Answer Happy

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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 do dae = 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? + 2000 dt? 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.