Lecture 5 September 8 PDF

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ECE 3353 Feedback Control Systems Lecture 5: Modeling of Mechanical Systems Fall 2020

Vittal S. Rao Electrical and Computer Engineering Texas Tech University September 8, 2020

Transfer Function • Modeling of Physical systems in Frequency Domain Input R(s)

Output C(s)

• Order of system = n = No. of Energy Storage Element • We evaluated the transfer function of circuit by writing governing equations using KVL or KCL • We develop a transfer function to mechanical systems

Summary of Variables • Summary of Through and Across variables of physical systems System

Through Variable

Across Variable

Electrical

Current (i)

Voltage Difference

Mechanical Translation

Force (F)

Velocity Difference (v)

Fluid

Volumetric rate flow (Q)

Pressure difference

Thermal

Heat Flow (q)

Temperature Difference

Mechanical Systems • Governing Differential Equations for Ideal Elements Element Translational Mechanical Energy Dissipater (Damper)

Inductive storage (spring)

Capacitive storage (Mass)

Rotational

Mechanical Systems • Modeling of Translational Mechanical Systems • Define positions, write directional sense for each mass in the system • Draw free body diagram for each of the masses, expressing the forces on them, in terms of mass positions • Write an equation for each mass, equating the algebraic sum of forces acting on them to zero

Example 1

Free Body Diagram

Transfer function between force and displacement

Example 2 • Examples

Free Body Diagram

Example 2 • Governing Equations • Mass 2

• Mass 1

Example 2

Example 3 • Problem 3 Free body diagram

Example 3

Example 4

Free body diagram: (Assuming input force=Y)

Example 4

Example 4

Example 5

Free body diagram:

Example 5

Example 6

Free body diagram:

Example 6

Example 6

Electromechanical Systems

Mechanical Systems

Electromechanical Systems

Electro-Mechanical-Hydraulic Systems

Governing Equations

Governing Equations

Governing Equations

Governing Equations

Block Diagram...