Meliorating the Performance of Heating Furnace System Using Proportional Integral Derivative Controller with Fractional Elements

Research output: ThesisMaster's Thesis


The milieu of the thesis is concentrated on melioration of heating furnace system performance. Heating furnace system over the years has suffered the huge loss of heat energy for the sake of safety of man power working around it. 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 regulated pressure, so that safety is not compromised. The analytical method of modelling the critical systems dynamically has been used to model the heating furnace system. The modelling of the heating furnace system has been done in integer order model using the traditional way of achieving the transfer function of the system from system’s basic differential equation which is formed using the standard mass, damping and spring element of the system. Also the modelling of the system is done in the fractional order model using the Grunwald-Letnikov formula whose literature is sufficiently present in the fractional calculus literature. The response of individual transfer function of heat furnace exhibits a very high value of steady state error along with a very sluggish response. It shows the wastage of heat energy due to higher steady state error and high settling time. The amelioration of heating furnace is done by designing the PID (proportional integral derivative) controller and the PIλDμ (fractional order proportional integral derivative) controller. The designing and tuning of the PID controller is done using various tuning techniques. For designing and tuning of the PIλDμ controller various tuning techniques and optimization techniques both and also only the optimization techniques are used. The various tuning techniques used are Ziegler-Nichols tuning technique, Cohen-Coon tuning technique, Astrom-Hagglund (AMIGO) tuning technique, Chien-Hrone-Reswick-1 tuning technique and Chien-Hrone-Reswick-2 tuning technique. The tuning techniques have been used to achieve the tuned values of tuning parameters of the controllers which are proportional gain (Kp), integral gain (Ki) and derivative gain (Kd). The various optimization techniques used are Nelder-Mead optimization technique, Interior-Point optimization technique, Active-Set optimization technique and Sequential Quadratic Programming optimization technique. The optimization technique algorithms are utilized to obtain the optimized value of tuning parameters and the differ-integrals λ and μ to design and tune the PIλDμ controller. All the techniques being used have their own pros and cons. The various controllers designed are used in a closed loop along with the heating furnace system (acts as plant or process in the closed loop system) and the output of the complete system is obtained and studied. This is done so as to achieve an improved heating furnace system that utilizes the maximum heat and also there is the minimum risk of explosion that may affect the people operating it or working around it. The overshoot is kept minimal so that there is minimum risk of explosion of the heating furnace system because of the high exertion of force by the gas on the inner wall of the furnace, the steady state error is nullified so that no extra amount of fuel is consumed by the plant and also the concentration has been laid on minimizing the settling time of the heating furnace.
Original languageEnglish
Awarding Institution
  • ITM University, Gwalior, Madhya Pradesh
  • Mohanty, Sumit, Supervisor, External person
Place of PublicationGwalior, India
Publication statusPublished - 11 Jun 2016



  • heating systems
  • furnace performance
  • fuel rate
  • gas pressure

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