Binbin Tao
ABSTRACT
This paper proposes a design solution of PID (Proportional-Integral-Derivative) bifurcation control for controlling the stabilization and bifurcation of a desired equilibrium on a delayed complex system with a variable parameter. Firstly, we stabilize the controlled system to the desired equilibrium by the function of the integrating element of the controller. Afterwards, we can achieve some conditions on the stability and Hopf bifurcation of the controlled system by means of linearizing the system at an ideal state and discussing the associated characteristic equation. Meanwhile, it is found that the regulation of controller is very effective for optimizing the performance of dynamics on the system. Finally, we set up several sets of experiments for validating the validity of theoretical analysis. In addition, we also provide some simulation diagrams, which can illustrate the relationship curve between various parameters and the bifurcation point on the controlled system.
- M. Xiao, W.X. Zheng, G.P. Jiang and J.D. Cao (2017). Stability and bifurcation of delayed fractional-order dual congestion control algorithms. IEEE Transactions on Automatic Control, 62(9), 4819--4826.Google Scholar
Cross Ref
- B.B. Tao, M. Xiao, Q.S. Sun and J.D. Cao (2018). Hopf bifurcation analysis of a delayed fractional-order genetic regulatory network model. Neurocomputing, 275, 677--686.Google ScholarDigital Library
- R. Al-Dujaily, N. Dahir, T. Mak, F. Xia and A. Yakovlev (2013). Dynamic programming-based runtime thermal management (DPRTM): an online thermal control strategy for 3D-NoC Systems. ACM Transactions on Design Automation of Electronic Systems, 19(1), 2.Google ScholarDigital Library
- L. Merigo, F. Padula, N. Latronico, M. Paltenghi and A. Visioli (2019). Optimized PID control of propofol and remifentanil coadministration for general anesthesia. Commun Nonlinear Sci Numer Simulat, 72, 194--212.Google ScholarCross Ref
- M. Xiao and J. Cao (2008). Genetic oscillation deduced from Hopf bifurcation in a genetic regulatory network with delays. Mathematical Biosciences, 215(1), 55--63.Google ScholarCross Ref
- D.W. Ding, X.Y. Zhang, J.D. Cao, N. Wang and D. Liang (2016). Bifurcation control of complex networks model via PD controller. Neurocomputing, 175, 1--9.Google ScholarDigital Library
- B.B. Tao, M. Xiao, G.P. Jiang and Q.S. Sun (2018). Bifurcation control of small-world networks with delays via PID controller. Asian Journal of Control, Article in Press, Doi: 10.1002/asjc.1958.Google Scholar
- Z.T. Zhusubaliyev, A. Medvedev and M.M. Silva (2014). Bifurcation analysis of PID-controlled neuromuscular blockade in closed-loop anesthesia. Journal of Process Control, 25, 152--163.Google ScholarCross Ref
- L. Merigo, F. Padula, N. Latronico, M. Paltenghi and A. Visioli (2019). Optimized PID control of propofol and remifentanil coadministration for general anesthesia. Commun Nonlinear Sci Numer Simulat, 72, 194--212.Google ScholarCross Ref
- E. Braverman and E. Liz (2012). On stabilization of equilibria using predictive control with and without pulses. Computers and Mathematics with Applications, 64, 2192--2201.Google ScholarDigital Library
Index Terms
- PID Controller Design Based on the Stabilization and Bifurcation of a Desired Equilibrium for a Delayed Complex System with a Variable Parameter
Recommendations
Optimization Design of PID Controller and its Application
ICMTMA '11: Proceedings of the 2011 Third International Conference on Measuring Technology and Mechatronics Automation - Volume 02PID control has been largely applied in the industry process control because of its robustness and easy realization, But it is very difficult to tune the three parameters of PID controller, which often leads to oscillation and overshoot of the ...
Optimization of a self-tuning PID type fuzzy controller and a PID controller for an inverted pendulum
By relating to the conventional PID and PID type fuzzy, an optimized PID type fuzzy controller and an optimized PID controller are designed for an inverted pendulum with two outputs. The optimized PID type fuzzy tunes its scaling factors on line. The ...
Sine-cosine-algorithm-based fractional order PID controller tuning for multivariable systems
The multivariable systems, used in several industrial processing systems, are controlled using multi-loop controllers. A novel fractional order proportional integral derivative (FOPID) controller design without decoupler for the multivariable system using ...
Comments