Total views : 224
Ameliorating the FOPID (PIλDμ) Controller Parameters for Heating Furnace using Optimization Techniques
Since the heating furnace system has emanated it has faced the problem of high power consumption, colossal amount of time to heat the substances and the vulnerability of getting exploded thus the objective of the paper is to achieve a system for same with less power consumption, whit time to heat the substances and making it safe from explosion. Using the mathematical way of modeling the dynamic critical systems the heating furnace is being modeled by using the damping, spring and mass elements. The integer order model of the system is being achieved by the Laplace transform and fractional order model for the same is obtained using the Grunwald-Letnikov formula. The Cohen-Coon tuning technique is being amalgamated with the Nelder-Mead, Interior-Point, Active-Set and Sequential Quadratic Programming optimization techniques respectively so as to design the FOPID controller for heating furnace. When the feedback systems were being formed then the outputs demonstrated that the system now consists the properties of less power consumption, less time to heat the substances along with less overshoot. Earlier the integer order model had the settling time (time taken to heat the substance), steady state error (power consumption) and overshoot (explosion) of 1500 seconds, 50% and 0% respectively. When the PID controller was designed for the same using Cohen-Coon tuning technique and forming a feedback system it had setting time of around 800 sec. and also the steady state error was brought to 0% but the overshoot went up to 35%. Therefore FOPID controller is being designed using the concocted technique that is the amalgamation of tuning technique and optimization techniques and forming and feedback system with FOM of heating furnace, the system yielded steady state error as 0%, where the settling time have been reduced to 300 seconds and overshoot between 7%-12%. Using the concocted technique that is the amalgamation of Cohen-Coon tuning technique with the optimization tuning techniques the FOPID controller was being formed for the FOM of the heating furnace which is being kept in feedback so as to form a system. Thus systems formed ameliorated the settling time i.e. time taken to heat the substance, the overshoot i.e. the vulnerability of getting exploded also remains low and the steady state error i.e. power consumption is also reduced drastically.
FOPID Controller, Heating Furnace, Optimization Techniques, Overshoot, Settling Time, Steady State Error.
- Srivastava S, Pandit VS. Studies on PI/PID controllers in the proportional integral plane via different performance indices. Proceedings of 1st ICCMI; India. 2016. p. 151–5.
- Bennet S. Development of the PID controller. IEEE Control Systems. 1993 Dec; 13(6): 58–65.
- Merrikh-Bayat F, Mirebrahimi N, Khalili MR. Discrete-time fractional-order PID controller: Definition, tuning, digital realization and some applications. International Journal of Control, Automation and Systems. Springer. 2015 Feb; 13(1):1–10.
- Shahri ME, Balochian S, Balochian H, Zhang Y. Design of fractional order PID controller for time delay systems using differential evolution algorithm. Indian Journal of Science and Technology. 2014 Sep; 7(9):1307–15.
- Gilchrist JD. Furnaces (Commonwealth library). 1st ed. Pergamon Press; 1963.
- Tepljakov A. Fractional-order calculus based identification and control of linear dynamic systems. [Doctoral dissertation, Master thesis], Tallinn: Tallinn University of Technology. 2011.
- Maiti D, Konar A. Approximation of a fractional order system by an Integer Order Model using Particle Swarm Optimization technique. Proceedings of CICCRA; India. 2008. p. 149–52.
- Podlubny I. Fractional derivatives: History, theory, application. Logan: Utah State University; 2005 Sep.
- Dannon HV. The fundamental theorem of the fractional calculus and the Meaning of Fractional Derivatives. Gauge Institute Journal. 2009; 5(1):1–26.
- Chen YQ, Petras I, Xue D. Fractional order control - A tutorial. Proceedings of ACC; USA. 2009. p. 1397–411.
- Podlubny I, Dorcak L, Kostial I. On fractional derivatives, fractional order dynamic systems and PID controllers. Proceedings of 36th CDC; USA. 1997. p. 4985–90.
- Chen YQ, Xue D, Dou H. Fractional calculus and biomimetic control. Proceedings of ROBIO; China. 2004. p. 901–6.
- Atangana A, Secer A. A note on fractional order derivatives and table of fractional derivatives of some special functions. Abstract and Applied Analysis. 2013 Apr; 2013(2013):1–8.
- Ziegler JG, Nichols NB. Optimum settings for automatic controllers. Transactions of American Society of Mechanical Engineers. 1942 Nov; 64(8):759–68.
- Astrom K, Hagglund T. PID controllers: Theory, design and tuning. 2nd ed. ISA: The Instrumentation, Systems and Automation Society; 1995.
- Wright MH. Nelder-Mead and other simplex method. Documenta Mathematica Extra; 2010 Aug. p. 271–6.
- Koh K, Kim SJ, Boyd SP. An interior-point method for large-scale l1-regularized logistic regression. Journal of Machine Learning Research. 2007 Jul; 8(8):1519–55.
- Hager WW, Zhang H. A new active set algorithm for box constrained optimization. SIAM Journal on Optimization. 2006 Aug; 17(2):526–57.
- Aleksei T, Eduard P, Jurl B. A flexible MATLAB tool for optimal fractional-order PID controller design subject to specifications. Proceedings of 31st CCC; China. 2012. p. 4698–703.
- Tepljakov A, Petlenkov E, Belikov J. FOPID controlling tuning for fractional FOPDT plants subject to design specifications in the frequency domain. Proceedings of ECC; Austria. 2015. p. 3507–12.
- Jones RW, Tham MT. Gain and phase margin controller tuning: FOPDT or IPDT model based methods. Proceedings of SICE Annual Conference; Japan. 2004. p. 1139–43.
- Xue D, Chen YQ, Atherton DP. Linear feedback control and design with MATLAB. 1st ed. Society for Industrial and Applied Mathematics; 2007.
- Basu A, Mohanty S, Sharma R. Meliorating the performance of heating furnace using FOPID controller. Proceedings of 2nd ICCAR; Hong Kong. 2016. p. 128–32.
- There are currently no refbacks.
This work is licensed under a Creative Commons Attribution 3.0 License.