Plant-Input-Mapping Discretization Method for a Feedback System in the State-Space Form

2021 ◽  
Author(s):  
Keisuke Yagi ◽  
Hiroaki Muto ◽  
Yoshikazu Mori
Keyword(s):  
Transfer Function ◽  
State Space ◽  
State Feedback ◽  
Closed Loop ◽  
Space Form ◽  
Feedback System ◽  
The State ◽  
Loop System ◽  
Closed Loop System ◽  
Digital Redesign

Abstract The paper proposes the digital redesign technique called plant-input-mapping (PIM) method for a feedback system described in the state-space form. The PIM method, which was originally presented in the transfer function form, focuses on the plant input signal via the plant input transfer function and discretizes it so as to satisfy the control zero principle in the resulting discrete-time closed-loop system, which leads to guaranteeing the closed-loop stability for any non-pathological sampling interval. In accordance with this approach, the proposed PIM method focuses on the control zeros included in the plant input signal. The paper proves that the matched-pole-zero discrete-time model of the plant input state-equation satisfies the control zero principle with the step-invariant model of the plant. Then, when the matched-pole-zero model is set as the target of model matching, the parameters of the state-space PIM controller employing the observer-based dynamic state-feedback can systematically be determined from the underlying continuous-time closed-loop system with guaranteed stability. This discretization process can immediately be applied to a state-feedback system and a class of multi-input multi-output systems without any modification, which cannot be discretized by the conventional PIM methods. The discretization performance of the proposed PIM method is evaluated through illustrative examples with comparable digital redesign methods, which reveal that the proposed method performs a good reproduction of the characteristics of the underlying closed-loop system.

scholarly journals Robust and Optimal Output-Feedback Control for Interval State-Space Model: Application to a Two-Degrees-of-Freedom Piezoelectric Tube Actuator

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Mounir Hammouche ◽  
Philippe Lutz ◽  
Micky Rakotondrabe
Keyword(s):  
State Space ◽  
Output Feedback ◽  
Degrees Of Freedom ◽  
Closed Loop ◽  
State Space Model ◽  
Output Feedback Control ◽  
Optimal Solution ◽  
Loop System ◽  
Closed Loop System ◽  
Optimal Output

The problem of robust and optimal output feedback design for interval state-space systems is addressed in this paper. Indeed, an algorithm based on set inversion via interval analysis (SIVIA) combined with interval eigenvalues computation and eigenvalues clustering techniques is proposed to seek for a set of robust gains. This recursive SIVIA-based algorithm allows to approximate with subpaving the set solutions [K] that satisfy the inclusion of the eigenvalues of the closed-loop system in a desired region in the complex plane. Moreover, the LQ tracker design is employed to find from the set solutions [K] the optimal solution that minimizes the inputs/outputs energy and ensures the best behaviors of the closed-loop system. Finally, the effectiveness of the algorithm is illustrated by a real experimentation on a piezoelectric tube actuator.

Determination of Most Desirable Nominal Closed Loop State Space System via Qualitative Ecological Principles

2014 ◽  
Author(s):  
Rama K. Yedavalli ◽  
Nagini Devarakonda
Keyword(s):  
State Space ◽  
Closed Loop ◽  
Self Regulation ◽  
Loop System ◽  
Convexity Property ◽  
Matrix Structure ◽  
System Matrix ◽  
Closed Loop System ◽  
Hurwitz Stability ◽  
Qualitative Robustness

This paper addresses the issue of determining the most desirable ‘Nominal Closed Loop Matrix’ structure in linear state space systems, by combining the concepts of ‘Quantitative Robustness’ and ‘Qualitative Robustness’. The qualitative robustness measure is based on the nature of interactions and interconnections of the system. The quantitative robustness is based on the nature of eigenvalue/eigenvector structure of the system. This type of analysis from both viewpoints sheds considerable insight on the desirable nominal system in engineering applications. Using these concepts it is shown that a specific quantitative set of matrices labeled ‘Quantitative Ecological Stable (QES) Matrices’ have features which qualify them as the most desirable nominal closed loop system matrices. Thus in this paper, we expand on the special features of the determinant of a matrix in terms of self-regulation, interactions and interconnections and specialize these features to the class of ‘Quantitative Ecological Stable (QES)’ matrices and show that for checking its Hurwitz stability, it is sufficient to check the positivity of only the constant coefficient of the characteristic polynomial of a matrix in a higher dimensional ‘Kronecker’ space. In addition, it is shown that these matrices possess the most attractive property among any matrix class, namely that their Determinants possess convexity property. Establishment of this optimal nominal closed loop system matrix structure paves the way for designing controllers which qualify as robust controllers for linear systems with real parameter uncertainty. The proposed concepts are illustrated with many useful examples.

