ME114Final Project Presentation
Operational Amplifiers
Introduction
Group Members Eric Kuiken Kevin Mcclain Joe Roeschen
Introduction
Scope Objectives Approach Analysis
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
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
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.
Overview of Operational Amplifiers Typical Op Amp Control Functions
Gain Integration Differentiation PI Controller PD Controller PID Controller
Overview of Operational Amplifiers Gain
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.
Overview of Operational Amplifiers Integration
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.
Overview of Operational Amplifiers Differentiation
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.
Overview of Operational Amplifiers Proportional-Integral-Derivative Controller
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.
Approach
Utilizing CAMPG to Develop Bond Graph Gain Controller
Approach
Derivative Causalities CAMPG automatically detects derivative
causalities and algebraic loops
Approach
Algebraic Loop Correction Algebraic loop corrected by the addition of the C9
element
Approach
Interface with MATLAB. Select MATLAB in the drop down interface menu
Approach
MATLAB CAMPG - MATLAB interface
Approach
MATLAB Run CAMPG – MATLAB Interface
Approach
MATLAB Obtain the system transfer functions and illustrate
the step, impulse, bode, and root locus diagrams
Approach
MATLAB Obtain the system transfer functions and illustrate
the step, impulse, bode, and root locus diagrams
Approach
MATLAB Step, impulse, bode, and root locus diagrams
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
Analysis
Conclusion See Operational Amplifiers in Controls ME 114
Final Project full report for remaining op amp analysis.