecraft can be robustly stabilized with the manipulator-based actuation. The closed-loop asymptotic stability is guaranteed within Lyapunov framework. Meanwhile, considering the constrained joint motion of the manipulator, the resulting control constraint issue is handled by developing an optimization based bound analysis method, which also facilitates the determination of control parameters. Two scenario numerical simulations demonstrate the effect of the designed control scheme.