UFMFV7-15-2: You have been Engaged as a Control Engineering Consultant to Design a System for a Pumped Storage: Control Assignment, UWE, Singapore

Coursework Objectives

You have been engaged as a control engineering consultant to design a system for a pumped storage flow control system. You will be expected to: work alone and will submit a formal report including the MATLAB code or SIMULINK.

• Derive the linear time-invariant (LTI) differential equations for the system.
• Obtain the system’s response to a unit step input with and without initial conditions.
• Determine the state-space model and the transfer function of the system.
• Analysis of the system’s stability using MATLAB functions or SIMULINK.
• Design a state feedback controller to meet or exceed the response requirements.
• Obtain a discrete-time model and design a state observer for the system.

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 modeled as a linear resistance R1. The resistance of the turbine supply pipe may be modeled 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

Qo , Qi ,Q = Volume flow rate (m3/sec)
A1, A2 = Cross sectional areas of the storage tank (m2)
R1, R2 = Proportionality constants of flow resistance (sec/m2)
H1, H2 = The height of the water level (m)

Q = (1/R) h ΔQ =A(Δh)

Proportional control

Problem 4 –Stability analysis

Figure 3 shows the proportional system with a unity feedback control loop. The demand flow (qd) would be set by a potentiometer having a unity gain. A variable gain K allows some adjustment to the system performance.

1. Find using the Routh array, the range of values of the gain K for the closed-loop system to be stable.
2. For the proportional controller gain K>0, plot the root locus diagram for the feedback control system of Figure 3.
3. Determine the controller gain K;, for a unit step input the output response Qo (t) has a damping ratio of 0.8 and the maximum overshoot 1.48%.

Pole placement design

Problem 5

1. Determine the controllability and observability of the plant.
2. Design a state feedback controller with the desired closed loop poles location at s = -5 + 2.23i, s = -5 2.23i.
3. Determine the closed-loop transfer function. Simulate the closed-loop response to a unitary step function input.                                                                   

Discrete-time system

Problem 6

4. Obtain the discrete transfer function G(z) by taking the z-transform of G(s) when it connected as shown in Figure 4.
5. Find the state space representation in a controllable canonical form for the discrete system.
6. Design a full order identity observer to place the desired observer poles at z = -15 and z = -15.