Abstract
This paper presents a new approximated integer delayed modeling and control technique for Continuous-time Fractional Delay Differential Equations (CFDDEs). Using the impulse response sequences of the CFDDE and the balanced model-reduction method, a delay-free discrete-time state-space model is constructed. Then, an equivalent Discrete-time Integer Delay Difference Equation (DIDDE) is obtained by transforming the obtained discrete-time state-space model into a controller-type block companion form. Furthermore, based on the obtained DIDDE, an equivalent Continuous-time Integer Delay Differential Equation (CIDDE) is determined by means of the newly developed Chebyshev's bilinear approximation method. For digital control of the CFDDE, an optimal Discrete-time Integer Delayed Control Law (DIDCL) is designed using the conventional discrete-time LQR approach together with the obtained delay-free discrete-time state-space model. On the other hand, for continuous-time control of the CFDDE, a Continuous-time Integer Delayed Control Law (CIDCL) is determined from the designed DIDCL by means of the inverse Chebyshev's bilinear approximation method. Finally, digital and analog integer delayed observers are constructed for the implementations of the developed DIDCL and CIDCL, respectively. An illustrative example is given to demonstrate the effectiveness of the proposed method.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: 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.