Robust Disturbance Rejection for a Class of Nonlinear Systems Using Disturbance Observers

2013 ◽  
Author(s):  
Ahmed H. El-Shaer ◽  
Abdulrahman H. Bajodah
Keyword(s):  
Nonlinear Systems ◽  
Disturbance Rejection ◽  
Disturbance Observer ◽  
Closed Loop ◽  
Inverted Pendulum ◽  
Single Input Single Output ◽  
Luenberger Observer ◽  
Single Output ◽  
Single Input ◽  
Bounded Disturbance

This paper is concerned with disturbance rejection performance in single-input single-output (SISO) nonlinear systems that are described by uncertain linear dynamics and bounded nonlinearities. First, the nonlinear terms are transformed into an equivalent bounded disturbance at the output of a linear system. Then, a disturbance observer (DOB) is added to the closed loop to achieve robust disturbance rejection. The DOB design is formulated as an extended Luenberger observer having internal dynamics with at least an eigenvalue at the origin. The synthesis of a (sub)optimal DOB is carried out by solving multi-objective H∞ sensitivity optimization. The design approach is applied to an inverted pendulum with actuator backlash. Closed loop response shows that tracking performance is indeed greatly enhanced with the DOB.

STABILITY OF SISO NONLINEAR SYSTEMS WITH PARAMETERS DISTURBANCES

2012 ◽  
Vol 26 (25) ◽  
pp. 1246008
Author(s):  
OLGA SHPILEVAYA
Keyword(s):  
Nonlinear Systems ◽  
System Dynamics ◽  
Control Systems ◽  
Lyapunov Method ◽  
Switched System ◽  
System Stability ◽  
Single Input Single Output ◽  
Single Output ◽  
System Output ◽  
Single Input

We study single-input single-output (SISO) control systems with the rapid piecewise-smooth parameters disturbances. The system dynamics are described by switched system models. The system output is regulated with the help of the nonlinear astatic controller with parameters which depend on some disturbance properties. The system stability is studied by second Lyapunov method.

Optimal Decoupled Disturbance Observers for Dual-Input Single-Output Systems

2014 ◽  
Vol 136 (5) ◽  
Author(s):  
Xu Chen ◽  
Masayoshi Tomizuka
Keyword(s):  
Disturbance Observer ◽  
Filter Design ◽  
Spectral Characteristics ◽  
Hard Disk Drives ◽  
Disk Drives ◽  
Single Input Single Output ◽  
Control Approach ◽  
Single Output ◽  
Dual Stage ◽  
Single Input

The disturbance observer (DOB) has been a popular robust control approach for servo enhancement in single-input single-output systems. This paper presents a new extension of the DOB idea to dual- and multi-input single-output systems, and discusses an optimal filter design technique for the related loop-shaping. The proposed decoupled disturbance observer (DDOB) provides the flexibility to use the most suitable actuators for compensating disturbances with different spectral characteristics. Such a generalization is helpful, e.g., for modern dual-stage hard disk drives, where enhanced servo design is becoming more and more essential in the presence of vibration disturbances.

A New Approach on Stabilization Control of an Inverted Pendulum, Using PID Controller

2011 ◽  
Vol 403-408 ◽  
pp. 4674-4680 ◽  
Author(s):  
Kaveh Razzaghi ◽  
Ali Akbar Jalali
Keyword(s):  
Inverted Pendulum ◽  
System Analysis ◽  
Single Input Single Output ◽  
Stabilization Control ◽  
Single Output ◽  
Standard Problem ◽  
Angle Of Deviation ◽  
Output System ◽  
Single Input ◽  
Two Parameters

Inverted Pendulum is a standard problem in control systems and is appropriate for depicting linear control principles. In this system there is an inverted pendulum connected to a cart that moves along a horizontal track with the help of a motor. We can determine the cart’s position and velocity from the motor and the rail track limits the cart’s movement in a bidirectional path. The pendulum’s angle of deviation and the position of the cart are determined by two sensors mounted on the system. Essential measurements and motor control signals are generated by a medium control board linking the computer and the system. Analysis of the results and yielding the control commands are done with the help of a MATLAB program. This is indeed a single input- dual output system because we must be able to control two parameters (pendulum’s angle and cart’s position) with just one control signal to the motor. Since the PID (Proportional Integral Derivative) controller is usually proper for SISO (Single Input Single Output) systems, we are eager to propose a procedure to control one of these parameters underneath the other. In this paper two tactics are described: 1. controlling the cart’s position beneath the pendulum’s angle, and 2. controlling the pendulum’s angle beneath the cart’s position. Regarding the results, one method is proven to be superior. We also mention some practical considerations in this paper.

Analytic Loop Shaping Methods in Quantitative Feedback Theory

1994 ◽  
Vol 116 (2) ◽  
pp. 169-177 ◽  
Author(s):  
D. F. Thompson ◽  
O. D. I. Nwokah
Keyword(s):  
Uncertain Systems ◽  
Closed Loop ◽  
Design Method ◽  
Control Design ◽  
Quantitative Feedback Theory ◽  
Single Input Single Output ◽  
Single Output ◽  
Direct Design ◽  
Single Input ◽  
Robust Control Design

Quantitative Feedback Theory (QFT), a robust control design method introduced by Horowitz, has been shown to be useful in many cases of multi-input, multi-output (MIMO) parametrically uncertain systems. Prominent is the capability for direct design to closed-loop frequency response specifications. In this paper, the theory and development of optimization-based algorithms for design of minimum-gain controllers is presented, including an illustrative example. Since MIMO QFT design is reduced to a series of equivalent single-input, single-output (SISO) designs, the emphasis is on the SISO case.

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