EC209: Control System - Voltage Source - Engineering Assignment Help

Assignment Task :

In all the following problems circuit elements value can be used from the following set: Resistor: 4.7 kΩ, 10 kΩ, 22 kΩ, Inductors: 2 mH, 5 mH, Capacitors: 10μF, 100 μF, DC voltage source: 10V, battery potential 5V, DC current source 0.5 A, Sinusoidal source with peak value 10 V, frequency variations from 10 Hz to 100 kHz. 

Parameter variations can be applied or chosen as per the relevant nature of the analysis. Sketch all necessary informative sketches. Results manifested either in tabular or graphical form must be accompanied with an analytical note. 

P1. An electric circuit is shown in Fig. below. Derive the appropriate differential equation model and also get a valid state-space representation of the same. In such system how you would differentiate the state equations from the output equations. 

P2. A control system is described in terms of its impulse response, h(t) and the associated transfer function, H(s), where H(s) comprises of 2 finite zeros at s = -0.8 and at s = -1.25 and three poles at locations s= -2 and s = -1.5±2j. The impulse response is delayed by an arbitrary time t= 5 seconds and also get switched on at the same instant, t = 5seconds. Analyse the transfer function of delayed and switched response while uncovering stability aspects, DC gain and impact driven by pole-zero addition/deletion. 

P3. In state-space methods; how you look at the notion of linearity and how you would analyse the zero state concept. At an arbitrary time, t = t0, find the zero state vector for the circuit shown below. How the zero state vector will vary for arbitrary time selection of parameter t0 as t0 = 5 seconds and 10 seconds.

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