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.

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.

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.

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.

OPTIMAL ADAPTIVE PREDICTION FOR SISO SYSTEMS

2009 ◽  
Vol 18 (05) ◽  
pp. 993-1003
Author(s):  
BEHNAM SHAHRRAVA
Keyword(s):  
Linear Time ◽  
Minimum Mean Square Error ◽  
Parameter Estimates ◽  
Single Input Single Output ◽  
Linear Time Invariant ◽  
Single Output ◽  
Noise Perturbation ◽  
Single Input ◽  
Time Invariant ◽  
Time Systems

An adaptive predictor that is optimal in the minimum mean-square error (MMSE) sense at each step is obtained for single-input, single-output (SISO) linear time-invariant discrete-time systems having general delay and white noise perturbation. The adaptive d-step-ahead predictor includes the uncertainty associated with the parameter and state estimates whereas conventional adaptive predictors, that are asymptotically optimal, ignore the uncertainty in the parameter estimates.

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.

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