From fractional-order to complex-order integrator loop gain: Robust control design and its stability analysis

2019 ◽  
Vol 41 (13) ◽  
pp. 3799-3807
Author(s):  
Mohammad Reza Rahmani ◽  
Ali Akbar Jalali
Keyword(s):  
Control System ◽  
Stability Analysis ◽  
Robust Control ◽  
Fractional Order ◽  
Design Procedure ◽  
Loop Control ◽  
Complex Order ◽  
Phase Slope ◽  
Nyquist Stability ◽  
Robust Control Design

Complex-order differintegral (COD) is the extended version of fractional-order one in which the differintegral order can be a complex number rather than a real number. In comparison with fractional-order differintegral (FOD), the distinguishing feature of the COD is that the phase slope of its Bode diagram is a function of imaginary part of the complex order of the COD. In this paper, by the use of this property of the COD, a robust control system is proposed. The design procedure and the realization of the proposed COD-based closed-loop control system are discussed. Since the phase of COD’s frequency response is a nonsymmetric function of frequency, stability analysis of the proposed control system is considered a problematic task. It is proven that for the stability of the control system, it is essential that the COD be applied in a limited frequency band that is derived by the use of the Nyquist stability criterion. Finally, some numerical examples are given to demonstrate the validity and superiority of the proposed complex-order control system.

scholarly journals The Effects of Weighting Functions on the Performances of Robust Control Systems

Proceedings ◽  
2020 ◽  
Vol 63 (1) ◽  
pp. 46
Author(s):  
Mircea Dulau ◽  
Stelian-Emilian Oltean
Keyword(s):  
Robust Control ◽  
Control Systems ◽  
Tracking Error ◽  
Weighting Functions ◽  
Loop Control ◽  
Frequency Sensitivity ◽  
Sensitivity Functions ◽  
Loop Control System ◽  
Robust Control Design ◽  
Robust Control Systems

An important stage in robust control design is to define the desired performances of the closed loop control system using the models of the frequency sensitivity functions S. If the frequency sensitivity functions remain within the limits imposed by these models, the control performances are met. In terms of the sensitivity functions, the specifications include: shape of S over selected frequency ranges, peak magnitude of S, bandwidth frequency, and tracking error at selected frequencies. In this context, this paper presents a study of the effects of the specifications of the weighting functions on the performances of robust control systems.

Adaptive synchronization of uncertain fractional-order chaotic systems using sliding mode control techniques

2019 ◽  
Vol 234 (1) ◽  
pp. 3-9 ◽  
Author(s):  
Bahram Yaghooti ◽  
Ali Siahi Shadbad ◽  
Kaveh Safavi ◽  
Hassan Salarieh
Keyword(s):  
Control System ◽  
Sliding Mode Control ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Closed Loop ◽  
Sliding Mode ◽  
Closed Loop Control ◽  
Loop Control ◽  
Closed Loop Control System ◽  
Loop Control System

In this article, an adaptive nonlinear controller is designed to synchronize two uncertain fractional-order chaotic systems using fractional-order sliding mode control. The controller structure and adaptation laws are chosen such that asymptotic stability of the closed-loop control system is guaranteed. The adaptation laws are being calculated from a proper sliding surface using the Lyapunov stability theory. This method guarantees the closed-loop control system robustness against the system uncertainties and external disturbances. Eventually, the presented method is used to synchronize two fractional-order gyro and Duffing systems, and the numerical simulation results demonstrate the effectiveness of this method.

Robust Optimal Control of MAV Based on Linear-Time Varying Decoupled Model Dynamics

2013 ◽  
Vol 198 ◽  
pp. 571-576 ◽  
Author(s):  
Arkadiusz Mystkowski
Keyword(s):  
Robust Control ◽  
Linear Time ◽  
Design Procedure ◽  
Serial Connection ◽  
Air Vehicle ◽  
Model Dynamics ◽  
Aerial Vehicle ◽  
Robust Control Design ◽  
Control Feedback ◽  
Nonlinear Robust

This paper discusses a nonlinear robust control design procedure to micro air vehicle that uses the singular value (μ) and μ-synthesis technique. The optimal robust control law that combines a linear parameters varying (LPV) of UAV (unmanned aerial vehicle) are realized by using serial connection of the Kestrel autopilot and the Gumstix microprocessor. Thus, the robust control feedback loops, which handle the uncertainty of aerodynamics derivatives, are used to ensure robustness stability of the UAV local dynamics in longitudinal and lateral control directions.

A NEW ROBUST CONTROL DESIGN PROCEDURE BASED ON A PE IDENTIFICATION UNCERTAINTY SET

2002 ◽  
Vol 35 (1) ◽  
pp. 145-150 ◽  
Author(s):  
X. Bombois ◽  
G. Scorletti ◽  
B.D.O. Anderson ◽  
M. Gevers ◽  
P. Van den Hof
Keyword(s):  
Robust Control ◽  
Design Procedure ◽  
Control Design ◽  
Uncertainty Set ◽  
Robust Control Design

scholarly journals Robust control strategy for improving the performance of a soft robotic link

2021 ◽  
pp. 499-506
Author(s):  
Luis Nagua ◽  
Jorge Muñoz ◽  
Lisbeth Mena ◽  
Concepcion A. Monje ◽  
Carlos Balaguer
Keyword(s):  
Control System ◽  
Robust Control ◽  
Fractional Order ◽  
Control Strategy ◽  
Parallel Mechanism ◽  
Pi Controller ◽  
Main Element ◽  
Flexion Extension ◽  
Robust Control System ◽  
Fractional Order Pi Controller

The robotic neck mechanism considered in this paper has as main element a soft link that emulates a human neck with two DOF (flexion, extension and lateral bending). The mechanism is based on a Cable-Driven Parallel Mechanism (CDPM) with components easy to manufacture in a 3D printer.Due to the soft link properties and the platform mechanics, it is important to provide a robust control system. Two designs, a robust PID controller and a Fractional Order PI controller (FOPI) are proposed and compared, the fractional order control showing an enhanced performance. Both control approaches are tested in the real prototype, validating the soft neck feasibility and showing the robustness of the platform to mass changes at the neck tip.

