JNTU
JNTU B.Tech III CONTROL SYSTEMS ENGINEERING Previous Question Paper (September - 2021 - R13)
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Compare and contrast the open loop and closed loop system with examples.
Answer
An open-loop control system is one where the control action is independent of the output. It does not have feedback, making it simple, inexpensive, and stable, but it is highly sensitive to external disturbances and parameter variations. An example is an electric toaster, where the heating duration is fixed regardless of the actual browning of the bread.
A closed-loop control system, or feedback control system, continuously compares the output with the desired input to generate an error signal that adjusts the control action. This provides higher accuracy and better disturbance rejection, though it is more complex, costly, and prone to instability. An example is an air conditioning system with a thermostat, which adjusts cooling based on the actual room temperature.
Write differential equations governing the rotational mechanical system for the following figure and also draw force current analogous circuit.
Answer
For a rotational mechanical system with moment of inertia J, damping coefficient B, and spring constant K, the governing differential equation is derived from D'Alembert's principle, where the sum of torques equals zero:
To draw the force-current analogy, we map mechanical variables to electrical variables as follows: Torque (T) to Current (i), Angular velocity (ω = dθ/dt) to Voltage (v), Moment of Inertia (J) to Capacitance (C), Damping (B) to Conductance (1/R), and Spring stiffness (K) to Inverse Inductance (1/L).
The resulting electrical circuit is a parallel RLC circuit where:
- The current source i(t) is in parallel with a capacitor C (representing J).
- A resistor R (where R = 1/B) is in parallel.
- An inductor L (where L = 1/K) is in parallel.
The node voltage v(t) in this circuit corresponds to the angular velocity ω(t) of the mechanical system.
Convert given block diagram in figure to signal flow graph and determine the transfer function using Mason’s gain formula.
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Consider given following figure, determine the overall transfer function using block diagram technique.
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For unity feedback system having open loop transfer function as G(s) = K(s+1) / [s^2(s^2+7s+12)]. Determine position, velocity and acceleration error coefficient.
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Find out, the K and T values of closed system as shown in figure so that the maximum overshoot in unit step response 25.6% and peak time is 3 sec. and assume J = 0.01 Kg-cm^2.
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Describe the significance of PI controller on the performances of system in detailed.
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The system response having unit step input as C(t) = 1 + 0.2e^(-60t) - 1.2e^(-10t). Determine the expression for closed loop transfer function, undamped natural frequency and damping ratio of the system.
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Draw the Root locus of unity feedback system having forward path transfer function G(s) = K / [s(s+1)(s+5)].
Determine the K value that gives continuous oscillation.
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Determine the K value corresponding to dominate closed loop with damping ratio is 0.7.
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A unity feedback control system is represented by the open loop transfer function G(s) = K(s+10) / [s(s+3)(s+7)].
Using Routh criterion, obtain the range of value of K for the system to be stable.
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Identify if K=1, all these roots of the characteristic equation of the system having damping factor greater than 0.5.
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The open loop transfer function having unity feedback system is given below. Sketch the Nyquist plot and determine the stability of the system. G(s) = K(s+5)(s+40) / [s^3(s+1.5)(s+100)].
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The linear continuous time plant of a system is given by the state equation: x' = Ax + Bu. Find the state transmission matrix.
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Explain the concepts of controllability and observability applied to linear continuous time control systems.
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