AMIE Study Circle

Comment on the stability of a control system whose characteristic equation is given b: \({s^5} + 24{s^4} + 24{s^3} + 48{s^2} - 25s - 50 = 0\) (AMIE Summer 2021) Solution s 5 1 24 -25 s 4 2 48 -50 s 3 a = 0 b = 0   s 2       s 1       s 0       \(\begin{array}{l}a = \frac{{1x48 - 24x2}}{2}\\b = \frac{{1x( - 50) - ( - 25x2)}}{2}\end{array}\) If all elements in a row are zero, then differentiate the coefficients of the above row. \(\begin{array}{l}\frac{{d(2{s^4} + 48{s^2} - 50)}}{{ds}}\\ = 8{s^3} + 96s\end{array}\) s 5 1 24 -25 s 4 2 48 -50 s 3 a = 0 (8) b = 0 (96)   ...

In a test on a Bakelite sample at 20 kV, 50 Hz by a Schering bridge, having a standard capacitor of 106 pF, balance was obtained with a capacitance of 0.35 pF in parallel with a non-inductive resistance of 318 ohms, the non-inductive resistance in the remaining arm of the bridge being 130 ohms. Determine the capacitance, the p.f. and equivalent series resistance of the specimen.    (AMIE Winter 2019, 2020, 10 marks)   \(\begin{array}{l}{C_2} = {C_1}\frac{{{R_4}}}{{{R_1}}} = 106x\frac{{318}}{{130}}\\ = 259.3\,pF\\r = {R_3}\frac{{{C_4}}}{{{C_1}}} = 130x\frac{{0.35x{{10}^{ - 6}}}}{{106x{{10}^{ - 12}}}}\\ = 0.429\,M\Omega \\pf\, = \,\omega r{C_2} = (2\pi x50)x0.429x{10^6}x259x{10^{ - 12}}\\ = \,0.035\end{array}\)   A 250-V 10-A dynamometer type wattmeter has resistance of current and potential coils of 0.5 and 12,500 ohms respectively. Find the percentage error due to each of the two methods of connection when unity p.f. loads at 250 volts are of (a) 4A (b) 12 A. Neglect...

Choose the correct answer for the following (10 x 2) 1. A system has the transfer function  . What will be the nature of its unit step response? (a) overdamped (b) underdamped (c) undamped (d) critically damped 2. A unity feedback system has its open-loop transfer function as  . What will be the range of which system will be stable? (a) 21/4 > K > 0 (b) 13 > K > 0 (c) 21/44 < K < ∞ (d) -6 < K < ∞ 3. Find out the breakaway and break-in points for the transfer function  (a) 0, -0.634 (b)  0, -2.366 (c) -2 + √2, -2 - √2 (d) -0.634, -2.366 4. For type-1 plant, with step and ramp inputs, the steady-state errors, are, respectively: (a) 0, 0 (b) 0, finite (c) finite, finite (d) finite, infinite 5. Increase in a gain of the proportional controller results in (a) increase in peak overshoot, decrease in peak-time. (b) decrease in peak overshoot, increase in peak time. (c) increase in both peak; overshoot and peak time. (d) decrease in both peak ove...

Answer the following questions (2 x 10) What is the effect of the addition of a zero to the forward path transfer function? The effects of the addition of zeros are as follows: There is a change in the shape of the root locus and it shifts towards the left of the s-plane. The stability of the system is enhanced. Range of K increases. Setting time speeds up. What correlation exists between time domain and frequency domain specification? The performance of a control system is normally measured in terms of its time-domain characteristics. It may equally be measured in frequency-domain since there are correlations between the frequency-domain and time-domain performances in a linear system so that the time-domain properties of the system can be predicted based on the frequency-domain analysis. Besides, the frequency domain approach provides an alternative perspective to the complex analysis and design problems of linear control systems in addition to the time-domain studies. The frequency-...

Answer the following in brief (2 x 10) What is the difference between linear and nonlinear systems? A control system is known as linear if it satisfies the additive property as well as the homogeneous property. Additive Property : If x and y belong to the domain of the function f, we can write f(x + y) = f(x) + f(y) Homogeneous Property: For any x belonging to the domain of the function f and for any scalar constant α, we can write f(αx) = αf(x) The principle of superposition is a combination of the above two properties. If a function satisfies the above two properties, it is said to be linear in nature. If f(x) = x 3 , it is obvious that f(x + y) = (x + y) 3  ≠ x 3  + y 3  and f(αx) = (αx) 3  = α 3 x 3  # α(x) 3 . Therefore the function f(x) = x 3  is non-linear. Explain the working standards in the measurement system. Working Standards Working standards are the principal tools of a measurement laboratory. They are used to check laboratory instruments for...

(A) Choose the correct answer: 2 x 5 1. The transfer function of a system is G(s) = 10/(1 + s). The steady-state error to unit step input when operated at unity feedback system is  (a) 10  (b) 0 (c) 1/11 (d) 10 2. Sphere gaps are used for the measurement of  (a) Instantaneous values of voltage (b) r.m.s. values of voltage (c) Peak values of voltage (d) Overage values of voltage 3.  The inductance of low Q can be measured by using (a) Schering Bridge (b) Anderson’s Bridge (c) Hay’s Bridge (d) De Sauty’s Bridge 4. An average responding rectifier type electronic ac voltmeter has its scale calibrated in terms of the RMS value of a sine wave. If a square wave voltage of peak amplitude of 100 V is measured using this voltmeter, what will be the reading indicated by the meter? (a) 200V (b) 100 V (c) 111 V (d) 100√2V 5. The given block diagram is equivalent to (a)  (b)  (c)  (d)  Answers 1. (c)  2. (c) a spark gap can be used for measurem...

Short answer type (2 x 4) Find the dimension of Torque in the SI unit of the M, L, T, I system. Dimension formula of torque = dimension formula of force X dimension formula of length [MLT -2 ][L]=[ML 2 T -2 ] Find the equivalent resistance of series connected two resistances R₁ = 40 ± 2% and R₂ = 60 ± 3%. R 1  + R 2  = 40 ± 2 + 60 ± 3 = 100 ±5% Write the type and order of a system whose transfer function is given by Order of the system can be defined as the value of the highest exponent that appears in the denominator of the transfer function. (Total number of poles). In the given expression highest exponent is 3. Hence the order of the system is 3. Find the no. of significant figures in  (a) 0.0012 (b) 12.00 (c) 1200 (d) 12 0.0012 has 2 significant figures. 12.00 has 4 significant figures. 1200 has 2 significant figures.  12 has 2 significant figures.  Significant figures are the digits of a number that are meaningful in terms of accuracy or precision. They inc...

Answer the following in brief (2x10) What do you understand by magnetic potential and how it is measured? the scalar quantity characteristic of a point in a magnetic field whose negative gradient equals the intensity or strength of the magnetic field and which represents the work required to bring a unit north pole from a point infinitely remote up to the point in question A tangent galvanometer is an absolute instrument, justify your answer. Absolute instruments provide the quantity to be measured in terms of the instrument constant and its deflection. For example, a tangent galvanometer gives the value of the current to be measured in terms of the tangent of the angle of deflection produced, the horizontal component of the earth’s magnetic field, the radius, and the number of turns of the wire used. Such instruments are used in laboratories and in similar institutions as standardizing instruments. Write the restoring torque equation for the gravity control instrument. When the coil i...