scholarly journals LMI Pole Regions for a Robust Discrete-Time Pole Placement Controller Design

Algorithms ◽  
2019 ◽  
Vol 12 (8) ◽  
pp. 167
Author(s):  
Danica Rosinová ◽  
Mária Hypiusová
Keyword(s):  
Discrete Time ◽  
Closed Loop ◽  
Controller Design ◽  
Loop System ◽  
Pole Placement ◽  
Linear Matrix ◽  
Closed Loop System ◽  
Robust Controller ◽  
Pole Placement Controller ◽  
Robust Controller Design

Herein, robust pole placement controller design for linear uncertain discrete time dynamic systems is addressed. The adopted approach uses the so called “D regions” where the closed loop system poles are determined to lie. The discrete time pole regions corresponding to the prescribed damping of the resulting closed loop system are studied. The key issue is to determine the appropriate convex approximation to the originally non-convex discrete-time system pole region, so that numerically efficient robust controller design algorithms based on Linear Matrix Inequalities (LMI) can be used. Several alternatives for relatively simple inner approximations and their corresponding LMI descriptions are presented. The developed LMI region for the prescribed damping can be arbitrarily combined with other LMI pole limitations (e.g., stability degree). Simple algorithms to calculate the matrices for LMI representation of the proposed convex pole regions are provided in a concise way. The results and their use in a robust controller design are illustrated on a case study of a laboratory magnetic levitation system.

A Novel Delay-Independent Robust Adaptive Controller Design for Uncertain Nonlinear Systems With Time-Varying State Delay

2019 ◽  
Vol 15 (1) ◽  
Author(s):  
Hadi Azmi ◽  
Alireza Yazdizadeh
Keyword(s):  
Nonlinear Systems ◽  
Linear Matrix Inequality ◽  
Closed Loop ◽  
Controller Design ◽  
Loop System ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
System Delay ◽  
Closed Loop System

Abstract In this paper, two novel adaptive control strategies are presented based on the linear matrix inequality for nonlinear Lipschitz systems. The proposed approaches are developed by creatively using Krasovskii stability theory to compensate parametric uncertainty, unknown time-varying internal delay, and bounded matched or mismatched disturbance effects in closed-loop system of nonlinear systems. The online adaptive tuning controllers are designed such that reference input tracking and asymptotic stability of the closed-loop system are guaranteed. A novel structural algorithm is developed based on linear matrix inequality (LMI) and boundaries of the system delay or uncertainty. The capabilities of the proposed tracking and regulation methods are verified by simulation of three physical uncertain nonlinear system with real practical parameters subject to internal or state time delay and disturbance.

Robust Controller Design to Achieve Active Damping for a MEMS Microphone

2008 ◽  
Author(s):  
Jinli Qu ◽  
Ronald N. Miles ◽  
N. Eva Wu
Keyword(s):  
Closed Loop ◽  
Controller Design ◽  
Active Damping ◽  
Closed Loop System ◽  
Robust Controller ◽  
Nonlinear Simulation ◽  
Mems Microphone ◽  
And Performance ◽  
The Stability ◽  
Robust Controller Design

This paper presented an H∞-controller design to achieve active damping for a MEMS microphone system. The parametric uncertainties introduced by linearization process were modeled. The stability and performance of the closed-loop system were analyzed for the uncertain microphone model and both were shown to be robust. The nonlinear simulation further verifies that the controller offers the desired performance.

A comparison of linear discrete-time design methods for servosystem control

1997 ◽  
Vol 211 (4) ◽  
pp. 281-300 ◽  
Author(s):  
A R Plummer
Keyword(s):  
Discrete Time ◽  
Closed Loop ◽  
Solution Method ◽  
Controller Design ◽  
Pole Placement ◽  
Closed Loop System ◽  
Linear Quadratic ◽  
Linear Quadratic Gaussian ◽  
Time Model ◽  
Sensitivity Functions

Three linear discrete-time model-based controller design techniques are compared: pole placement, linear quadratic Gaussian (LQG) and H∞ control. It is shown that design choices can be made for all three controllers by considering the effect on the sensitivity functions of the closed-loop system. Also all three controllers can be implemented using an identical controller structure. A comparative study of the application of the techniques to an electromechanical servosystem is made. The controllers are designed from a discrete-time plant model estimated from experimental data, and a polynomial-based solution method is used in each case. It is concluded that acceptable performance can be achieved using any of the controllers if informed design choices are made.

