P-D Feedback for Decoupling and Pole Assignment of Singular Systems

1998 ◽  
Vol 120 (3) ◽  
pp. 378-388 ◽  
Author(s):  
F. N. Koumboulis ◽  
B. G. Mertzios
Keyword(s):  
Closed Loop ◽  
Singular Systems ◽  
Sufficient Conditions ◽  
Pole Assignment ◽  
Loop System ◽  
Necessary And Sufficient Conditions ◽  
Algebraic Equations ◽  
Input Output ◽  
Closed Loop System ◽  
Necessary And Sufficient

The problem of reducing a multi input-multi output system to many single input-single output systems, namely the problem of input-output decoupling, is studied for the case of singular systems i.e., for systems described by dynamic and algebraic equations. The problem of input-output decoupling with simultaneous arbitrary pole assignment, via proportional plus derivative (P-D) state feedback, is extensively solved. The general explicit expression of all P-D controllers solving the decoupling problem is determined. The general form of the diagonal elements of the decoupled closed-loop system is proven to be in a form having a fixed numerator polynomial and an arbitrary denominator polynomial. The necessary and sufficient conditions for the solvability of the problem of decoupling with simultaneous asymptotic stabilizability or arbitrary pole assignment are established. Furthermore, the necessary and sufficient conditions for decoupling with simultaneous impulse elimination, as well as the necessary and sufficient conditions for decoupling with arbitrary assignment of the finite and infinite poles of the closed-loop system, are established.

scholarly journals Optimal Pole Assignment of Linear Systems by the Sylvester Matrix Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Hua-Feng He ◽  
Guang-Bin Cai ◽  
Xiao-Jun Han
Keyword(s):  
Assignment Problem ◽  
Closed Loop ◽  
Sufficient Conditions ◽  
Pole Assignment ◽  
Loop System ◽  
Linear Matrix ◽  
Feedback Gain ◽  
Matrix Equations ◽  
Closed Loop System ◽  
Linear Matrix Equations

The problem of state feedback optimal pole assignment is to design a feedback gain such that the closed-loop system has desired eigenvalues and such that certain quadratic performance index is minimized. Optimal pole assignment controller can guarantee both good dynamic response and well robustness properties of the closed-loop system. With the help of a class of linear matrix equations, necessary and sufficient conditions for the existence of a solution to the optimal pole assignment problem are proposed in this paper. By properly choosing the free parameters in the parametric solutions to this class of linear matrix equations, complete solutions to the optimal pole assignment problem can be obtained. A numerical example is used to illustrate the effectiveness of the proposed approach.

Output Feedback Assignability for Nonlinear Min-Max Systems

2011 ◽  
Vol 314-316 ◽  
pp. 374-379
Author(s):  
Hong Yun Wei ◽  
Zhong Xun Zhu ◽  
Yue Gang Tao ◽  
Wen De Chen
Keyword(s):  
Output Feedback ◽  
Cycle Time ◽  
Closed Loop ◽  
Loop System ◽  
Closed Loop System ◽  
Sufficient Criterion ◽  
Feedback Cycle ◽  
Necessary And Sufficient ◽  
Coloring Graph

This paper investigates the output feedback cycle time assignability of the min-max systems which are more complex than the systems studied in recent years. Max-plus projection representation for the closed-loop system with min-max output feedback is introduced. The coloring graph is presented and applied to analyze the structure of systems effectively. The necessary and sufficient criterion for the output feedback cycle time assignability is established which is an extension of the results studied before. The methods are constructive in nature.

scholarly journals Zeroing of state variables in fractional descriptor electrical circuits by state-feedbacks

2014 ◽  
Vol 63 (3) ◽  
pp. 321-333
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Closed Loop ◽  
Sufficient Conditions ◽  
The State ◽  
Necessary And Sufficient Conditions ◽  
State Variables ◽  
Electrical Circuits ◽  
Closed Loop Systems ◽  
Necessary And Sufficient

Abstract The problem of zeroing of the state variables in fractional descriptor electrical circuits by state-feedbacks is formulated and solved. Necessary and sufficient conditions for the existence of gain matrices such that the state variables of closed-loop systems are zero for time greater zero are established. The procedure of choice of the gain matrices is demonstrated on simple descriptor electrical circuits with regular pencils

scholarly journals Stability of arbitrarily switched discrete-time linear singular systems of index-1

2018 ◽  
Vol 34 (4) ◽  
Author(s):  
Pham Thi Linh
Keyword(s):  
Exponential Stability ◽  
Discrete Time ◽  
Switched Systems ◽  
Singular Systems ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Positive Switched Systems ◽  
Necessary And Sufficient ◽  
Time Linear

In this paper, the index-1 notion for arbitrarily switched discrete-time linear singular systems (SDLS) has been introduced. Based on the Bohl exponents of SDLS as well as properties of associated positive switched systems, some necessary and sufficient conditions have been established for exponential stability.

