Me330 lecture7
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This document discusses control systems and summarizes key concepts from lecture 7: 1) Electronic systems have high input impedance, low output impedance, and high gain due to operational amplifiers. Op-amps provide feedback and different impedance terms in example circuits. 2) Electrical and mechanical systems can be combined. Lorentz force and Faraday's law relate current, magnetic fields, and motion in devices like DC servomotors. 3) Transfer functions describe the input-output behavior of electrical, mechanical, and combined electro-mechanical systems. The overall transfer function is derived by substituting Lorentz and Faraday equations into the individual system transfer functions.
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This document discusses modeling mechanical systems for control systems. It covers:
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1. The document discusses different cases for taking the inverse Laplace transform of a function F(s), depending on the characteristics of the denominator of F(s).
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This document discusses the process of solving differential equations representing dynamical systems using Laplace transforms. It involves 4 main steps: 1) Represent the differential equation in the Laplace domain as a "transfer function", 2) Transform the input function to the Laplace domain, 3) Multiply the transfer function by the input function, 4) Take the inverse Laplace transform to find the time domain response. It also discusses partial fraction expansion, which simplifies functions for taking the inverse Laplace transform using lookup tables. There are three cases for partial fraction expansion depending on the roots of the denominator polynomial.Me330 lecture2
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Me330 lecture7
- 1. ME 330 Control Systems SP 2011 Lecture 7
- 2. Electronic Systems Series Impedances Parallel Impedances
- 3. Electronic Systems Operational Amplifiers High input impedance, Z i = inf Low output impedance, Z o = 0 High gain, A = inf If v i+ is connected to ground, v i+ = 0, A v i+ v i- v o
- 4. Electronic Example 1 Op-amp feedback of the output voltage High impedance of op-amp Thus, High gain of op-amp
- 5. Electronic Example 2 Op-amp with different impedance terms C 1 R 1 R 2 C 2 Recall the rules about series and parallel impedances
- 6. Electrical Mechanical Systems Combinations of electrical and mechanical systems dc servomotor
- 7. Electrical Mechanical Systems Lorentz Force: magnetic field applies a force proportional to current. r = radius of motor armature B = strength of magnetic field l = length of conductor N = number of coil windings Faradays Law: conductor moving in magnetic field creates potential voltage proportional to velocity. back EMF
- 8. Transfer function for electrical system Electrical Mechanical Systems Overall transfer function: Input = V a (s) Output = m (s) Internal = I a (s) , V b (s) , T m (s) V a (t) Transfer function for mechanical system
- 9. Electrical Mechanical Systems Lorentz Force and Faradays Law Substitute into electrical and mechanical transfer functions
- 10. Electrical Mechanical Systems Re-arranging the transfer function Intimidating coefficients, but simple general form Suppose V a (t) = u(t)
- 11. Next Lectures Direct transfer function manipulation.