ECE 4545: Control Systems Winter 2012
Department of Electrical Engineering,
The University of Lahore, Lahore
Quiz # 2
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1.
a. What pole locations characterize:
i. the overdamped system
ii. the critically damped system
iii. the underdamped system
iv. the undamped system
b. Given the pole locations of a system, how can you find its transient characteristics?
(Hint: relate them with the second order system characteristics)
c. How positive real parts of poles of a system leads to instability?
2. The response of the deflection of a fluid-filled catheter to changes in pressure can be modeled using a second-order model. Knowledge of the parameters of the model is important because in cardiovascular applications the undamped natural frequency should be close to five times the heart rate. However, due to sterility and other considerations, measurement of the parameters is difficult. A method to obtain transfer functions using measurements of the amplitudes of two consecutive peaks of the response and their timing has been developed (Glantz, 1979). Assume that Figure P4.13 is obtained from catheter measurements. Using the information shown and assuming a second-order model excited by a unit step input, find the corresponding transfer function.
3. A common application of control systems is in regulating the temperature of a chemical process (Figure P6.13). The flow of a chemical reactant to a process is controlled by an actuator and valve. The reactant causes the temperature in the vat to change. This temperature is sensed and compared to a desired set-point temperature in a closed loop, where the flow of reactant is adjusted to yield the desired temperature. In Chapter 9, we will learn how a PID controller is used to improve the performance of such process control systems. Figure P6.13 shows the control system prior to the addition of the PID controller. The PID controller is replaced by the shaded box with a gain of unity. For this system, prior to the design of the PID controller, find the range of amplifier gain, K, to keep the system stable.
Figure for Problem No. 2
Figure for Problem No. 3
Rules:
Group work is allowed for this quiz however each member of group must write in his own words and handwriting (or typed).
This is an open material exam.
There will be 4 quizzes in total and result of best 3 will be counted towards final assessment.