Analogous system 4
- 1. OUTLINE Introduction to Analogous System. Force-Voltage Analogy. Force-Current Analogy. Example on Analogous System. Mechanical Equivalent Network. SYED HASAN SAEED 1
- 2. ANALOGOUS SYSTEM Apply KVL in Series RLC Circuit aaanna SYED HASAN SAEED )2( 1 )1( 1 2 2 q Cdt qd L dt dq RE or idt Cdt di LRiE 2
- 3. Consider parallel RLC circuit and apply KCL SYED HASAN SAEED )4( 1 )( 1 , )3( 1 2 2 dt d C Ldt d R I dt d EEdt dt dE CEdt LR E I 3
- 4. We know the equation of mechanical system Compare equation(5) with equation(2) FORCE –VOLTAGE ANALOGY (f-v) SYED HASAN SAEED )5()( )()( )( 2 2 tKx dt tdx B dt txd MtF S.NO. TRANSLATIONAL SYSTEM ELECTRICAL SYSTEM 1. Force (F) Voltage (E) 2. Mass (M) Inductance (L) 3. Stiffness (K), Elastance (1/K) Reciprocal of C, Capacitance (C) 4. Damping coefficient (B) Resistance (R) 5. Displacement (x) Charge (q) 4
- 5. Compare equation (5) with equation (4) FORCE-CURRENT ANALOGY SYED HASAN SAEED S.NO. TRANSLATIONAL SYSTEM ELECTRICAL SYSTEM 1. Force (F) Current (I) 2. Mass (M) Capacitance (C) 3. Damping coefficient (B) Reciprocal of resistance (1/R) i.e conductance (G) 4. Stiffness (K), Elastance (1/K) Reciprocal of inductance (1/L) 5. Displacement (x) Flux linkage (φ) 6. Velocity Voltage (E) x 5
- 6. For rotational system Torque-voltage (T-V) analogy Compare equation(2) with equation (6) SYED HASAN SAEED 6 )6()( )()( )( tK dt td B dt td JtT S.NO. ROTATIONAL SYSTEM ELECTRICAL SYSTEM 1. Torque (T) Voltage (E) 2. Moment of inertia (J) Inductance (L) 3. Damping coefficient (B) Resistance (R) 4. Stiffness (K), Elastance (1/K) Reciprocal of capacitance (1/C). Capacitance (C) 5. Angular displacement (θ) Charge (q) 6. Angular velocity (ω) Current (I)
- 7. Compare equation (4) with equation (6) TORQUE(T)-CURRENT (I) ANALOGY SYED HASAN SAEED 7 S.NO. ROTATIONAL SYSTEM ELECTRICAL SYSTEM 1. Torque (T) Current (I) 2. Moment of inertia (J) Capacitance (C) 3. Damping coefficient (B) Reciprocal of resistance (R), conductance (G) 4. Stiffness (K), Elastance (1/K) Reciprocal of inductance (1/L) 5. Angular displacement (ω) Flux linkage (φ)
- 8. Draw the analogous electrical network of the given fig. using f-v analogy SYED HASAN SAEED 8
- 9. MECHANICAL EQUIVALENT NETWORK PROCEDURE TO DRAW THE MECHANICAL EQUVALENT NETWORK: Step 1: Draw a reference line. Step 2: Corresponding to the displacement x1 x2 ….select the nodes. Step 3: Connect one end of masses to the reference line Step 4: Connect other elements of the system to the nodes. Step 5: Apply nodal analysis, write the system equations. SYED HASAN SAEED 9
- 10. Example: Draw the mechanical network of the given system SYED HASAN SAEED 10
- 11. THANK YOU FOR YOUR ATTENTION SYED HASAN SAEED 11