A Linear Feedback Control Framework for Optimally Locating Passive Vibration Isolators With Known Stiffness and Damping Parameters

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
Jihyun Lee ◽  
Amir H. Ghasemi ◽  
Chinedum E. Okwudire ◽  
Jeffrey Scruggs
Keyword(s):  
Feedback Control ◽  
Transfer Functions ◽  
Linear Time ◽  
Optimal Placement ◽  
Linear Feedback ◽  
Feedback Gain ◽  
Placement Problem ◽  
Vibration Isolators ◽  
Linear Time Invariant ◽  
Stiffness And Damping

This paper investigates the problem of optimally locating passive vibration isolators to minimize unwanted vibration caused by exogenous disturbance forces. The stiffness and damping parameters of the isolators are assumed to be known, leaving the isolator locations, which are nonlinearly related to system states, as unknown optimization variables. An approach for reformulating the nonlinear isolator placement problem as a linear time-invariant (LTI) feedback control problem, by linking fictitious control forces to fictitious measured outputs using a nonzero feedforward term, is proposed. Accordingly, the isolator locations show up within a static output feedback gain matrix which can be optimized, using methods from optimal control theory, to minimize the H2 and/or H∞ norms of transfer functions representing unwanted vibration. The proposed framework also allows well-established LTI control theories to be applied to the analyses of the optimal isolator placement problem and its results. The merits of the proposed approach are demonstrated using single and multivariable case studies related to isolator placement in precision manufacturing machines. However, the framework is applicable to optimal placement of passive isolators, suspensions, or dampers in automotive, aerospace, civil, and other applications.

A Control Theoretic Framework for Optimally Locating Passive Vibration Isolators to Minimize Residual Vibration

2015 ◽  
Author(s):  
Amir H. Ghasemi ◽  
Jihyun Lee ◽  
Chinedum E. Okwudire
Keyword(s):  
Feedback Gain ◽  
Residual Vibration ◽  
Placement Problem ◽  
Vibration Isolators ◽  
Design Variables ◽  
Exogenous Disturbance ◽  
Ultra Precision ◽  
System States ◽  
Control Forces ◽  
Stiffness And Damping

This paper investigates the problem of optimally locating passive vibration isolators to minimize residual vibration caused by exogenous disturbance forces. The stiffness and damping properties of the isolators are assumed to be known and the task is to determine the isolator locations, which are nonlinearly related to system states. This paper proposes an approach for reformulating the nonlinear isolator placement problem as a LTI control problem by linking the control forces to measured outputs using a feedforward term. Accordingly, the isolator locations show up as a static output feedback gain matrix which is optimized for residual vibration reduction using standard H∞ optimal control methods. Simulations and experiments on SISO and MIMO case studies are used to demonstrate the merits of the proposed approach. Even though presented in the specific context of ultra-precision manufacturing machines, the proposed method is applicable to the optimal design of other passive systems with nonlinear relationships between design variables and system states.

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.

Parameter Uncertainty Modeling Using the Multidimensional Principal Curves

2010 ◽  
Vol 132 (5) ◽  
Author(s):  
M. Sepasi ◽  
F. Sassani ◽  
R. Nagamune
Keyword(s):  
Transfer Functions ◽  
Linear Time ◽  
Optimization Technique ◽  
Parametric Uncertainty ◽  
Uncertainty Modeling ◽  
Principal Component ◽  
Linear Matrix ◽  
Linear Time Invariant ◽  
Uncertain Variables ◽  
Uncertainty Model

This paper proposes a technique to model uncertainties associated with linear time-invariant systems. It is assumed that the uncertainties are only due to parametric variations caused by independent uncertain variables. By assuming that a set of a finite number of rational transfer functions of a fixed order is given, as well as the number of independent uncertain variables that affect the parametric uncertainties, the proposed technique seeks an optimal parametric uncertainty model as a function of uncertain variables that explains the set of transfer functions. Finding such an optimal parametric uncertainty model is formulated as a noncovex optimization problem, which is then solved by a combination of a linear matrix inequality and a nonlinear optimization technique. To find an initial condition for solving this nonconvex problem, the nonlinear principal component analysis based on the multidimensional principal curve is employed. The effectiveness of the proposed technique is verified through both illustrative and practical examples.

scholarly journals The Best Achievableℋ2Tracking Performances for SIMO Feedback Control Systems

