Lyapunov-based output-feedback adaptive stabilization of minimum phase second-order systems

2003 ◽  
Author(s):  
H.S. Sane ◽  
D.S. Bernstein ◽  
H.J. Sussmann
Keyword(s):  
Output Feedback ◽  
Second Order ◽  
Minimum Phase ◽  
Adaptive Stabilization ◽  
Second Order Systems

scholarly journals Minimum-Phase Second-Order Systems and the Spectrum of the Semigroup Generator

PAMM ◽  
2006 ◽  
Vol 6 (1) ◽  
pp. 631-632
Author(s):  
Birgit Jacob ◽  
Kirsten Morris ◽  
Carsten Trunk
Keyword(s):  
Second Order ◽  
Minimum Phase ◽  
Second Order Systems ◽  
Semigroup Generator

Placing Minimum Phase Zeros to Shape Transient Response: Generalization From Control of Hybrid Power Systems

2017 ◽  
Author(s):  
Bilal S. Salih ◽  
Tuhin K. Das
Keyword(s):  
Power Systems ◽  
Transient Response ◽  
Transfer Functions ◽  
Higher Order ◽  
Second Order ◽  
Step Response ◽  
Minimum Phase ◽  
Hybrid Power Systems ◽  
Hybrid Power ◽  
Second Order Systems

Conservation of energy can be applied in designing control of hybrid power systems to manage power demand and supply. In practice, it can be used for designing decentralized controllers. In this paper, this idea is analyzed in a generalized theoretical framework. The problem is transformed to that of using minimum phase zeros to generate a specific type of transient response admitted by dynamical systems. Here, the transient step response is shaped using an underlying conservation principle. In this paper, emphasis is placed on second order systems. However, the analysis can be extended to higher order transfer functions. Analytical results relating zero location to the matched/ mismatched areas of the transient response are established for a class of second order systems. A combination of feedback and feedforward actions are shown to achieve the desired zero placement/addition and the desired transient response. The proposed analysis promises extension to nonlinear systems. Optimization studies also seem appropriate, especially for higher order transfer functions.

Adaptive Stabilization of Linear Second-Order Systems with Bounded Time-Varying Coefficients

2004 ◽  
Vol 10 (7) ◽  
pp. 963-978 ◽  
Author(s):  
Alexander V. Roup ◽  
Dennis S. Bernstein
Keyword(s):  
Linear Time ◽  
Adaptive Controller ◽  
Second Order ◽  
Lyapunov Methods ◽  
Time Varying ◽  
Adaptive Stabilization ◽  
Varying Coefficients ◽  
System States ◽  
Time Varying Coefficients ◽  
Second Order Systems

We consider adaptive stabilization for a class of linear time-varying second-order systems. Interpreting the system states as position and velocity, the system is assumed to have unknown, non-paranetric, bounded time-varying damping and stiffness coefficients. The coefficient bounds need not be known to implement the adaptive controller. Lyapunov methods are used to prove global convergence of the system states. For illustration, the controller is used to stabilize several example systems.

Novel control strategy for non-minimum-phase unstable second order systems: generalised predictor based approach

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Anil Bhaskaran ◽  
Chandramohan Goud Ediga ◽  
Seshagiri Rao Ambati
Keyword(s):  
Time Delay ◽  
Direct Synthesis ◽  
Synthesis Method ◽  
Absolute Error ◽  
Second Order ◽  
Delay Systems ◽  
Minimum Phase ◽  
Current Output ◽  
Servo Tracking ◽  
Second Order Systems

Abstract A control structure based on generalized predictor is proposed to control non-minimum phase unstable second order processes with time delay. The scheme contains a predictor structure and a direct synthesis method based primary controller for servo tracking. The predictor structure consists of two filters acting on input and current output which are designed to provide noise attenuation and disturbance rejection. A set-point filter minimises the overshoot caused by the introduction of additional zeros of the controller in the overall closed loop transfer function so as to smooth the tracking performance. Different second order unstable time delay systems are considered and Integral Absolute Error (IAE) and Total Variation (TV) measures are used for comparing the performances quantitatively. The method is implemented experimentally on an inverted pendulum. The proposed predictive strategy is found to provide enhanced control performances in comparison to the existing literature methods.

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