M = 30kg
K = 800N/m
Kd = 200 Ns/m

Make reasoned assumptions where necessary

1. The suspension system above has been resolved into its key components which are regarded as a perfect spring with a spring stiffness. k, a perfect damper with a damping coefficients of IQ, and an equivalent mass, M.

Use fundamental principles to derive a mathematical model for the above circuit?

2. Show how the model can be manipulated into the form of the standard re order transfer function in terms of time constant and damping ratio. Derive subsidiary models for system constants?

3. For the system derived above design an equivalent electrical model with the same response characteristics as the mechanical system with a force of 150 Newtons suddenly applied.

4. With a unit step change applied to the input, produce a graph of the output response in the time domain using an appropriate scale to show response time?

Comment on the graph?

5. Design a compensator using a combination of lead, lag. proportional, Integral or derivative control that you consider appropriate to minimise overshoot and settling time.

6. Determine some compensator system constants then, using your controller in series with the process, show how the controlled system responds in comparison to the uncontrolled system? Comment on your controlled system response?