MMAN3200: Linear System and Control - Engineering Assessment Answer

TASK:

Pre-tasks
1. Determine the transfer function G1(s) of the one-tank system where qi is the input and h is the output variable.
2. Determine the transfer function G2C(s) of the two-tank system where qi is the input and h is the output variable.

Experiment
1. Two tanks are connected in a cascade configuration (Figure 2). A step voltage input is applied and h(t) and h2(t) are recorded.
2. A negative feedback loop is applied to the two-tank cascade system such that the input variable is the desired h2FB (Figure 3). The step response h2FB(t) is recorded.
3. In the negative feedback loop system the proportional controller (KFB) is replaced with a PI controller (Figure 4) and the step response recorded.

Tasks
1 Based on the h(t) graph determine the values of A1 and R1. 
2 Based on the h2(t) graph determine the values of A2 and R2. 
3 Based on the h2FB(t) graph determine the value of KFB. Also determine the steady state error of the closed loop system.
4 Assume the two tanks are now connected in series with all parameters being the same as before.
a) Obtain the transfer function of the new system Go(s).
b) Apply a unity gain negative feedback and plot the root locus of the closed loop system.
c) Determine the value of K that results in the optimal behaviour of the system.
d) Explain (in up to 50 words) why you believe that your selection is the optimal one.

5 If the industrial process requires the water level in the second tank to be d, what magnitude of the step input would satisfy this requirement?
6 For the cascade system in figure 2 assume a surge takes place upstream from the first tank after the steady state is established (h2=d). The surge is modelled as an impulse function of magnitude b. Using all parameters defined on Page 2 (that are based on your ID number) find the effect of the surge on h2. Plot h2
vs. time.

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