1. MODELING OF ELECTRICAL SYSTEMS
1st METHOD
Current Law
(Kirchoff)
Voltage Law
2nd METHOD
Current Law
Magnetic Energy, Electrical Energy, Virtual Work:
Application of Lagrange’s Equation
2nd method is used in this course.

2. FUNDAMENTAL ELEMENTS OF ELECTRICAL SYSTEMS
Passive Elements
Active Elements - + L C R
Op-Amp
Analogy Between Mechanical and Electrical Systems . .. x
Displacement
(m)
Velocity
(m/s)
Acceleration
(m/s2) m
Mass
(kg) k
Spring Stiffness
(N/m) c
Damping Constant
(Ns/m) f
Force
(N)
Generalized Coordinates q
Charge
(Coulomb) i
Current
(Amper) L
Inductance
(Henry)
1/C
C:Capacitance
(Farad) R
Resistance
(Ohm) V
Voltage
(Volt) nt
Generalized Charges
Lagrange’s Equation

3. Analogy Between Mechanical and Electrical Systems. .. x
Displacement
(m)
Velocity
(m/s)
Acceleration
(m/s2) m
Mass
(kg) k
Spring Constant
(N/m) c
Damping Constant
(Ns/m) f
Force
(N) . .. θ
Angular Dispalement
(rad)
Angular Velocity
(rad/s)
Angular Acceleration
(rad/s2) IG
Mass moment of inertia
(kg-m2) Kr
Rotational spring constant
(Nm/rad) Cr
Rotational damping constant
Nm/(rad/s) M
Moment
(Nm) q
Charge
(Coulomb) i
Current
(Amper) L
Inductance
(Henry)
1/C
C:Capacitance
(Farad) R
Resistance
(Ohm) V
Voltage
(Volt) E2 E1 E1 E2 δW δW

4. Modeling of Electrical Systems:
Current through R1=
Example 3.1:
V1: Input
q and q2 : Generalized charges L C V1 + - R1 R2 Qq
Qq2
L=3.4 mH, C=286 µF, R1=3.2 Ω, R2=4.5 Ω
D(s)= s s s=0
Eigenvalues: 0, ±418.70i (ξ=0.768)

5. No current flow through Op-Amp
Example 3.2 C1 - + V1 V2 R1 R2 R3 C2
No current flow through Op-Amp
Input : V1
Generalized charges: q1, q2, q3
For Op-Amp : V+=V-=0

6. R1=15.9 kΩ, R2=837 Ω, R3=318 kΩ, C1=C2=0.005 µF
Eigenvalues: 0, ± i (ξ=0.05)

7. V2 R2 - + V1 R1
GAIN CIRCUIT R2 - + V1 R1 V2 R
V2'

8. INTEGRAL CIRCUIT C R V1 V2 - +
Negative sign can be eliminated bu adding an extra gain circuit with gain=1

9. - + V1 Vc R V2 V3 R V2 V1 - + Vc

10. PID circuit is used frequently in Control Systems.- + R1 R4 C4 C3 R3 R V1 V2
PID Control Circuit
PID circuit is used frequently in Control Systems.