Abstract
The paper deals with a graphical approach to investigation of robust stability for a feedback control loop with an uncertain fractional order time-delay plant and integer order or fractional order controller. Robust stability analysis is based on plotting the value sets for a suitable range of frequencies and subsequent verification of the zero exclusion condition fulfillment. The computational examples present the typical shapes of the value sets of a family of closed-loop characteristic quasipolynomials for a fractional order plant with uncertain gain, time constant, or time-delay term, respectively, and also for combined cases. Moreover, the practically oriented example focused on robust stability analysis of main irrigation canal pool controlled by either classical integer order PID or fractional order PI controller is included as well.
Highlights
IntroductionThe fractional order calculus (FOC) and its engineering applications represent attractive research field with rapidly growing amount of related scientific works
The fractional order calculus (FOC) and its engineering applications represent attractive research field with rapidly growing amount of related scientific works. This progress is understandable since the use of differentiation and integration under an arbitrary real or even complex number of the operations provides efficient tool for many real-life problems and since the knowledge of suitable and relatively comprehensible mathematical instruments for fractional order issues has increased lately
The FOC has already been useful in areas such as bioengineering, viscoelasticity, electronics, robotics, control theory, and signal processing [6, 7]
Summary
The fractional order calculus (FOC) and its engineering applications represent attractive research field with rapidly growing amount of related scientific works. This paper is focused on a graphical approach to robust stability analysis and especially on its application to fractional order time-delay control systems. The control loop studied in the computational examples consists of a fractional order time-delay plant with uncertain parameters and standard integer order PID controller. A number of computational examples and visualizations of the value sets for closed loop containing a fractional order time-delay plant with various uncertain parameters are shown in the extensive Section 4.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