Fractional Order Differentiation and Robust Control Design

2015 ◽  
Author(s):  
Jocelyn Sabatier ◽  
Patrick Lanusse ◽  
Pierre Melchior ◽  
Alain Oustaloup
Keyword(s):  
Robust Control ◽  
Fractional Order ◽  
Control Design ◽  
Robust Control Design

scholarly journals Robust Control Design for an Uncertain Macroeconomic Dynamical System with Unknown Characteristics and Inequality Control Constraint

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Xiaorui Xie ◽  
Ye-Hwa Chen
Keyword(s):  
Dynamical System ◽  
Robust Control ◽  
Design Procedure ◽  
Control Design ◽  
Uniform Boundedness ◽  
Salient Feature ◽  
Uncertain System ◽  
Stabilization Policy ◽  
Bounded Controls ◽  
Robust Control Design

The stabilization problem of a macroeconomic dynamical system is considered in this paper. The main features of this system are that the system uncertainties may be unknown functions of state and time but with known bounds. Furthermore, the control inputs are subject to constraints, which is a salient feature in an economic control problem. To ensure that the controls are within the specified boundaries, in our control design procedure, a creative diffeomorphism, which converts bounded controls into unbounded corresponding signals by choosing an appropriate transformation function, is proposed. For the uncertain system, a deterministic robust control is designed to render the practical stability: uniform boundedness and uniform ultimate boundedness. The range of the input bounds is related to the uncertainties and can be designed according to the actual situation. Numerical simulations are performed to verify the effectiveness of the stabilization policy.

scholarly journals PEMODELAN SISTEM DAN ANALISIS KESTABILAN DINAMIK PESAWAT UAV (MODELING SYSTEM AND DYNAMIC STABILITY ANALYSIS OF UAV)

2012 ◽  
Vol 10 (1) ◽  
Author(s):  
Eko Budi Purwanto
Keyword(s):  
Control System ◽  
Stability Analysis ◽  
Robust Control ◽  
Oscillation Mode ◽  
Dynamic Modelling ◽  
Dynamic Parameter ◽  
Aerial Photographs ◽  
Steady State Condition ◽  
Design And Implementation ◽  
Test And Evaluation

Mission of Unmanned Aerial Vehicle (UAV) “Elang Avionik” is surveillance and aerial photographs. Therefore the flight of UAV must be stable and controlable, and first step activity is dynamic modelling and stability analisys. The problems of UAV system is disturbance, noise of sensor, MIMO and uncertainty dynamic model. For good result using the multivariable robust control, with some step research that is: (1)modeling and stability analysis, (2) design and implementation of PID control system, (3) flight dynamic parameter identification, (4) design and implementation of hardware in the loop simulation, (5) design and implementation of multivariable robust control, (6) test and evaluation of system. Simulation result show that the eigen value in longitudinal is: phugoid mode = –0,061293±0,40526i and non-oscillation mode = –6,1121±4,9253. In lateral directional is:dutch roll mode = –0,91089±5,7994i, spiral mode= –0,036563, and roll subsidence mode = –12,7181. Location of poles system on the left of imaginary axis, the means that the character of system is dynamic stable. But settling time to steady state condition is very long and improved by control system design. Key word: State space, Longitudinal, Lateral, Stable static, Stable dynamic

Lyapunov Direct Design of Robust Control for Electrical-Mechanical Systems Composed of Cascaded Nonlinear Uncertain Subsystems

1995 ◽  
Vol 117 (1) ◽  
pp. 54-62 ◽  
Author(s):  
Zhihua Qu ◽  
Darren M. Dawson
Keyword(s):  
Robust Control ◽  
Uncertain Systems ◽  
Mechanical Systems ◽  
Design Procedure ◽  
Robust Controllers ◽  
Global Exponential Convergence ◽  
Direct Design ◽  
Uniform Ultimate Boundedness ◽  
Robust Control Design ◽  
The Individual

Robust control design of nonlinear uncertain systems is investigated. A system under consideration consists of finite nonlinear systems which are cascaded and have significant uncertainties. Such a system arises naturally from many real physical systems, especially mechanical systems. An important feature of these systems is that they do not satisfy the assumption of the standard matching conditions required by most existing robust control results. General classes of cascaded uncertain systems are identified for which robust controllers are obtained explicitly in terms of the bounding functions of the uncertainties. The resulting robust controllers guarantee stability of global uniform ultimate boundedness or global exponential convergence to zero. The controls are designed by a two-step systematic design procedure. First, design fictitious robust controllers for input of individual subsystem as if every subsystem had an independent control. Then, a recursive mapping is proposed which maps the individual fictitious controls recursively into the only control of the overall system.

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