This paper systematically analyzes linear oscillators, e.g., spring-mass-damper systems or RLC-circuits that are controlled by an extension of a phase-locked loop (PLL). These systems are often used in measurement applications where the stability and dynamics directly influence the measurement quality. Therefore, a description of the control loop in terms of phase signals is sought. However, the classical oscillator turns into a highly nonlinear system when it is formulated in amplitude/phase-variables of its input and output signals. Up to now, there were made either ab-initio assumptions of slowly varying parameters or trial-and-error designs. The novel approach proposed in this paper derives a universally valid description in state space form which enables the use of standard methods of nonlinear system theory. Using this description, the stability of phase controlled oscillators is analyzed by means of Lyapunov functions. A linearization is applied in order to effectively design the controller and optimize the closed-loop dynamics. Simulations with the original nonlinear systems are conducted to justify the linear approach. Thereby, two application scenarios are under consideration: Tracking of the desired target value (target phase shift) and resonance tracking (changes of the system parameters). It is found that including the phase dynamics of the oscillator significantly improves the description of the closed-loop behavior. Finally, the results are validated experimentally for an application measuring the viscosity of fluids.
Skip Nav Destination
Article navigation
July 2016
Research-Article
Dynamics and Stability of Phase Controlled Oscillators
Tobias Brack,
Tobias Brack
Department of Mechanical and
Process Engineering,
Institute for Mechanical Systems,
ETH Zurich,
Zurich 8092, Switzerland
e-mail: brack@imes.mavt.ethz.ch
Process Engineering,
Institute for Mechanical Systems,
ETH Zurich,
Zurich 8092, Switzerland
e-mail: brack@imes.mavt.ethz.ch
Search for other works by this author on:
Dominik Kern,
Dominik Kern
Professorship of Applied
Mechanics and Dynamics,
Faculty for Mechanical Engineering,
Chemnitz University of Technology,
Chemnitz 09107, Germany
e-mail: dominik.kern@mb.tu-chemnitz.de
Mechanics and Dynamics,
Faculty for Mechanical Engineering,
Chemnitz University of Technology,
Chemnitz 09107, Germany
e-mail: dominik.kern@mb.tu-chemnitz.de
Search for other works by this author on:
Mengdi Chen,
Mengdi Chen
Department of Mechanical and
Process Engineering,
Institute for Mechanical Systems,
ETH Zurich,
Zurich 8092, Switzerland
e-mail: mengdichen@googlemail.com
Process Engineering,
Institute for Mechanical Systems,
ETH Zurich,
Zurich 8092, Switzerland
e-mail: mengdichen@googlemail.com
Search for other works by this author on:
Jürg Dual
Jürg Dual
Professor
Fellow ASME
Department of Mechanical and
Process Engineering,
Institute for Mechanical Systems,
ETH Zurich,
Zurich 8092, Switzerland
e-mail: dual@imes.mavt.ethz.ch
Fellow ASME
Department of Mechanical and
Process Engineering,
Institute for Mechanical Systems,
ETH Zurich,
Zurich 8092, Switzerland
e-mail: dual@imes.mavt.ethz.ch
Search for other works by this author on:
Tobias Brack
Department of Mechanical and
Process Engineering,
Institute for Mechanical Systems,
ETH Zurich,
Zurich 8092, Switzerland
e-mail: brack@imes.mavt.ethz.ch
Process Engineering,
Institute for Mechanical Systems,
ETH Zurich,
Zurich 8092, Switzerland
e-mail: brack@imes.mavt.ethz.ch
Dominik Kern
Professorship of Applied
Mechanics and Dynamics,
Faculty for Mechanical Engineering,
Chemnitz University of Technology,
Chemnitz 09107, Germany
e-mail: dominik.kern@mb.tu-chemnitz.de
Mechanics and Dynamics,
Faculty for Mechanical Engineering,
Chemnitz University of Technology,
Chemnitz 09107, Germany
e-mail: dominik.kern@mb.tu-chemnitz.de
Mengdi Chen
Department of Mechanical and
Process Engineering,
Institute for Mechanical Systems,
ETH Zurich,
Zurich 8092, Switzerland
e-mail: mengdichen@googlemail.com
Process Engineering,
Institute for Mechanical Systems,
ETH Zurich,
Zurich 8092, Switzerland
e-mail: mengdichen@googlemail.com
Jürg Dual
Professor
Fellow ASME
Department of Mechanical and
Process Engineering,
Institute for Mechanical Systems,
ETH Zurich,
Zurich 8092, Switzerland
e-mail: dual@imes.mavt.ethz.ch
Fellow ASME
Department of Mechanical and
Process Engineering,
Institute for Mechanical Systems,
ETH Zurich,
Zurich 8092, Switzerland
e-mail: dual@imes.mavt.ethz.ch
1Corresponding author.
Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received April 8, 2015; final manuscript received March 22, 2016; published online May 13, 2016. Assoc. Editor: Yang Shi.
J. Dyn. Sys., Meas., Control. Jul 2016, 138(7): 071007 (12 pages)
Published Online: May 13, 2016
Article history
Received:
April 8, 2015
Revised:
March 22, 2016
Citation
Brack, T., Kern, D., Chen, M., and Dual, J. (May 13, 2016). "Dynamics and Stability of Phase Controlled Oscillators." ASME. J. Dyn. Sys., Meas., Control. July 2016; 138(7): 071007. https://doi.org/10.1115/1.4033176
Download citation file:
Get Email Alerts
Cited By
An Adaptive Sliding-Mode Observer-Based Fuzzy PI Control Method for Temperature Control of Laser Soldering Process
J. Dyn. Sys., Meas., Control
Fault detection of automotive engine system based on Canonical Variate Analysis combined with Bhattacharyya Distance
J. Dyn. Sys., Meas., Control
Multi Combustor Turbine Engine Acceleration Process Control Law Design
J. Dyn. Sys., Meas., Control (July 2025)
Related Articles
A New Model-Based Control Structure for Position Tracking in an Electro-Hydraulic Servo System With Acceleration Constraint
J. Dyn. Sys., Meas., Control (December,2017)
Nonlinear Robust Output Stabilization for Mechanical Systems Based on Luenberger-Like Controller/Observer
J. Dyn. Sys., Meas., Control (August,2017)
Dynamic High-Gain Observer to Estimate Pneumatic Actuator Temperatures
J. Dyn. Sys., Meas., Control (February,2016)
Using Constrained Bilinear Quadratic Regulator for the Optimal Semi-Active Control Problem
J. Dyn. Sys., Meas., Control (November,2017)
Related Proceedings Papers
Related Chapters
Dynamic Simulations to Become Expert in Order to Set Fuzzy Rules in Real Systems
International Conference on Advanced Computer Theory and Engineering, 4th (ICACTE 2011)
New H∞ Controllers Design for Networked Control System with Disturbance Based on Asynchronous Dynamical System
International Conference on Advanced Computer Theory and Engineering (ICACTE 2009)
Fault-Tolerant Control of Sensors and Actuators Applied to Wind Energy Systems
Electrical and Mechanical Fault Diagnosis in Wind Energy Conversion Systems