Improving Stability Margins via Time Delay Control

2013 ◽  
Author(s):  
A. Galip Ulsoy
Keyword(s):  
Time Delay ◽  
Time Delays ◽  
Linear Time ◽  
Mechanical Vibration ◽  
Stability Margins ◽  
Single Input Single Output ◽  
Time Delay Control ◽  
Linear Time Invariant ◽  
Single Output ◽  
Delay Control

While time delays typically lead to poor control performance, and even instability, previous research has shown that introduction of time delays in controlling a dynamic system can, in some cases, be beneficial. This paper presents a new benefit of time delay control for single-input single-output linear time invariant systems: it can be used to improve robustness, as measured by increased stability margins. The proposed method utilizes time delays to approximate state-derivative feedback, which can be used, together with state feedback, to reduce sensitivity and improve robustness. Additional sensors are not required since the state-derivatives are approximated using available measurements and time delays. The method is introduced using a scalar example, then applied to a single degree-of-freedom mechanical vibration control problem in simulations to demonstrate excellent performance with improved stability margins.

Stability of Uncertain Linear Systems With Time Delay

1991 ◽  
Vol 113 (4) ◽  
pp. 558-567 ◽  
Author(s):  
K. Youcef-Toumi ◽  
J. Bobbett
Keyword(s):  
Time Delay ◽  
Linear Time ◽  
Sufficient Condition ◽  
Single Input Single Output ◽  
Time Delay Control ◽  
Linear Time Invariant ◽  
Single Output ◽  
Uncertain Dynamics ◽  
Delay Control ◽  
The Stability

The control of systems with uncertain dynamics and unpredictable disturbances has raised some challenging problems. This is particularly important when high system performance is to be guaranteed at all times. Recently, Time Delay Control has been suggested as an alternative control scheme. The proposed control system does not require an explicit plant model nor does it depend on the estimation of specific plant parameters. Rather, it combines adaptation with past observations to directly estimate the effect of the plant dynamics. This paper outlines the Time Delay Control law for a class of linear dynamic systems and then presents a sufficient condition for stability of linear uncertain systems with time delay. The ideas of Nyquist and Kharitonov are used in the development of a sufficient condition, which does not resort to using approximations for time delay. Like Nyquist, the condition depends on maps of the Nyquist path and, like Kharitonov, stability depends on four functions each yielding a stable system. In this paper we combine these ideas to determine the stability of systems where the Time Delay Controller is applied to single input single output, linear time-invariant plants whose coefficients are known to vary within certain defined intervals. The development is carried out in the context of Time Delay Control but it can be applied in more general cases. Two examples will illustrate the approach and the usefulness of the technique.

Time-Delayed Control of SISO Systems for Improved Stability Margins

2014 ◽  
Vol 137 (4) ◽  
Author(s):  
A. Galip Ulsoy
Keyword(s):  
Time Delays ◽  
Linear Time ◽  
Stability Margins ◽  
Single Input Single Output ◽  
Linear Time Invariant ◽  
Single Output ◽  
Improved Stability ◽  
Single Input ◽  
Delay Differential ◽  
Time Invariant

While time delays typically lead to poor control performance, and even instability, previous research shows that time delays can, in some cases, be beneficial. This paper presents a new benefit of time-delayed control (TDC) for single-input single-output (SISO) linear time invariant (LTI) systems: it can be used to improve robustness. Time delays can be used to approximate state derivative feedback (SSD), which together with state feedback (SF) can reduce sensitivity and improve stability margins. Additional sensors are not required since the state derivatives are approximated using available measurements and time delays. A systematic design approach, based on solution of delay differential equations (DDEs) using the Lambert W method, is presented using a scalar example. The method is then applied to both single- and two-degree of freedom (DOF) mechanical systems. The simulation results demonstrate excellent performance with improved stability margins.

Complementary Sensitivity Design of PID Controllers for Arbitrary-Order Transfer Functions With Time Delay

2008 ◽  
Author(s):  
Tooran Emami ◽  
John M. Watkins
Keyword(s):  
Time Delay ◽  
Transfer Functions ◽  
Linear Time ◽  
Order System ◽  
Pid Controllers ◽  
Single Input Single Output ◽  
Linear Time Invariant ◽  
Single Output ◽  
Plant Transfer ◽  
Time Invariant

A graphical technique for finding all proportional integral derivative (PID) controllers that stabilize a given single-input-single-output (SISO) linear time-invariant (LTI) system of any order system with time delay has been solved. In this paper a method is introduced that finds all PID controllers that also satisfy an H∞ complementary sensitivity constraint. This problem can be solved by finding all PID controllers that simultaneously stabilize the closed-loop characteristic polynomial and satisfy constraints defined by a set of related complex polynomials. A key advantage of this procedure is the fact that it does not require the plant transfer function, only its frequency response.

A Time Delay Controller for Systems With Unknown Dynamics

1990 ◽  
Vol 112 (1) ◽  
pp. 133-142 ◽  
Author(s):  
Kamal Youcef-Toumi ◽  
Osamu Ito
Keyword(s):  
Time Delay ◽  
Control Method ◽  
Linear Time ◽  
Structure Stability ◽  
State Variables ◽  
Single Input Single Output ◽  
Linear Time Invariant ◽  
Single Output ◽  
Single Input ◽  
Time Invariant

This paper focuses on the control of systems with unknown dynamics and deals with the class of systems described by x˙=f(x,t) + h(x,t) + B(x,t)u + d(t) where h(x,t) and d(t) are unknown dynamics and unexpected disturbances, respectively. A new control method, Time Delay Control (TDC), is proposed for such systems. Under the assumption of accessibility to all the state variables and estimates of their delayed derivatives, the TDC is characterized by a simple estimation technique that evaluates a function representing the effect of uncertainties. This is accomplished using time delay. The control system’s structure, stability and design issues are discussed for linear time-invariant and single-input-single-output systems. Finally, the control performance was evaluated through both simulations and experiments. The theoretical and experimental results indicate that this control method shows excellent robustness properties to unknown dynamics and disturbances.

