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 Decentralised PI controller design based on dynamic interaction decoupling in the closed-loop behaviour of a flotation process

2021 ◽  
Vol 11 (6) ◽  
pp. 4865
Author(s):  
Nomzamo Tshemese-Mvandaba ◽  
R. Tzoneva ◽  
M. E. S. Mnguni
Keyword(s):  
Closed Loop ◽  
Controller Design ◽  
Design Procedure ◽  
Loop System ◽  
Closed Loop System ◽  
Flotation Process ◽  
Loop Control ◽  
Decoupling Method ◽  
Pi Controllers ◽  
Interconnected Model

An enhanced method for design of decenralised proportional integral (PI) controllers to control various variables of flotation columns is proposed. These columns are multivariable processes characterised by multiple interacting manipulated and controlled variables. The control of more than one variable is not an easy problem to solve as a change in a specific manipulated variable affects more than one controlled variable. Paper proposes an improved method for design of decentralized PI controllers through the introduction of decoupling of the interconnected model of the process. Decoupling the system model has proven to be an effective strategy to reduce the influence of the interactions in the closed-loop control and consistently to keep the system stable. The mathematical derivations and the algorithm of the design procedure are described in detail. The behaviour and performance of the closed-loop systems without and with the application of the decoupling method was investigated and compared through simulations in MATLAB/Simulink. The results show that the decouplers - based closed-loop system has better performance than the closed-loop system without decouplers. The highest improvement (2 to 50 times) is in the steady-state error and 1.2 to 7 times in the settling and rising time. Controllers can easily be implemented.

Passivity-Based Stabilization of Underactuated Mechanical Systems

2013 ◽  
Vol 421 ◽  
pp. 16-22
Author(s):  
Shan Shan Wu ◽  
Wei Huo
Keyword(s):  
Closed Loop ◽  
Control Method ◽  
Controller Design ◽  
Design Method ◽  
Mechanical Systems ◽  
Matching Condition ◽  
Loop System ◽  
Closed Loop System ◽  
Underactuated Mechanical Systems ◽  
Stabilization Control

A new stabilization control method for underactuated linear mechanical systems is presented in this paper. By proper setting the desired closed-loop system, the matching condition for controller design is reduced to one equation and an adjustable parameter (damping coefficient) is introduced to the controller. Stability of the closed-loop system is proved based on passivity. As an application example, stabilization control of 2-DOF Pendubot is studied. The system is linearized at its equilibrium point and the proposed controller design method is applied to the linearized system. The procedure of solving matching condition and design controller for the Pendubot is provided. The simulation results verify feasibility of the proposed method.

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.

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 A proportional controller based on clustering theory: an academic example of a machine learning discipline

2018 ◽  
Vol 210 ◽  
pp. 02005
Author(s):  
Leonardo Acho ◽  
Pablo Buenestado
Keyword(s):  
Machine Learning ◽  
Closed Loop ◽  
Controller Design ◽  
Loop System ◽  
Slew Rate ◽  
Closed Loop System ◽  
Real Experiment ◽  
Proportional Controller ◽  
Rate Limit

The main objective of this paper is to present a controller design based on the K-means clustering theory. The controller is realized in such way that when the plant output is located outside of the designed clustering set, the controller forces it to be in it. Moreover, and according to our real experiment applied to stabilize an unstable integrator plant, our controller approach design is also robust against un-vanishing perturbations and nonlinearity effects on the overall closed-loop system such as saturation, slew-rate limit, and limit bandwidth frequency operation.

H∞ CONTROL DESIGN OF A MULTITANK SYSTEM

2020 ◽  
Vol 70 (3) ◽  
pp. 26-33
Author(s):  
Andrey Yonchev ◽  
Martin Mladenov
Keyword(s):  
Mathematical Model ◽  
Modeling And Simulation ◽  
Closed Loop ◽  
Controller Design ◽  
Control Design ◽  
Loop System ◽  
Optimal Controller ◽  
Closed Loop System ◽  
Pump Operation ◽  
Physical Plant

This paper considers MATLAB® modeling and simulation of H∞ controller and its realization on the Multitank System. The first task is to study the physical plant of the laboratory Multitank System and to apply a given mathematical model for optimal controller design. The general objective of the derived regulator is to reach and stabilize the level in the tanks by an adjustment of the pump operation or/and valves settings. Finally, it is necessary to simulate the obtained closed-loop system and to test its workability.

Two-degree-of-freedom compensator design for disturbance attenuation problem via higher order sinusoidal input describing functions theory

2019 ◽  
pp. 014233121988037
Author(s):  
Bilal Erol ◽  
Muhammed Ali Oz ◽  
Levent Ucun
Keyword(s):  
Closed Loop ◽  
Controller Design ◽  
Higher Order ◽  
Loop System ◽  
Disturbance Attenuation ◽  
Closed Loop System ◽  
Describing Functions ◽  
Sinusoidal Input ◽  
Bounded Uncertainties ◽  
Norm Bounded Uncertainties

In order to deal with disturbance attenuation problem in the presence of norm bounded uncertainties, different techniques involving [Formula: see text]/[Formula: see text] and linear quadratic regulator (LQR) designs exist in literature. The major drawbacks of these approaches may be classified as obtaining controllers with high order terms and too much computational load during the controller design. Hence, two-degree-of freedeom (2-DOF) controller design is taken into consideration in this study in order to avoid some of these drawbacks in the controller design and implementation process for disturbance attenuation problem. Here, the procedure for the design of 2-DOF structure is divided into two parts: designing [Formula: see text] controller to stabilize the closed loop system and implementing a higher order sinusoidal input describing functions (HOSIDF)-based compensator as a secondary controller in order to increase the disturbance attenuation performance of the overall closed loop system where the norm bounded uncertainties already exist. Thanks to the Lur’e type system definition that is also used in the design process of HOSIDF compensator, the research also proves that the proposed 2-DOF design structure is suitable to be implemented into the systems involving nonlinearities such as actuator saturation.

Design of Compensators for Actuator Saturation

1995 ◽  
Vol 209 (3) ◽  
pp. 157-164 ◽  
Author(s):  
C W Chan ◽  
K Hui
Keyword(s):  
Control Problem ◽  
Closed Loop ◽  
Actuator Saturation ◽  
Design Procedure ◽  
Loop System ◽  
Linear Control ◽  
Closed Loop System ◽  
Set Point ◽  
Non Linear ◽  
Linear Disturbance

Actuator saturation is a common non-linear control problem; if it is not being compensated properly, the system can become unstable. When the actuator saturates, the control that cannot be implemented can be interpreted as a non-linear disturbance being injected into the closed-loop system. After transformation, the applied set-point is altered by the disturbance, giving the effective set-point. If the effective instead of the applied set-point is used to calculate the control, no actuator saturation occurs. Since the effective set-point always replaces the applied set-point whenever the actuator saturates, a compensator can be designed aiming to produce a more acceptable effective set-point. The conditions for its implementation are given, followed by the properties of the effective set-point. A procedure for selecting the parameter of the compensator is also described. Examples are presented to illustrate the design procedure and to compare the performance of the proposed and the existing compensators.

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