SISO Continuous-System Reduction via Impulse Response Gramian by Iterative Formulae

2005 ◽  
Vol 128 (2) ◽  
pp. 391-393 ◽  
Author(s):  
Younseok Choo ◽  
Dongmin Kim
Keyword(s):  
Impulse Response ◽  
Linear Time ◽  
Order Reduction ◽  
Continuous System ◽  
Original System ◽  
Initial Time ◽  
Continuous Systems ◽  
System Matrix ◽  
Single Input Single Output ◽  
Single Output

This paper concerns the order reduction of single-input single-output (SISO) linear time-invariant continuous systems based on the impulse response Gramian. From the recursive relationship among the Gramians, a new formula is derived for computing the system matrix in controllability canonical form. The result is applied to the model reduction problem. Reduced models obtained approximate the reduced-order Gramians while preserving some initial time moments and Markov parameters of the original system.

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.

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.

Lumped and Distributed Parameter System Identification Via Shifted Legendre Polynomials

1988 ◽  
Vol 110 (4) ◽  
pp. 436-440 ◽  
Author(s):  
B. M. Mohan ◽  
K. B. Datta
Keyword(s):  
Linear Time ◽  
Operational Matrix ◽  
Distributed Parameter ◽  
Parameter System ◽  
Legendre Series ◽  
Single Input Single Output ◽  
Linear Time Invariant ◽  
Single Output ◽  
Single Input ◽  
Time Invariant

In this paper, one shot operational matrix for repeated integration of the shifted Legendre polynomial basis vector is developed and double-shifted Legendre series is introduced to approximate functions of two independent variables. Then using these, systematic algorithms for the identification of linear time-invariant single input-single output continuous lumped and distributed parameter systems are presented. Illustrative examples are provided with satisfactory results.

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.

Adaptive Tracking Control of Linear Uncertain Mechanical Systems Subjected to Unknown Sinusoidal Disturbances

2003 ◽  
Vol 125 (1) ◽  
pp. 129-134 ◽  
Author(s):  
B. Xian ◽  
N. Jalili ◽  
D. M. Dawson and ◽  
Y. Fang
Keyword(s):  
Disturbance Rejection ◽  
Linear Time ◽  
Mechanical Systems ◽  
Control Input ◽  
Unknown Parameters ◽  
Adaptation Algorithm ◽  
Single Input Single Output ◽  
Adaptive Tracking Control ◽  
Linear Time Invariant ◽  
Single Output

The design and implementation of an adaptive disturbance rejection approach is presented for single-input-single-output linear-time-invariant uncertain mechanical systems subject to sinusoidal disturbances with unknown amplitudes and frequencies. The proposed technique suggests construction of a set of stabilizing tuning functions via a state estimate observer in a backstepping fashion to achieve asymptotic disturbance rejection. The tuning functions design is based on a single Lyapunov function incorporating both the error states and update law, 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 both simulations and experiments for a single-degree-of-freedom system with unknown parameters and subject to an unknown sinusoidal disturbance. Significant matching between the simulation and experimental results is observed.

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