STATE-SPACE DESCRIPTION AND ANALYSIS OF THE CLOSED-LOOP SYSTEM

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.

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

Volume 3: Industrial Applications; Modeling for Oil and Gas, Control and Validation, Estimation, and Control of Automotive Systems; Multi-Agent and Networked Systems; Control System Design; Physical Human-Robot Interaction; Rehabilitation Robotics; Sensing and Actuation for Control; Biomedical Systems; Time Delay Systems and Stability; Unmanned Ground and Surface Robotics; Vehicle Motion Controls; Vibration Analysis and Isolation; Vibration and Control for Energy Harvesting; Wind Energy ◽

10.1115/dscc2014-6181 ◽

2014 ◽

Cited By ~ 2

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.

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

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.4052040 ◽

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.

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

International Journal of Power Electronics and Drive Systems (IJPEDS) ◽

10.11591/ijpeds.v11.i4.pp2116-2125 ◽

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 (Kp, Ki, Kd) 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 (Mp), rise time (tr), and settling time (ts). 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.

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

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.4031957 ◽

2015 ◽

Vol 138 (2) ◽

Cited By ~ 1

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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