Verify systems controllable and observable matricesb

All calculations must be presented within the report. The report should include an introduction, results for each task, a discussion of findings, concluding statements and references. For each task, a proper description of the methodology is expected. For example, during block simplification, it is important to outline the process undertaken.

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Report Marks Allocated
Derivation, analysis and calculations 90%
Report presentation, discussion and references 10%

Pumped Storage Flow Control System:
In this system, water is drawn off to supply a turbine to produce electrical power. The amount of water flow (Qo), depends upon the fluctuating electrical power requirements of the turbine and generator. The water is supplied to the storage tanks from a secondary water supply. The two storage tanks are connected together through a shut-off valve, which may be modelled as a linear resistance R1. The resistance of the turbine supply pipe may be modelled as a linear resistance R2.

System Modelling
Given the following data to the system:
The cross sectional area of tank 1and tank 2 is 1 (m2). The linear resistance have the values R1 = 0.5 s/m2 and R2 = 0.5 s/m2

b)Plot H1, (t) and H2 (t) of part (a) versus t and comment on the qualitative differences.

c)Obtain the plot H1, (t) and H2 (t) when Qi (t)=0 and the initial conditions are H1(0) = 10 and H2 (0)= 0

Proportional control

Problem 4 –Stability analysis (15%)

b)For the proportional controller gain K>0, plot the root locus diagram for the feedback control system of

Figure 3. [4 marks]

Pole placement design

Problem 5 (20%)

input. [5 marks]

Discrete time system

qi(k)
	T =0.1s

Figure 4

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