Asymptotic trends in time-varying oscillatory period for a dual-staged torsional system

2016 ◽  
Vol 231 (22) ◽  
pp. 4126-4138
Author(s):  
Michael D Krak ◽  
Rajendra Singh
Keyword(s):  
Linear System ◽  
Mechanical System ◽  
Time Domain ◽  
Effective Stiffness ◽  
Step Response ◽  
Analysis Tool ◽  
Time Varying ◽  
Non Linear ◽  
Non Linear System ◽  
Oscillatory Period

The primary goal of this article is to propose a new analysis tool that estimates the asymptotic trends in the time-varying oscillatory period of a non-linear mechanical system. The scope is limited to the step-response of a torsional oscillator containing a dry friction element and dual-staged spring. Prior work on the stochastic linearization techniques is extended and modified for application in time domain. Subsequently, an instantaneous expected value operator and the concept of instantaneous effective stiffness are proposed. The non-linear system is approximated at some instant during the step-response by a linear time-invariant mechanical system that utilizes the instantaneous effective stiffness concept. The oscillatory period of the non-linear step-response at that instant is then approximated by the natural period of the corresponding linear system. The proposed method is rigorously illustrated via two computational example cases (a near backlash and near pre-load non-linearities), and the necessary digital signal processing parameters for time domain analysis are investigated. Finally, the feasibility and applicability of the proposed method is demonstrated by estimating the softening and hardening trends in the time-varying oscillatory period of the measured response for two laboratory experiments that contain clearance elements and multi-staged torsional springs.

Input-to-state stabilisation for a general non-linear system with time-varying input delay

2017 ◽  
Vol 11 (16) ◽  
pp. 2793-2800 ◽  
Author(s):  
Xiushan Cai ◽  
Lingxin Meng ◽  
Cong Lin ◽  
Wei Zhang ◽  
Leibo Liu
Keyword(s):  
Linear System ◽  
Input Delay ◽  
Time Varying ◽  
Non Linear ◽  
Non Linear System

A novel robust fuzzy control of an uncertain system

2016 ◽  
Vol 39 (3) ◽  
pp. 324-333 ◽  
Author(s):  
Abdurrahman Bayrak ◽  
Handan Gürsoy ◽  
Mehmet Önder Efe
Keyword(s):  
Linear System ◽  
Fuzzy Control ◽  
Control Method ◽  
Sliding Mode ◽  
Poor Performance ◽  
Uncertain System ◽  
Step Response ◽  
Non Linear ◽  
Non Linear System ◽  
Noisy Measurements

This paper presents a robust control method combining the conventional proportional–integral–derivative (PID) scheme and the sliding mode fuzzy control scheme for a second-order non-linear system having uncertainties in the system dynamics. The goal of the proposed scheme is to force the response of the uncertain plant to follow that of the nominal model. The first phase of the design approach is to obtain a nominal PID controller for the nominal plant model. The poor performance of the sole PID scheme on the uncertain non-linear system motivates the proposal of the technique discussed here. To compensate for the deficiencies in the unit step response of the uncertain system, a fuzzy compensation scheme based on sliding mode control (SMC) is proposed and the PID loop is augmented by the proposed approach. It is shown that the performance with the proposed scheme is better than the sole PID-based control system. With the proposed technique, the response of the uncertain system converges to of the nominal system with admissible controller outputs. Furthermore, simulation results show that the proposed method produces consistent results even with noisy measurements.

A novel LSSVM-L Hammerstein model structure for system identification and nonlinear model predictive control of CSTR servo and regulatory control

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Akshaykumar Naregalkar ◽  
Subbulekshmi Durairaj
Keyword(s):  
Linear System ◽  
Regulatory Control ◽  
Hammerstein Model ◽  
Support Vector ◽  
Model Structure ◽  
Linear Dynamics ◽  
Vector Machines ◽  
Non Linear ◽  
Laguerre Filters ◽  
Non Linear System

Abstract A continuous stirred tank reactor (CSTR) servo and the regulatory control problem are challenging because of their highly non-linear nature, frequent changes in operating points, and frequent disturbances. System identification is one of the important steps in the CSTR model-based control design. In earlier work, a non-linear system model comprises a linear subsystem followed by static nonlinearities and represented with Laguerre filters followed by the LSSVM (least squares support vector machines). This model structure solves linear dynamics first and then associated nonlinearities. Unlike earlier works, the proposed LSSVM-L (least squares support vector machines and Laguerre filters) Hammerstein model structure solves the nonlinearities associated with the non-linear system first and then linear dynamics. Thus, the proposed Hammerstein’s model structure deals with the nonlinearities before affecting the entire system, decreasing the model complexity and providing a simple model structure. This new Hammerstein model is stable, precise, and simple to implement and provides the CSTR model with a good model fit%. Simulation studies illustrate the benefit and effectiveness of the proposed LSSVM-L Hammerstein model and its efficacy as a non-linear model predictive controller for the servo and regulatory control problem.

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