Feedback Control of Linear Distributed Systems

1967 ◽  
Vol 89 (2) ◽  
pp. 379-383 ◽  
Author(s):  
Donald M. Wiberg
Keyword(s):  
Boundary Condition ◽  
Distributed Systems ◽  
Feedback Control ◽  
Closed Loop ◽  
The State ◽  
Loop System ◽  
Closed Loop System ◽  
Loop Equation ◽  
Control Feedback ◽  
And Control

The optimum feedback control of controllable linear distributed stationary systems is discussed. A linear closed-loop system is assured by restricting the criterion to be the integral of quadratics in the state and control. Feedback is obtained by expansion of the linear closed-loop equation in terms of uncoupled modes. By incorporating symbolic functions into the formulation, one can treat boundary condition control and point observable systems that are null-delta controllable.

scholarly journals Boundary stabilization and disturbance rejection for an unstable time fractional diffusion-wave equation

2022 ◽  
Author(s):  
Hua-Cheng Zhou ◽  
Ze-Hao Wu ◽  
Bao-Zhu Guo ◽  
Yangquan Chen
Keyword(s):  
Output Feedback ◽  
Disturbance Rejection ◽  
State Feedback ◽  
Closed Loop ◽  
External Disturbance ◽  
Fractional Diffusion ◽  
Loop System ◽  
Boundary Stabilization ◽  
Closed Loop System ◽  
Diffusion Wave

In this paper, we study boundary stabilization and disturbance rejection problem for an unstable time fractional diffusion-wave equation with Caputo time fractional derivative. For the case of no boundary external disturbance, both state feedback control and output feedback control via Neumann boundary actuation are proposed by the classical backstepping method. It is proved that the state feedback makes the closed-loop system Mittag-Leffler stable and the output feedback makes the closed-loop system asymptotically stable. When there is boundary external disturbance, we propose a disturbance estimator constructed by two infinite dimensional auxiliary systems to recover the external disturbance. A novel control law is then designed to compensate for the external disturbance in real time, and rigorous mathematical proofs are presented to show that the resulting closed-loop system is Mittag-Leffler stable and the states of all subsystems involved are uniformly bounded. As a result, we completely resolve, from a theoretical perspective, two long-standing unsolved mathematical control problems raised in [Nonlinear Dynam., 38(2004), 339-354] where all results were verified by simulations only.

Global Stabilization for a class of nonlinear fractional-order systems

2019 ◽  
Vol 10 (01) ◽  
pp. 1941009 ◽  
Author(s):  
Taide Liu ◽  
Feng Wang ◽  
Wanchun Lu ◽  
Xuhuan Wang
Keyword(s):  
Lyapunov Function ◽  
Fractional Order ◽  
Closed Loop ◽  
The State ◽  
Loop System ◽  
Global Stabilization ◽  
Fractional Order Systems ◽  
Closed Loop System ◽  
Integer Order ◽  
Backstepping Algorithm

The problem of Mittag–Leffler stabilization (MLS) is studied for a class of nonlinear non-integer order systems. The stabilizer is constructed by using the Lyapunov function and backstepping algorithm. The continuous controller is designed to ensure that the state of the nonlinear fractional-order closed-loop system converges to the equilibrium. Two simulation examples are given to illustrate the effectiveness of the method.

scholarly journals Stability and Stabilization of Networked Control System with Forward and Backward Random Time Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Ye-Guo Sun ◽  
Qing-Zheng Gao
Keyword(s):  
State Feedback ◽  
Closed Loop ◽  
Networked Control Systems ◽  
Networked Control System ◽  
Loop System ◽  
State Feedback Control ◽  
Networked Control ◽  
Random Time ◽  
Closed Loop System ◽  
Stochastically Stable

This paper deals with the problem of stabilization for a class of networked control systems (NCSs) with random time delay via the state feedback control. Both sensor-to-controller and controller-to-actuator delays are modeled as Markov processes, and the resulting closed-loop system is modeled as a Markovian jump linear system (MJLS). Based on Lyapunov stability theorem combined with Razumikhin-based technique, a new delay-dependent stochastic stability criterion in terms of bilinear matrix inequalities (BMIs) for the system is derived. A state feedback controller that makes the closed-loop system stochastically stable is designed, which can be solved by the proposed algorithm. Simulations are included to demonstrate the theoretical result.

