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ME114 Final Project Presentation

ME114 Final Project Presentation. Operational Amplifiers. Introduction. Group Members Eric Kuiken Kevin Mcclain Joe Roeschen. Introduction. Scope Objectives Approach Analysis. Scope.

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ME114 Final Project Presentation

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  1. ME114Final Project Presentation Operational Amplifiers

  2. Introduction • Group Members • Eric Kuiken • Kevin Mcclain • Joe Roeschen

  3. Introduction • Scope • Objectives • Approach • Analysis

  4. Scope • Model and analyze each of the operational amplifiers (op amp) listed on page 559 Table 9.10 of text using CAMPG, MATLAB, and SIMULINK. • Gain Controller modeling analysis shown

  5. Objectives • Obtain the differential equations • Obtain the state space variables • Obtain the transfer functions of the system • Determine the frequency response, Bode Plot, and Root Locus Plots

  6. Overview of Operational Amplifiers • Definition of an Op Amp • A high-gain DC amplifier with two inputs and one output. The output is equal to the difference between the voltages on the two inputs multiplied by the gain of the amplifier. • Operating characteristics of an op amp depend on the components external to the amplifier.

  7. Overview of Operational Amplifiers • Typical Op Amp Control Functions • Gain • Integration • Differentiation • PI Controller • PD Controller • PID Controller

  8. Overview of Operational Amplifiers • Gain

  9. Overview of Operational Amplifiers • Gain • Used in closed loop control systems. • Represents the relationship between the input and output signals commonly expressed amplitude of the output divided by the input signals. • Op amp most commonly represented as either an Inverting or Non-inverting amplifier. • Inverting amplifiers change the sign and the level of the input signal. • Non-inverting amplifier circuit can increase the size of the signal, remain the same, but it can not decrease.

  10. Overview of Operational Amplifiers • Integration

  11. Overview of Operational Amplifiers • Integration • Utilized in controls to eliminate steady state error in closed loop systems. • The integral mode changes the output of a control signal by an amount proportional to the integral of the error. • Most commonly used to eliminate residual error after a proportional control or proportional / derivative control has been applied. • The Integrating op amp produces an output that is proportional to the integral of the input voltage.

  12. Overview of Operational Amplifiers • Differentiation

  13. Overview of Operational Amplifiers • Differentiation • The derivative control changes the output of a control signal proportionally to the rate of change of the error signal. • Method of error control is needed to help anticipate variations in the measure variable, set point, or both by means of observing the rate of change of the error. • The differentiator op amp produces an output that is proportional to the rate of change of the input voltage. • Used to eliminate oscillations and anticipate system variations. • Usually used in conjunction with Proportional or with Proportional and Integral modes.

  14. Overview of Operational Amplifiers • Proportional-Integral-Derivative Controller

  15. Overview of Operational Amplifiers • Proportional-Integral-Derivative (PID) Controller • The PID control is a combination of the proportional, integral, and derivative controls modes. • Used on processes with sudden, large load changes when one or two control mode control is not capable of keeping error within acceptable ranges. • Integral mode eliminates the proportional offset caused by large load changes. • Derivative mode reduces the tendency toward oscillations and provides a control action that anticipates changes in the error signal. • The PID op amp produces an output that is an accumulation of the error from the proportional, integral, and derivative modes.

  16. Approach • Utilizing CAMPG to Develop Bond Graph • Gain Controller

  17. Approach • Derivative Causalities • CAMPG automatically detects derivative causalities and algebraic loops

  18. Approach • Algebraic Loop Correction • Algebraic loop corrected by the addition of the C9 element

  19. Approach • Interface with MATLAB. • Select MATLAB in the drop down interface menu

  20. Approach • MATLAB • CAMPG - MATLAB interface

  21. Approach • MATLAB • Run CAMPG – MATLAB Interface

  22. Approach • MATLAB • Obtain the system transfer functions and illustrate the step, impulse, bode, and root locus diagrams

  23. Approach • MATLAB • Obtain the system transfer functions and illustrate the step, impulse, bode, and root locus diagrams

  24. Approach • MATLAB • Step, impulse, bode, and root locus diagrams

  25. Approach • CAMPG to MATLAB • Transfer Functions obtained from CAMPG / Matlab campgsym.m: (Note: C9 = 1/10000 and R2, R18 = 1 for simulation) Characteristic Polynomial s + 20000 ... Transfer Functions Matrix H ... [ 10000 10000 ] [- --------- ---------] [ s + 20000 s + 20000] Transfer function from input 1 to output: -10000 --------- s + 20000 Transfer function from input 2 to output: 10000 --------- s + 20000

  26. Analysis • Conclusion • See Operational Amplifiers in Controls ME 114 Final Project full report for remaining op amp analysis.

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