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im stuck if q1 and 2 where i had to...

Question: im stuck if q1 and 2 where i had to...

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I’m stuck if Q1 and 2) where I had to determine the missing variables please help

Transient Behaviour of First and Second Order Dynamic System Setup: Analogue Circuits OBJECTIVE: To study the time responses of first and second order electrical circuits introduction to general first and second order engineering systems, when they are subiectet inpt. to a step 1. FIRST ORDER SYSTEM 1.1 System Modelling The circuit shown in Fig. 1.1 is an example of a first order system.our wuuKand and It can be described by the following physical equations: Where VR(t) i()R is the voltage drop across the resistor R which depends on the current i(t). The current through the circuit is equal to the current through the capacitor which is given as Here denotes the first derivative with respect to time. Combining the equations results in the linear differential equation Vi 匕 Figure 1.1 an example of the first order system: RC network Its transfer function can be written in the form U(s) V(s) s+α Here Y(s) is the Laplace transform of the system output, y(t), and U(s) is the transform of the input u(C). In general, measuring the output voltage might be associated with some delay caused by the sensor The general form of a first order system with time delay is therefore U(s) ,(s) s+α Here, Id is a time delay

The system in equation (1.2) is therefore denominator) located at s w a. When the transform of the system output will be one which has one real pole (i.e, the root of the TF ystem is subjected to a step input of magnitude V, the is 13) e1 Derive the transfer Aumction of ahis RC mtwork by taking the eqeation (t.) pelating the input V to the output V, and obtain the parameters K and a in equation (2.2) in serms of R amd c The gain of the network for a DC inpt (Ge at sero freqwency) is Fill in the appropriate syabol for in the Moodle Quiz. 2 Apply the Final Value Theorem, which states that to the expression for Y(s) and fAnd the steady-state gain of the system. The steady state gain and the DC gain for a step input are ? Choose the appropriate o ption for ? in the Moodle quiz The inverse Laplace transform of Y() is given by Find the value of y(oo) from the time-domain equation above and confirm that it agrees with your answer obtained in 02. In the circuit studied here K = α-1/r and so y(t) = V[1-e-ar] = V[1-e-t/r] t 20 The response of the system is shown in Figure 1.2. It rises from 0 at the time at which the step input is applied, and inverse-exponentially approaches its final value. y(t) t (ms) Figure 1.2 Step response of the first order system with zero time delay: Note the time constant

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