Examples Write the transfer function of the electrical

Examples: Write the transfer function of the electrical circuit including Op-Amp (Operational Amplifier). Write the Matlab program to calculate the eigenvalues of the system. R 2 L R 1 + V 1(t) clc; clear a=[120 412 7500]; roots(a) C V 2(t)

Examples: The equation of motion of the system whose mass can be neglected is given as f(t) k c x(t) k=4000 N/m, c=50 Ns/m a) Find the transfer function. b) Find the response to the input in the form of f(t)=40 e-4 t. c) Find the response to the input in the form of f(t)=40 cos(3 t-1). d) Find the response to the input in the form of f(t)=100 e -2 tcos(5 t+1). e) Find the response to the input in the form of f(t)=10δ(t) (Impulse input with magnitude 10 Ns) f) Find the response to the input in the form of f(t)=50 u(t) (Step input with magnitude 50 N) g) Write the form of the exponential input, for which the system works at resonance. a) b)

Examples: c) f(t)=40 cos(3 t-1) s=3 i >>s=3 i; >>hs=1/(50*s+4000) >>gen=abs(hs) >>fi=angle(hs) Img φH Re >>s=-2+5 i; d) f(t)=100 e-2 tcos(5 t+1) s=-2+5 i >>hs=1/(50*s+4000) >>gen=abs(hs) >>fi=angle(hs) Img φH Re

Examples: e) f(t)=10δ(t) f) f(t)=50 u(t) clc; clear num=[1]; den=[1 80 0]; [r, p, k]=residue(num, den) Residue Theorem

Examples: Steady State Value xss=0. 0125 g) Exponential input for resonance; The s value, which makes the denominator of the transfer function zero causes the system resonance. The s value for resonance is s=-80. So, the form of the exponential function for resonance condition is The resonance condition does not depend on the input amplitude A.

Examples: Consider the electrical circuit including Op-Amp. Where v 1 is the input and v 2 is the output a) Find the Laplace transform of the output V 2(s) to a step input with magnitude 12 V. Calculate the steady-state value of the output v 2 ss. b) Write the matlab code to calculate the |H(s)| and φHs for an exponential-harmonic input in the form of v 1(t)=24 e-0. 2 t cos(5 t-0. 2). clc; clear s=-0. 2+5 i; hs=-2500/(120*s^2+412*s+7500); hg=abs(hs) hfi=angle(hs)

Examples: In the calculation procedure of a system response, the result of the Matlab command [r, p, k]=residue(pay, payda) gives the r and p vectors as r=-2+3 i, -2 -3 i, 6, -2 ve p=-4+6 i, -4 -6 i, -3, 0. Find the system response x(t) using the given r and p. Find the steady-state response. Img Re -2 -3 or xss=-2 Steady-state value