Design of a stabilizing controller for discrete-time switched delay systems with affine parametric uncertainties

2018 ◽  
Vol 41 (1) ◽  
pp. 14-22 ◽  
Author(s):  
NA Baleghi ◽  
MH Shafiei
Keyword(s):  
Discrete Time ◽  
Closed Loop ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Loop System ◽  
Delay Systems ◽  
Linear Matrix ◽  
Parametric Uncertainties ◽  
Closed Loop System ◽  
Stabilizing Controller

This paper studies the stabilization problem of discrete-time switched systems in the presence of a time-varying delay and parametric uncertainties. The main goal is to provide a state feedback controller to guarantee the stability of the closed-loop system with an evaluated average dwell time. In this regard, an appropriate Lyapunov–Krasovskii functional is constructed and the sufficient conditions for stability of the closed-loop system are developed in terms of feasibility testing of proposed linear matrix inequalities. These conditions only depend on the upper bounds of the time delay and uncertain parameters. Additionally, a numerical example is provided to verify the theoretical results.

scholarly journals Robust H∞ Loop Shaping Controller Synthesis for SISO Systems by Complex Modular Functions

2021 ◽  
Vol 26 (1) ◽  
pp. 21
Author(s):  
Ahmad Taher Azar ◽  
Fernando E. Serrano ◽  
Nashwa Ahmad Kamal
Keyword(s):  
Design Methodology ◽  
Closed Loop ◽  
Complex Analysis ◽  
Controller Design ◽  
Filter Design ◽  
Design Procedure ◽  
Elliptic Functions ◽  
Loop System ◽  
Closed Loop System ◽  
Loop Shaping

In this paper, a loop shaping controller design methodology for single input and a single output (SISO) system is proposed. The theoretical background for this approach is based on complex elliptic functions which allow a flexible design of a SISO controller considering that elliptic functions have a double periodicity. The gain and phase margins of the closed-loop system can be selected appropriately with this new loop shaping design procedure. The loop shaping design methodology consists of implementing suitable filters to obtain a desired frequency response of the closed-loop system by selecting appropriate poles and zeros by the Abel theorem that are fundamental in the theory of the elliptic functions. The elliptic function properties are implemented to facilitate the loop shaping controller design along with their fundamental background and contributions from the complex analysis that are very useful in the automatic control field. Finally, apart from the filter design, a PID controller loop shaping synthesis is proposed implementing a similar design procedure as the first part of this study.

scholarly journals Robust LFC Strategy for Wind Integrated Time-Delay Power System Using EID Compensation

Energies ◽  
2019 ◽  
Vol 12 (17) ◽  
pp. 3223 ◽  
Author(s):  
Liu ◽  
Zhang ◽  
Zou
Keyword(s):  
Time Delay ◽  
Power System ◽  
Closed Loop ◽  
Frequency Control ◽  
Loop System ◽  
Load Frequency Control ◽  
System Stability ◽  
Linear Matrix ◽  
Closed Loop System ◽  
The Stability

This paper presents an active disturbance rejection control (ADRC) technique for load frequency control of a wind integrated power system when communication delays are considered. To improve the stability of frequency control, equivalent input disturbances (EID) compensation is used to eliminate the influence of the load variation. In wind integrated power systems, two area controllers are designed to guarantee the stability of the overall closed-loop system. First, a simplified frequency response model of the wind integrated time-delay power system was established. Then the state-space model of the closed-loop system was built by employing state observers. The system stability conditions and controller parameters can be solved by some linear matrix inequalities (LMIs) forms. Finally, the case studies were tested using MATLAB/SIMULINK software and the simulation results show its robustness and effectiveness to maintain power-system stability.

Gain Scheduled Control of Gas Turbine Engines: Stability and Verification

2013 ◽  
Vol 136 (3) ◽  
Author(s):  
Mehrdad Pakmehr ◽  
Nathan Fitzgerald ◽  
Eric M. Feron ◽  
Jeff S. Shamma ◽  
Alireza Behbahani
Keyword(s):  
Convex Optimization ◽  
Gas Turbine ◽  
Closed Loop ◽  
Gas Turbine Engine ◽  
Loop System ◽  
Linear Matrix ◽  
Closed Loop System ◽  
Turbine Engine ◽  
Gain Scheduled Controller ◽  
Gain Scheduled

A stable gain scheduled controller for a gas turbine engine that drives a variable pitch propeller is developed and described. A stability proof is developed for gain scheduled closed-loop system using global linearization and linear matrix inequality (LMI) techniques. Using convex optimization tools, a single quadratic Lyapunov function is computed for multiple linearizations near equilibrium and nonequilibrium points of the nonlinear closed-loop system. This approach guarantees stability of the closed-loop gas turbine engine system. To verify the stability of the closed-loop system on-line, an optimization problem is proposed, which is solvable using convex optimization tools. Simulation results show that the developed gain scheduled controller is capable to regulate a turboshaft engine for large thrust commands in a stable fashion with proper tracking performance.

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