2007 ◽  
Vol 2007 ◽  
pp. 1-12 ◽  
Author(s):  
Shinji Hara ◽  
Toni Bakhtiar ◽  
Masaaki Kanno
Keyword(s):  
Feedback Control ◽  
Control Systems ◽  
Linear Time ◽  
Tracking Error ◽  
Control Input ◽  
Discrete Time System ◽  
Time System ◽  
Linear Time Invariant ◽  
Augmentation Strategy ◽  
Feedback Control Systems

This paper is concerned with the inherentℋ2tracking performance limitation of single-input and multiple-output (SIMO) linear time-invariant (LTI) feedback control systems. The performance is measured by the tracking error between a step reference input and the plant output with additional penalty on control input. We employ the plant augmentation strategy, which enables us to derive analytical closed-form expressions of the best achievable performance not only for discrete-time system, but also for continuous-time system by exploiting the delta domain version of the expressions.

scholarly journals On Switched Control Design of Linear Time-Invariant Systems with Polytopic Uncertainties

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Wallysonn A. de Souza ◽  
Marcelo C. M. Teixeira ◽  
Máira P. A. Santim ◽  
Rodrigo Cardim ◽  
Edvaldo Assunção
Keyword(s):  
Lyapunov Function ◽  
Linear Time ◽  
Time Derivative ◽  
Control Design ◽  
Feedback Gain ◽  
Linear Time Invariant ◽  
Switched Control ◽  
Polytopic Uncertainties ◽  
Linear Time Invariant Systems ◽  
Time Invariant

This paper proposes a new switched control design method for some classes of linear time-invariant systems with polytopic uncertainties. This method uses a quadratic Lyapunov function to design the feedback controller gains based on linear matrix inequalities (LMIs). The controller gain is chosen by a switching law that returns the smallest value of the time derivative of the Lyapunov function. The proposed methodology offers less conservative alternative than the well-known controller for uncertain systems with only one state feedback gain. The control design of a magnetic levitator illustrates the procedure.

Stochastic Estimation of Human Ankle Mechanical Impedance in Lateral/Medial Rotation

2014 ◽  
Author(s):  
Evandro M. Ficanha ◽  
Mohammad Rastgaar
Keyword(s):  
Degrees Of Freedom ◽  
Muscle Activation ◽  
Transfer Functions ◽  
Linear Time ◽  
Mechanical Impedance ◽  
Linear Time Invariant ◽  
Ankle Impedance ◽  
Human Ankle ◽  
Medial Rotation ◽  
The Difference

This article compares stochastic estimates of human ankle mechanical impedance when ankle muscles were fully relaxed and co-contracting antagonistically. We employed Anklebot, a rehabilitation robot for the ankle to provide torque perturbations. Surface electromyography (EMG) was used to monitor muscle activation levels and these EMG signals were displayed to subjects who attempted to maintain them constant. Time histories of ankle torques and angles in the lateral/medial (LM) directions were recorded. The results also compared with the ankle impedance in inversion-eversion (IE) and dorsiflexion-plantarflexion (DP). Linear time-invariant transfer functions between the measured torques and angles were estimated for the Anklebot alone and when a human subject wore it; the difference between these functions provided an estimate of ankle mechanical impedance. High coherence was observed over a frequency range up to 30 Hz. The main effect of muscle activation was to increase the magnitude of ankle mechanical impedance in all degrees of freedom of ankle.

scholarly journals Analysis and Experimental Evaluation of Power Line Transmission Parameters for Power Line Communication

2015 ◽  
Vol 15 (2) ◽  
pp. 64-71 ◽  
Author(s):  
P. Mlynek ◽  
J. Misurec ◽  
M. Koutny ◽  
R. Fujdiak ◽  
T. Jedlicka
Keyword(s):  
Transfer Functions ◽  
Linear Time ◽  
Power Line ◽  
Power Line Communication ◽  
Numerical Verification ◽  
Electrical Cable ◽  
Linear Time Invariant ◽  
Transmission Parameters ◽  
Channel Frequency Response ◽  
Time Invariant

Abstract The article describes a way of evaluating the power line channel frequency response and input impedance by means of the linear time-invariant (LTI) power line generator. Two possible methods are introduced for the calculation of primary parameters: the first method depends on the physical realization and physical dimension of the cable, and the second method is derived from the data provided by typical electrical cable manufacturers. Based on these methods, a comparison of transfer functions was made. This is followed by measurement evaluation and numerical verification on a simple topology

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