AMA COMPUTER COLLEGE SANTIAGO CAMPUS

ACTIVITY #3

TRANSFER FUNCTION

Group 3 Course

Mart Dave Cayaban BSCOE/BSECESheena Jane MiguelWynner Ronn Silva

July 29, 2013 Subject: EENG03

I.INTRODUCTION1.TRANSFER FUNCTION - ATransfer Functionis the ratio of the output of a system to the input of a system, in the Laplace domain considering its initial conditions and equilibrium point to be zero. If we have an input function ofX(s), and an output functionY(s), we define the transfer functionH(s)to be:[Transfer Function]

Readers who have read theCircuit Theorybook will recognize the transfer function as being the impedance, admittance, impedance ratio of a voltage divider or the admittance ratio of a current divider.

2. SYSTEM RESPONSE- The order of a system is defined as being the highest power of derivative in the differential equation, or being the highest power of s in the denominator of the transfer function. A first-order system only has s to the power one in the denominator, while a second-order system has the highestpower of s in the denominator being two.

Types of the input functions (or test input signals) commonly used are: Impulse function: In the time domain, u(t) = cd(t). In the s domain, U(s) = c. Step function: In the time domain, u(t) = c. In the s domain, U(s) = c/s. Ramp function: In the time domain, u(t) = ct. In the s domain, U(s) = c/s2. Sinusoidal function: In the time domain, u(t) = csin(wt). In the s domain, U(s) = cw/(s2+w2).It is a primary function of control engineering to establish the response of the system to a particular input.. Considering a step input of xi= xa.. applied from time t = 0. It can be proved that the response of the system =xo= xa(1-cosn.t )....By makingn2= (k1k2)/M

Note: In reality the actual mass would not oscillate but would tend to stop due to friction forces within the system.Assuming zero or low friction the reponse is clearly unacceptable. The ideal response is for the system to rapidly move to the required position xa.This can be conveniently achieved by introducing additional damping to the system.Damping is included by attaching a viscous damper to the mass.This damping would introduce a Force (Fd) which is proportional the velocity of the mass. Fd= - C.Dxowhere C is the damping factor.II.PROBLEMS1.

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d. PLOT THE IMPULSE REPONSE CURVE

1. s=poly(0,'s')num= 1;den=s+2;xs=syslin('c',num/den);t=-8:.1:8;xt=csim('impulse',t,xs)plot2d(t,xt)

2. s=poly(0,'s')num=(4*(s^3))+(4*(s^2));den=(4*(s^3))+(12*(s^2))+(10*s)+2;xs=syslin('c',num/den);t=-8:.1:8;xt=csim('impulse',t,xs)plot2d(t,xt)

PLOT THE UNIT STEP RESPONSE CURVE

1. s=poly(0,'s')num=1;den=s+2;xs=syslin('c',num/den);t=-8:.1:8;xt=csim('step',t,xs)plot2d(t,xt)

2. s=poly(0,'s')num=(4*(s^3))+(4*(s^2));den=(4*(s^3))+(12*(s^2))+(10*s)+2;xs=syslin('c',num/den);t=-8:.1:8;xt=csim('step',t,xs)plot2d(t,xt)