control system theory and applications

An electrical heater of heat capacity Ch connected via a thermal resistance Rho to the oven, heat capacity Co. The oven loses heat to the environment, at temperature Te, through the thermal resistance Ro of its insulation. The temperature controller adjusts the power dissipated in the heating elements, W, by comparing the oven temperature, To, with the set-point temperature Ts. Deliverables 1- Get the response of the system vs. Step function and calculate system parameters such as steady state error, Overshoot, Settling time and Rise time. 2- Comparing to a second order system what is the natural frequency of the system what is the damping ratio. What kind of system is it? (underdamped, overdamped, critically damped) 3- Try to apply the following controllers: A) Proportional only B) Proportional and Derivative (PD) C) Proportional and Integrating (PI) D) Proportional and Integrating and Derivative. (PID) Show the plot of the time response and discuss the effects on the system parameters. ( i.e. steady state error, Overshoot, Settling time and Rise time.) 4- Draw the Pole and Zero map and discuss stability? Is the system stable? 5- Apply Routh-Horwitz criterion to find the suitable range of values for Kp (proportional value gain) in order for the system to be stable. 6- Plot the Routh-Locus and discuss the effects of changing Kp on system poles. 7- Draw the Bode plots and find Phase and Gain margin.