1. PID control is used to control and maintain processes. It can be used to control physical variables such as temperature, pressure, flow rate, and tank level. The technique is widely used in today’s manufacturing industry to achieve accurate process control under different process conditions.
Write a brief report discussing the role of PID’s in control systems.
3 marks
I. Given the simple mass, spring, and damper problem.
Find
I. The modeling equation of this system (F input, x output).
1 mark
II. The transfer function.
1 mark
Let M = 1 kg b = 10 N s/m k = 20 N/m F = 1 N
III. Find Open-Loop Step Response using Simulink. (Include block diagram and graph in solution)
2 marks IV. From the Open-Loop Step Response, determine.
a) Final Value
b) The steady-state error
c) The rise time.
d) The settling time.
2 marks
V. Design a proportional controller (Kp) to improve the output (Natural frequency 𝜔𝑛=17.89). Show your working out for the transfer function and produce the new block diagram and graph.
3 marks
VI. Compare the two graphs discussing the over-shoot and difference in rise-time, steady-state and settling time.
2 marks
VII. Design a proportional derivative controller (Kds) to improve the output (the damping co-efficient
=0.56 and 𝜔𝑛=17.89). Include the new block diagram and graph in the solution.
4 marks
VIII. Add a new scope in you final block diagram and add a PID gain with the values of Kp and Kd from above.