Stable observer-based controller design for robust state-feedback pole assignment

2000 ◽  
Vol 214 (4) ◽  
pp. 313-318 ◽  
Author(s):  
G P Liu ◽  
G R Duan ◽  
S Daley
Keyword(s):  
Frequency Domain ◽  
Stability Problem ◽  
State Feedback ◽  
Closed Loop ◽  
Controller Design ◽  
Pole Assignment ◽  
Loop System ◽  
Closed Loop System ◽  
Sensitive Function ◽  
The Stability

The design of stable observer-based controllers for robust pole assignment is addressed in this paper. The stability problem of these dynamical controllers is investigated, which is often ignored during the controller design. A design formulation of stable observer controllers is presented using state-feedback pole assignment techniques. Although the design formulation is principally aimed at the design of a stable controller, the mixed sensitive function in the frequency domain is also considered to improve the robustness of the closed-loop system. This ensures that the closed-loop system has good robustness and the controller is stable.

scholarly journals Design, modelling and simulation of controlled sepic DC-DC converter-based genetic algorithm

2020 ◽  
Vol 11 (4) ◽  
pp. 2116
Author(s):  
Mohammed Omar Ali ◽  
Ali Hussein Ahmad
Keyword(s):  
Genetic Algorithm ◽  
State Space ◽  
Closed Loop ◽  
Modelling And Simulation ◽  
Loop System ◽  
Superior Performance ◽  
Step Response ◽  
System Modelling ◽  
Closed Loop System ◽  
Simulation And Optimization

This paper discusses various aspects of a single-ended primary inductance DC-DC converter (SEPIC). The focus is on design, modelling, and simulation results of a SEPIC converter. The study analyses the principle of SEPIC operation when operated in continuous conduction mode (CCM). Additionally, the mathematical equations for the design modules are calculated as per converter requirements. State-space equations are used to formulate the state-space model of the SEPIC converter. To satisfy the best-performance criterion of the system, the parameters for controller (K<sub>p</sub>, K<sub>i</sub>, K<sub>d</sub>) should be tuned or optimized using the genetic algorithm (GA) optimization technique. Controller parameters are determined using an objective function that minimises the integral time absolute error (ITAE). Simulations performed on a closed-loop system reveal that the step response with a PID controlled based GA displayed superior performance. A closed-loop system has a substantially bigger stability region compared to an open-loop system. The simulation optimised performance metrics like maximum overshoot percentage (M<sub>p</sub>), rise time (t<sub>r</sub>), and settling time (t<sub>s</sub>). MATLAB/Simulink R2018a® and m-file code are used for the system modelling, simulation, and optimization of the PID controller parameters based on the GA.

Determination of Most Desirable Nominal Closed-Loop State Space System Via Qualitative Ecological Principles

2015 ◽  
Vol 138 (2) ◽  
Author(s):  
Nagini Devarakonda ◽  
Rama K. Yedavalli
Keyword(s):  
State Space ◽  
Closed Loop ◽  
Point Of View ◽  
Loop System ◽  
Matrix Structure ◽  
System Matrix ◽  
Closed Loop System ◽  
Qualitative Robustness ◽  
Ecological Principles ◽  
Linear State

This paper addresses the issue of determining the most desirable “nominal closed-loop matrix” structure in linear state space systems, from stability robustness point of view, by combining the concepts of “quantitative robustness” and “qualitative robustness.” The qualitative robustness measure is based on the nature of interactions and interconnections of the system. The quantitative robustness is based on the nature of eigenvalue/eigenvector structure of the system. This type of analysis from both viewpoints sheds considerable insight on the desirable nominal system in engineering applications. Using these concepts, it is shown that three classes of quantitative matrices labeled “target sign stable (TSS) matrices,” “target pseudosymmetric (TPS) matrices,” and finally “quantitative ecological stable (QES) matrices” have features which qualify them as the most desirable nominal closed-loop system matrices. In this paper, we elaborate on the special features of these sets of matrices and justify why these classes of matrices are well suited to be the most desirable nominal closed-loop matrices in the linear state space framework. Establishment of this most desirable nominal closed-loop system matrix structure paves the way for designing controllers which qualify as robust controllers for linear systems with real parameter uncertainty. The proposed concepts are illustrated with many useful examples.

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