Event-triggered Hꝏ control for NCS with time-delay and packet losses

2019 ◽  
Vol 37 (3) ◽  
pp. 918-934
Author(s):  
Jing Bai ◽  
Ying Wang ◽  
Li-Ying Zhao
Keyword(s):  
Time Delay ◽  
Closed Loop ◽  
Discrete Event ◽  
Sufficient Conditions ◽  
Loop System ◽  
Linear Matrix ◽  
Time Varying ◽  
Closed Loop System ◽  
Packet Losses ◽  
Event Triggered

Abstract This paper is concerned with the discrete event-triggered dynamic output-feedback ${H}_{\infty }$ control problem for the uncertain networked control system, where the time-varying sampling, network-induced delay and packet losses are taken into account simultaneously. The random packet losses are described via the Bernoulli distribution. And then, the closed-loop system is modelled as an augmented time-delay system with interval time-varying delay. By using the Lyapunov stability theory and the augmented state space method, the sufficient conditions for the asymptotic stability of the closed-loop system are proposed in the form of linear matrix inequalities. At the same time, the design method of the ${H}_{\infty }$ controller is created. Finally, a numerical example is employed to illustrate the effectiveness of the proposed method.

Output Feedback Algorithm for Nonlinear Systems with Compensation of Bounded Disturbances and Measurement Noises

2019 ◽  
Vol 20 (1) ◽  
pp. 3-15 ◽  
Author(s):  
I. B. Furtat ◽  
P. A. Gushchin ◽  
A. A. Peregudin
Keyword(s):  
Output Feedback ◽  
Closed Loop ◽  
Sufficient Conditions ◽  
Loop System ◽  
Partial Recovery ◽  
Closed Loop System ◽  
External Disturbances ◽  
Control Schemes ◽  
Measurement Noises ◽  
Feedback Algorithm

The output feedback algorithm for dynamic plants with compensation of parametric uncertainty, external disturbances and measurement noises is synthesized. The plants are described by a nonlinear system of differential equations with vector input and output signals. Unlike most existing control schemes in this paper the dimensions of the measurement interference and the output signal are equal, the sources of the signals of disturbances and disturbances are different, parametric and external disturbances can be present in any equation of the plant model. For simultaneous compensation of disturbances and measurement noises it is proposed to consider two channels. On the first channel a part of the measurement noises will be estimated which will allow partial recovery the information about the plant noisy output. On the second channel the disturbances will be compensated. Thus, at least two independent measurement channels are required for simultaneous compensation of disturbances and measurement noises. Sufficient conditions for calculating the parameters of the algorithm in the form of solvability of the linear matrix inequality are obtained. It is shown that the equation of a closed-loop system obtained on the basis of the proposed algorithm depends on the disturbances and the smallest component of the measurement noise. However, if the smallest component cannot be identified a priory, the results of the transients depend on the component of the noise that will be selected in the synthesis of the control system. Thus, unlike most existing control schemes, where the equation of a closed-loop system depends on disturbance and noise, the resulting algorithm provides better transients, because they do not depend on the entire noise vector, but only on its smallest (one) component. The simulations for a third-order nonlinear plant and the synchronization of an electrical generator connected to the power grid are presented. Numerical examples illustrate the effectiveness of the proposed scheme and the robustness with respect to random components in the noises and disturbances.

Robust nonfragile observer-based H2/H∞ controller

2016 ◽  
Vol 24 (4) ◽  
pp. 722-738 ◽  
Author(s):  
Atta Oveisi ◽  
Tamara Nestorović
Keyword(s):  
Control System ◽  
Real Time ◽  
Closed Loop ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Loop System ◽  
Linear Matrix ◽  
Closed Loop System ◽  
Real Time System ◽  
Structured Uncertainty

A robust nonfragile observer-based controller for a linear time-invariant system with structured uncertainty is introduced. The [Formula: see text] robust stability of the closed-loop system is guaranteed by use of the Lyapunov theorem in the presence of undesirable disturbance. For the sake of addressing the fragility problem, independent sets of time-dependent gain-uncertainties are assumed to be existing for the controller and the observer elements. In order to satisfy the arbitrary H2-normed constraints for the control system and to enable automatic determination of the optimal [Formula: see text] bound of the performance functions in disturbance rejection control, additional necessary and sufficient conditions are presented in a linear matrix equality/inequality framework. The [Formula: see text] observer-based controller is then transformed into an optimization problem of coupled set of linear matrix equalities/inequality that can be solved iteratively by use of numerical software such as Scilab. Finally, concerning the evaluation of the performance of the controller, the control system is implemented in real time on a mechanical system, aiming at vibration suppression. The plant under study is a multi-input single-output clamped-free piezo-laminated smart beam. The nominal mathematical reduced-order model of the beam with piezo-actuators is used to design the proposed controller and then the control system is implemented experimentally on the full-order real-time system. The results show that the closed-loop system has a robust performance in rejecting the disturbance in the presence of the structured uncertainty and in the presence of the unmodeled dynamics.

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