Download to read offline
Uploaded byKALPANA K
Electrical analogous of mechanical translational system
This document discusses electrical analogies of mechanical translational systems. There are two types of analogies: force-voltage and force-current. Force-voltage analogy models mechanical equations as electrical mesh equations. Force-current analogy models mechanical equations as electrical node equations. Two example problems are presented to illustrate drawing the analogous electrical circuits and verifying with mesh/node equations. Homework is assigned to practice drawing and verifying additional analogous circuits.
In this document
Powered by AI
Introduction of the course IC 8451 & Control Systems by Arasu Engineering College, Department of Electrical and Electronics Engineering.
Discussion of electrical analogies for mechanical systems includes force voltage and force current analogies with corresponding elements.
Examples illustrating the formulation of differential equations and the drawing of electrical analogous circuits for mechanical systems.
Detailed free body diagrams of mechanical systems showing opposing forces for M1, M2, and M3.
Formulation of mesh and node equations for force voltage and force current analogous circuits along with a homework assignment.
More Related Content
Similar to Electrical analogous of mechanical translational system
Electrical analogous of mechanical translational system
- 1. IC 8451&CONTROL SYSTEMS Departmentof Electrical and Electronics Engineering Approved by AICTE | Affiliated to Anna University | Accredited by NAAC | Accredited NBA | Recognized by UGC under 2(f) and 12(B) Chennai Main Road, Kumbakonam- 612 501. ARASU ENGINEERING COLLEGE 1
- 2. ARASU ENGINEERING COLLEGE IC 8451&CONTROL SYSTEMS 2 Preparedby Mrs.K.Kalpana.,M.E.,(Ph.D)., Department of Electrical and Electronics Engineering
- 3. ARASU ENGINEERING COLLEGE IC 8451&CONTROL SYSTEMS 3 Electrical Analogous of mechanical translational systems There are two types of electrical analogies of translational mechanical systems. Those are force voltage analogy and force current analogy. Force Voltage Analogy In force voltage analogy, the mathematical equations of translational mechanical system are compared with mesh equations of the electrical system. Translational Mechanical System Electrical System Force(F) Voltage(V) Mass(M) Inductance(L) Frictional Coefficient(B) Resistance(R) Spring Constant(K) Reciprocal of Capacitance (1/c) Displacement(x) Charge(q) Velocity(v) Current(i)
- 4. Force CurrentAnalogy In force current analogy, the mathematical equations of the translational mechanical system are compared with the nodal equations of the electrical system. ARASU ENGINEERING COLLEGE IC 8451&CONTROL SYSTEMS 4 Translational Mechanical System Electrical System Force(F) Current(i) Mass(M) Capacitance(C) Frictional coefficient(B) Reciprocal of Resistance(1/R) Spring constant(K) Reciprocal of Inductance(1/L) Displacement(x) Magnetic Flux(ψ) Velocity(v) Voltage(V)
- 5. Analogous elementsin Force voltage analogy ARASU ENGINEERING COLLEGE IC 8451&CONTROL SYSTEMS 5
- 6. ARASU ENGINEERING COLLEGE IC 8451&CONTROL SYSTEMS 6 Analogouselements in Force current analogy
- 7. ARASU ENGINEERING COLLEGE IC 8451&CONTROL SYSTEMS 7 EXAMPLE PROBLEM 1 Write the differential equations governing the mechanical system shown in fig. Draw the force voltage and force current electrical analogous circuits and verify by writing mesh and node equations. The free body diagram of M1 is shown in fig. The opposing forces are fm1,fb1,fb12,fk1
- 8. The freebody diagram of M1 is shown in fig. The opposing forces are fm2,fb2,fb12,fk1 and fk2 ARASU ENGINEERING COLLEGE IC 8451&CONTROL SYSTEMS 8
- 9. Force voltageanalogous circuit The electrical analogous elements for the elements of mechanical systems are f(t) - e(t) , M1- L1, M2- L2, B1- R1, B2- R2 ,B12- R12, K1-1/C1, K2-1/C2 The mesh equations are Force -voltage analogous circuit ARASU ENGINEERING COLLEGE IC 8451&CONTROL SYSTEMS 9
- 10. Force currentanalogous circuit The electrical analogous elements for the elements of mechanical systems are f(t) - i(t) , M1- C1, M2 -C2, B1-1/R1, B2-1/R2 ,B12-1/R12, K1-1/L1, K2-1/L2 The node equations are ARASU ENGINEERING COLLEGE IC 8451&CONTROL SYSTEMS 10
- 11. Force currentanalogous circuit ARASU ENGINEERING COLLEGE IC 8451&CONTROL SYSTEMS 11
- 12. EXAMPLE PROBLEM2 Write the differential equations governing the mechanical system shown in fig. Draw the force voltage and force current electrical analogous circuits and verify by writing mesh and node equations. ARASU ENGINEERING COLLEGE IC 8451&CONTROL SYSTEMS 12
- 13. The freebody diagram of M1 is shown in fig. The opposing forces are marked as fm1, fb1, and fk1, fk2 ARASU ENGINEERING COLLEGE IC 8451&CONTROL SYSTEMS 13
- 14. ARASU ENGINEERING COLLEGE IC 8451&CONTROL SYSTEMS 14 Freebody diagram of M2 is shown in fig. The opposing forces are marked as fm2 , fb3, fk2 & fk3.
- 15. ARASU ENGINEERING COLLEGE IC 8451&CONTROL SYSTEMS 15 Thefree body diagram of M3 is shown in fig. The opposing forces are marked as fm3, f b3 and fk3
- 16. ARASU ENGINEERING COLLEGE IC 8451&CONTROL SYSTEMS 16 FORCEVOLTAGE ANALOGOUS CIRCUIT MESH EQUATIONS
- 17. ARASU ENGINEERING COLLEGE IC 8451&CONTROL SYSTEMS 17 FORCEVOLTAGE ANALOGOUS CIRCUIT FORCE CURRENT ANALOGOUS CIRCUIT
- 18. ARASU ENGINEERING COLLEGE IC 8451&CONTROL SYSTEMS 18 NODEEQUATIONS FORCE CURRENT ANALOGOUS CIRCUIT
- 19. ARASU ENGINEERING COLLEGE IC 8451&CONTROL SYSTEMS 19 HOMEWORK PROBLEM Write differential equations governing mechanical system shown in fig. Draw force voltage and force current electrical analogous circuits and verify by writing mesh and node equations.