Geometrical design of fractional PDμ controllers for linear time-invariant fractional-order systems with time delay

2019 ◽  
Vol 233 (7) ◽  
pp. 815-829
Author(s):  
Adrián Josué Guel-Cortez ◽  
César-Fernando Méndez-Barrios ◽  
Emilio Jorge González-Galván ◽  
Gilberto Mejía-Rodríguez ◽  
Liliana Félix
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Linear Time ◽  
Simple Procedure ◽  
Geometric Approach ◽  
Fractional Order Systems ◽  
Single Input Single Output ◽  
Linear Time Invariant ◽  
Single Output ◽  
Time Invariant

This article presents a simple procedure that allows a practical design of fractional –[Formula: see text] controllers for single-input single-output linear time-invariant fractional-order systems subject to a constant time delay. The methodology is based on a geometric approach, which provides practical guidelines to design stabilizing and non-fragile PDμ controllers. The simplicity of the proposed approach is illustrated by considering several numerical examples encountered in the control literature. Moreover, with the aim of showing the performance of the PDμ over a classical PD controller, both controllers were implemented at the end of the article in an experimental test-bench consisting a teleoperated robotic system.

Optimal Nonlinear Estimation of Linear Stochastic Systems: The Multivariable Extension

1996 ◽  
Vol 118 (2) ◽  
pp. 350-353 ◽  
Author(s):  
M. A. Hopkins ◽  
H. F. VanLandingham
Keyword(s):  
Stochastic Systems ◽  
Transfer Functions ◽  
Mimo Systems ◽  
Linear Time ◽  
Nonlinear Method ◽  
Single Input Single Output ◽  
Linear Time Invariant ◽  
Single Output ◽  
Time Invariant ◽  
Time Systems

This paper extends to multi-input multi-output (MIMO) systems a nonlinear method of simultaneous parameter and state estimation that appeared in the ASME JDSM&C (September, 1994), for single-input single-output (SISO) systems. The method is called pseudo-linear identification (PLID), and applies to stochastic linear time-invariant discrete-time systems. No assumptions are required about pole or zero locations; nor about relative degree, except that the system transfer functions must be strictly proper. In the earlier paper, proofs of optimality and convergence were given. Extensions of those proofs to the MIMO case are also given here.

Design and Realtime Implementation of an Adaptive Variation Absorber for Uncertain Mechanical Systems Subjected to Unknown Disturbances

2004 ◽  
Vol 10 (1) ◽  
pp. 55-84
Author(s):  
Raffi Derkhorenian ◽  
Nader Jalili ◽  
D M Dawson
Keyword(s):  
Degrees Of Freedom ◽  
Controller Design ◽  
Linear Time ◽  
Vibration Absorber ◽  
Primary System ◽  
Control Input ◽  
Adaptation Algorithm ◽  
Single Input Single Output ◽  
Linear Time Invariant ◽  
Single Output

In this paper we describe the design and implementation of a nonlinear adaptive disturbance rejection approach for single-input-single-output linear-time-invariant uncertain systems subject to sinusoidal disturbances with unknown amplitude and frequency. This is an extension of our earlier study to a more complicated plant, a two-degrees-of-freedom (2DOF) system representing a vibration absorber setting. The controller design is based on a single Lyapunov function incorporating both the error states and the update laws and, hence, global stability and improved transient performance are readily achieved. Utilizing only the system output, a virtual control input is used in place of non-measurable and unknown signals. The performance of the adaptation algorithm is demonstrated through real-time simulations, both for regulation and tracking, on a 2DOF system representing an active vibration absorber setup. It is shown that when the primary system is subjected to an unknown sinusoidal disturbance, the proposed controller in the absorber subsection completely suppresses the primary system vibration in the presence of unknown disturbance.

Nonlinear PI Compensators That Achieve High Performance

1997 ◽  
Vol 119 (1) ◽  
pp. 105-110 ◽  
Author(s):  
S. M. Shahruz ◽  
A. L. Schwartz
Keyword(s):  
High Performance ◽  
Optimization Problem ◽  
Linear Time ◽  
Feedback System ◽  
Single Input Single Output ◽  
Linear Time Invariant ◽  
Single Output ◽  
Single Input ◽  
Nonlinear Compensator ◽  
Time Invariant

In this paper, linear time-invariant single-input single-output (SISO) systems that are stabilizable by a (linear) proportional and integral (PI) compensator are considered. For such systems a five-parameter nonlinear PI compensator is proposed. The parameters of the proposed compensator are tuned by solving an optimization problem. The optimization problem always has a solution. Additionally, a general non-linear PI compensator is proposed and is approximated by easy-to-compute compensators, for instance, a six-parameter nonlinear compensator. The parameters of the approximate compensators are tuned to satisfy an optimality condition. The superiority of the proposed nonlinear PI compensators over the linear PI compensator is discussed and is demonstrated for a feedback system.

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