undefined | unit 1 modelling of systems

Unit-1Modelling of Systems Q1) Compare open and closed loop control systems?
A1)

Open Loop System	Closed Loop system
1.It does Not have any feedback.	1. This system comprise of feedback
2.As no feedback so easier to build.	2.As it has feedback so difficult to build
3.Theaccuracy of this system depends on the calibration of input.	3.They are accuracy because of the feedback.
4.Open Loop system are more stable.	4.In closed Loop system stability depends on system components.
5.optimization is not possible	5. optimization is possible
6.These systems are not reliable.	They are more reliable

Q2) What are positive feedback systems?A2)

Fig 1 Closed Loop control systemIn positive feedback systems the feedback signal is added to the input signal. The positive feedback is used only in oscillators. The transfer function is given asC(s)/ R(S) = G(s)/ 1-G(S) H(S) Q3) Draw the free body diagram and write the differential equation for system below.

A3) The free body diagram for M1 will be

F(t) = M1 d2/dt2x1+ B1 d/dt (x1-x2) + k1(x1-x2)

Similarly, for M2we have

K1(x1-x2) + B1d/dt(x1-x2) = k2x2+M2d2/dt2+B2dx2/dt

Q4) Find V0(s)/Vi(s)?A4) Let Z1 = R2 11 1/c2

=R2*1/c2s/R2+1/c2s

Z1= R2/1+R2c2s

Let Z2 = R1+1/c1s

Z2= 1+R1c1s/c1s

V0(s)/vi(s) = z2/z1+z2

= 1+R1c1s/c1s/R2/1+R2c2s+1+R1c1s/c1s

V0(s)/v0(s) =(c1+R1c1s) (1+R2c2s)/R2c1s+1+sR1c1s2R1R2c1c2

Q5) Explain force-voltage analogy?A5) If the dynamic characteristics of an electrical system is identical to that of a mechanical system, then the electrical system is said to be analogous to the mechanical system. This can be done by comparing the mathematical models of both the systems.

Fig 2 Mechanical SystemThe equation for above mechanical system is given byf(t) = M

+kx (1) For series RLC circuit the mathematical equation is given as

Fig 3 Electrical System V(t)= Ri + L

i =

V(t) = L

+ R

(2)Comparing 1 and 2 we see that

F(t) v(t)

x q

M L

B R

Q6) Explain force-current analogy?A6) For parallel RLC circuit shown below the KCL equation is written as

Fig 4 Electrical Circuiti(t) = C

v =

i(t) = C

+ R

(3) Comparing 1 and 3 we find that

F(t) i(t)

M C

B 1/R

k 1/L Q7) What is friction and how it is useful for physical systems?A7) The friction exists in physical systems whenever mechanical surfaces are operated in sliding contact. The friction can bei) Coulomb Friction Force: This is the force of sliding friction between dry surface and is normally constant.ii) Viscous Friction Force: The force between a ansid body and a fluid medium is called as viscous friction force.iii) Stiction: The force required to initiate motion between two contacting surfaces. The frictional force acts in opposite direction to that of velocity. Sometimes friction is necessary in the physical system in order to improve the dynamic response of the system. Q8) What are feedforward and tracking systems?A8)Feedforward System:The feedback system is which work to reduce the error it’s the system. In some system where the disturbances input can be provided beforehand, its effect can be eliminated by feedforward system. Tracking System:The main objective of such system is to trace any particular location as direction of a targeted value on continuous basic. The basic examples of tracking, Range tracking, Tracking in phased array radars. Q9) What are control systems explain with block diagram?A9) A control system is a set of mechanical or electronic devices which control the other devices. In control system behaviours of the system is desired by differential equation.

Fig 5 Block diagram for closed loop control systemThe above figure shows a feedback system with a control system. The components of control system are:

The actuator takes the signal transforms it accordingly and causes some action.

Sensors are used to measure continuous and discrete process variables.

Controllers are those elements which adjust the actuators in response to the measurement.

Q10) Explain D’Alembert’s Principle?A10) For anybody, the algebraic sum of externally applied forces and the forces resisting motion in any given direction is zero.Ex.

Fig 6 Mechanical System In above figure applying D’Alembert’s principle to write the equation of motion As force f(t) acts downwards all other forces (of k, B, x) acts Opposite to it considering f(t) as the and all other forces negative.F(t)+fm (t) + fD(t) +fx(t) =0f(t)- M d2x(t)/dt2+B dx(t)/dt +x(t)

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