- Temperature Control To Meet Design Requirements An Electric Furnace Intended For The Heat Treatment Of Objects Consists 1 (101.46 KiB) Viewed 23 times
- Temperature Control To Meet Design Requirements An Electric Furnace Intended For The Heat Treatment Of Objects Consists 2 (87.66 KiB) Viewed 23 times
Temperature control to meet design requirements An electric furnace intended for the heat treatment of objects consists of a closed enclosure heated by an electrical resistance which supplied by a voltage v(t). Ten objects can be treated simultaneously in the furnace. The heat treatment consists of maintaining the objects for 1 hour at a temperature of 1,200 °C (regulated in an optimal way because the objects are destroyed if the temperature exceeds 1,400 °C). between each two treatments, a time of 24 minutes is necessary to cool the oven and handling of products. The electric furnace is governed by the differential equation de de + 2000 = 0.02v(t) dt Questions a - determine the following Open loop transfer function G(s) of the electric furnace. Static gain. What would happen if the furnace was powered continuously and in an open loop? Assuming, despite everything, that we apply a 100 V input to the electric furnace in open loop. b - after what time would a temperature of 1200 °C be reached in the oven? We decide to control the temperature in the electric furnace by using a temperature sensor which delivers a voltage u(t). The sensor is governed by the differential equation du u(t) + 2 - = 510-30(t) dt
We also interduce a gain K in the feedforward loop. c - Draw a block diagram of the control loop and determine the closed loop transfer function. Determine the stability conditions of this system. d - Imposing a phase margin Ag = 45°, determine the value of the rise time in the closed loop system. e-We obviously want to regulate the temperature of the electric furnace at 1,200 °C. Determine the value of the setpoint to be introduced into the system. With the system tuned to obtain a phase margin Ag = 45°, what is the maximum temperature reached in the electric furnace? Conclude. f - we would like to limit the overshoot at 10%, determine the raise time and how many object can be treated in 24 hours. d - We want to reach a processing rate of 100 objects per 24 hours. Determine the value of K that allow us to meet this objective. What is the phase margin then? What type of corrector should be added to the feedforward loop in order to limit the overshoot at 10% while maintain the desired processing rate