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 Robust Stability of Fractional-Order Linear Time-Invariant Systems: Parametric versus Unstructured Uncertainty Models

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Radek Matušů ◽  
Bilal Şenol ◽  
Libor Pekař
Keyword(s):  
Fractional Order ◽  
Robust Stability ◽  
Linear Time ◽  
Parametric Uncertainty ◽  
Uncertainty Modeling ◽  
Single Input Single Output ◽  
Linear Time Invariant ◽  
Robust Stability Analysis ◽  
Uncertainty Models ◽  
Time Invariant

The main aim of this paper is to present and compare three approaches to uncertainty modeling and robust stability analysis for fractional-order (FO) linear time-invariant (LTI) single-input single-output (SISO) uncertain systems. The investigated objects are described either via FO models with parametric uncertainty, by means of FO unstructured multiplicative uncertainty models, or through FO unstructured additive uncertainty models, while the unstructured models are constructed on the basis of appropriate selection of a nominal plant and a weight function. Robust stability investigation for systems with parametric uncertainty uses the combination of plotting the value sets and application of the zero exclusion condition. For the case of systems with unstructured uncertainty, the graphical interpretation of the utilized robust stability test is based mainly on the envelopes of the Nyquist diagrams. The theoretical foundations are followed by two extensive, illustrative examples where the plant models are created; the robust stability of feedback control loops is analyzed, and obtained results are discussed.

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.

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 PID Controller Design Based on Global Optimization Technique with Additional Constraints

2016 ◽  
Vol 67 (3) ◽  
pp. 160-168 ◽  
Author(s):  
Stepan Ozana ◽  
Tomas Docekal
Keyword(s):  
Global Optimization ◽  
Pid Controller ◽  
Controller Design ◽  
Linear Time ◽  
Optimization Technique ◽  
Phase Margin ◽  
Linear Time Invariant ◽  
Pid Controller Design ◽  
Static Systems ◽  
Time Invariant

Abstract This paper deals with design of PID controller with the use of methods of global optimization implemented in Matlab environment and Optimization Toolbox. It is based on minimization of a chosen integral criterion with respect to additional requirements on control quality such as overshoot, phase margin and limits for manipulated value. The objective function also respects user-defined weigh coefficients for its particular terms for a different penalization of individual requirements that often clash each other such as for example overshoot and phase margin. The described solution is designated for continuous linear time-invariant static systems up to 4th order and thus efficient for the most of real control processes in practice.

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

A Passive Fault-Tolerant Switched Control Approach for Linear Multivariable Systems: Application to a Quadcopter Unmanned Aerial Vehicle Model

2019 ◽  
Vol 142 (3) ◽  
Author(s):  
Hasan Başak ◽  
Emre Kemer ◽  
Emmanuel Prempain
Keyword(s):  
Output Feedback ◽  
State Feedback ◽  
Fault Tolerant ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Passive State ◽  
Linear Matrix ◽  
Control Approach ◽  
Linear Time Invariant ◽  
L2 Norm

Abstract This paper proposes synthesis algorithms for the design of passive state- and output-feedback fault-tolerant controllers. Sufficient conditions for the existence and the construction of such fault-tolerant controllers are given in terms of linear matrix inequalities (LMIs) which can be solved efficiently. The state-feedback fault-tolerant controller consists of a family of state-feedback gains switched appropriately according to a stabilizing switching signal so that the closed-loop system satisfies a performance requirement expressed in terms of system L2 norm. Similarly, the output feedback controller consists of a family of full-order linear, time-invariant controllers switched according to a stabilizing signal that depends only on the controller states. Both approaches are passive in the sense that they do not rely on the detection and/or the estimation of the faults. The proposed approaches are tested on a nonlinear model of a quadcopter. Simulation results show that satisfactory stability, tracking, and disturbance rejection are maintained despite of time-varying actuator faults.

A Static Anti-Windup Compensator Design Technique for Robust Regional Pole Placement

2006 ◽  
Author(s):  
Brandon Hencey ◽  
Andrew Alleyne
Keyword(s):  
Closed Loop ◽  
Linear Time ◽  
Pole Placement ◽  
Linear Matrix ◽  
Test Bed ◽  
Hydraulic Test ◽  
Linear Time Invariant ◽  
Loop Dynamics ◽  
Performance Deterioration ◽  
Time Invariant

This paper develops a new method of designing anti-windup compensators using the concept of robust pole placement using linear matrix inequality (LMI) regions. The anti-windup problem seeks to minimize the closed loop performance deterioration due to input nonlinearities such as saturation for a given linear time-invariant plant and controller. Existing LMI-based anti-windup synthesis techniques do not explicitly provide a method to account for robust pole placement. This paper suggests a LMI-based method that not only attempts to minimize performance deterioration, but also explicitly restricts the anti-windup closed loop dynamics to an admissible set. Finally, the techniques discussed in this paper are demonstrated on a hydraulic test bed.

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