Dynamic modeling of heating furnace & enhancing the performance with PIλDμ controller for fractional order model using optimization techniques

Over the year heating furnace system has always suffered a huge loss of heat energy the line of safety of man power. The flow of fuel into chamber of furnace, basically limits the gas pressure inside furnace. So, proper relation between fuel flow rate and gas pressure inside furnace is essential to ensure a proper utilization of heat with minimum settling time and minimum overshoot, so that safety is not compromised. This paper enlightens design of a proper integer order model (IOM) of heating furnace which is further converted into a fractional order model (FOM). This fractional order model is used with PID controllers in closed loop. For enhancing the performance of PID controller, fractional elements are used. Therefore, PIλDμ controller is optimized properly for a smooth, low overshoot response with a very low settling time. These proposed results may be implemented properly in small scale furnaces or large scale industrial furnaces.

[1]  William W. Hager,et al.  A New Active Set Algorithm for Box Constrained Optimization , 2006, SIAM J. Optim..

[2]  I. Podlubny Fractional differential equations , 1998 .

[3]  Eduard Petlenkov,et al.  A flexible MATLAB tool for optimal fractional-order PID controller design subject to specifications , 2012, Proceedings of the 31st Chinese Control Conference.

[4]  Paul T. Boggs,et al.  Sequential Quadratic Programming , 1995, Acta Numerica.

[5]  Pratibha Tiwari,et al.  Optimal Tuning of Fractional Order PID Controller for DC Motor Speed Control Using Particle Swarm Optimization , 2013 .

[6]  Margaret H. Wright,et al.  Nelder, Mead, and the other simplex method , 2012 .

[7]  Hyo-Sung Ahn,et al.  Fractional-order integral and derivative controller for temperature profile tracking , 2009 .

[8]  George E. Totten,et al.  Steel Heat Treatment Handbook , 2005 .

[9]  Y. Chen,et al.  A fractional order PID tuning algorithm for a class of fractional order plants , 2005, IEEE International Conference Mechatronics and Automation, 2005.

[10]  Amit Konar,et al.  Approximation of a Fractional Order System by an Integer Order Model Using Particle Swarm Optimization Technique , 2008, ArXiv.

[11]  Stephen P. Boyd,et al.  An Interior-Point Method for Large-Scale l1-Regularized Logistic Regression , 2007, J. Mach. Learn. Res..

[12]  Saeed Balochian,et al.  Fractional PID controller for a High performance Drilling Machine , 2012 .

[13]  Louis Brand The Fundamental Theorem of the Calculus , 1955 .