1. ME 270 Final 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 270 Final Project full report for remaining op amp analysis.