scholarly journals Computing frequency response of non‐parametric uncertainty model of MIMO systems using υ‐gap metric optimization

2021 ◽  
Author(s):  
Seyed Masoud Tabibian ◽  
Mohammad Ataei ◽  
Hamid Reza Koofigar
Keyword(s):  
Frequency Response ◽  
Mimo Systems ◽  
Parametric Uncertainty ◽  
Gap Metric ◽  
Uncertainty Model ◽  
Non Parametric

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.

Improved Control of a Steering Wheel Vibration Simulator

2006 ◽  
Author(s):  
James A. Mynderse ◽  
George T.-C. Chiu
Keyword(s):  
Frequency Response ◽  
Grip Force ◽  
Phase Error ◽  
Human Perception ◽  
Feedback Controller ◽  
Steering Wheel ◽  
Linear Matrix ◽  
Output Tracking Control ◽  
Uncertainty Model ◽  
Wheel Vibration

The improved control of a steering wheel vibration simulator capable of reproducing a set of desired vibration/acceleration signals is presented. The simulator is to be used in characterizing human perception of vibration as transmitted to the hand through the steering wheel. Accelerometers are used to record the acceleration at the top of the steering wheel in both the up-down (z) and side-to-side (y) directions. The plant is modeled by frequency response measurements including an uncertainty model generated from measured changes in system frequency response due to variations in subject grip force. The simulator control problem is formulated as a 2-input, 1-output tracking control of the z-axis while minimizing the y-axis response. A two degree-of-freedom controller is synthesized with a stabilizing feedback controller and a zero phase error tracking feedforward controller. The feedback controller is designed using linear matrix inequality techniques and ensures robust stability of the coupled closed-loop system with uncertainty due to subject grip force. Simulation and experimental results to verify the effectiveness of the simulator are presented.

On the Taylor series asymptotic tracking control of robots

Robotica ◽  
2018 ◽  
Vol 37 (3) ◽  
pp. 405-427 ◽  
Author(s):  
Seyed Mohammad Ahmadi ◽  
Mohammad Mehdi Fateh
Keyword(s):  
Taylor Series ◽  
Tracking Control ◽  
Robot Manipulators ◽  
Tracking Error ◽  
Parametric Uncertainty ◽  
Series System ◽  
Control Methods ◽  
Asymptotic Tracking ◽  
Modelling Error ◽  
Non Parametric

SUMMARYAchieving the asymptotic tracking control of electrically driven robot manipulators is a challenging problem due to approximation/modelling error arising from parametric and non-parametric uncertainty. Thanks to the specific property of Taylor series systems as they are universal approximators, this research outlines two robust control schemes using an adaptive Taylor series system for robot manipulators, including actuators' dynamics. First, an indirect adaptive controller is designed such as to approximate an uncertain continuous function by using a Taylor series system in the proposed control law. Second, a direct adaptive scheme is established to employ the Taylor series system as a controller. In both controllers, not only a robustifying term is constructed using the estimation of the upper bound of approximation/modelling error, but the closed-loop stability, as well as the asymptotic convergence of joint-space tracking error and its time derivative, is ensured. Due to the design of the Taylor series system in the tracking error space, our technique clearly has an advantage over fuzzy and neural network-based control methods in terms of the small number of tuning parameters and inputs. The proposed methods are simple, model free in decentralized forms, no need for uncertainty bounding functions and perfectly capable of dealing with parametric and non-parametric uncertainty and measurement noise. Finally, simulation results are introduced to confirm the efficiency of the proposed control methods.

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