ME 270Final 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 270

Final Project full report for remaining op amp analysis.