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ME 421 Concept Map

Concept map for Mechanical Systems and Control
by

Joe Cossette

on 16 December 2010

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Transcript of ME 421 Concept Map

Given a desired response,
we can design a system
with appropriate parameters ME 421 System Modeling Mechanical Electrical Fluid Response Time Response Ramp Impulse Step Differential
Equations Numerical
Methods Laplace
Transforms Assumed
Solution
Method Solution Transfer
Function Partial
Fractions Controls Tracking Error Analytical Spring Proportional Derivative PID Control Types Integral Lag Control Design Tools Laws Experimental Disturbance
Rejection Damper Mass Standard Forms Leading 1 Component Relations Inductance Open-Loop Constant 1 Capacitance Resistance Closed-loop
Feedback Op-Amp On-Off Laws 2 states (on or off)
Simple, Inexepensive
Lots of Switching
Not fine control Proportional to error
Simple
Limited Control
Instability Possible Component Relations Component Relations Increase system type
Eliminates steady state error Predicts
Speeds up system
Noise Tank Cylinder Valve Like PI but not as effective
High pass filter
Reduces steady state error Laminar Turbulent Orfice Laws Lead Like PD but not as accurate
Low pass filter
Improves speed
Less noise Zc <Pc Zc >Pc Numerator Dynamics Limitations T_cl 2nd order or less
Computationally intensive
Trial and error needed to overcome numerator dynamics Strengths Find multiple gains Zeigler-Nichols Constant 1 Identify dynamic quantities


Instability prediction
Error of system
Value of steady state Error Constants Limitations Unity feedback only
Ess only Strengths No G_cl needed Coupled Systems Hydraulic (Fluid-Mech.) Electric Motors (Elec.-Mech.) Fluid-Thermal Equivalent Systems Complementary Solution 1. Input step, ramp, or impulse
2. Find specifications from graph
3. Put transfer function in standard from
4. Find dynamic quantities Particular Solution Xp Limitations Trial and error method Strengths PID gains from experiment
No model needed Final Solution Method Look at closed loop denominator
# of unstable poles = # of sign changes in first column Free Forced Transient Steady State Root Locus Limitations Requires Matlab (SISOTools) Strengths Find gain, poles, zeros for any constants
No G_cl needed Magnitude Criterion
Angle Criterion SISOTool Dynamic Quantities Example: Sand being loaded into the back of a truck over time Example: A hammer striking a nail MatLab Simulink Software that helps create appropriate control systems Graphical programming that works with matlab
Important uses
Create a ODE to see effect on input
Input a ramp or step into system
Filter inputs
Make different control systems (i.e. on-off, PID) Program that uses written code
Important uses
Solve mathematical equations
Solve ODEs
Solve transfer functions
Making plots
Time Response
Pole Zero Maps
Solve complex systems with multiple inputs Example: Turning on a light Common Denominator Method
Find Common Denominator
Set numerator to B(s)
Match coefficients of power of s
Solve for system Example So what? Solution to ODE gives behavior of system
All solutions can be identified in either form Superposition 1: Steady State and Transient Superposition 2: Free and Forced Combines effects of P, I, and D control Thermal Component Relations Laws Energy Storage Conservation of Energy Heat Transfer Conduction Convection Routh Stability Limitations Stability only
Needs G_cl Strengths Find multiple gains Block Reduction Steady State Error, Difference between desired and actual response at steady state Steady State Response, Value at steady state Settling Time, Time for response to reach and stay withing 2% of steady state Peak Overshoot Maximum response above steady state Damping Coefficient, Percentage Overshoot Percent of steady state that is reached at peak Peak Time, tp Time at which Mp occurs Rise Time, tr Time to cross Xss for the first time Delay Time, td Time to 50% of Xss Specifications Frequency Response To Transfer Function Slopes Phase Other Bode Plot Sinusoidal
Excitation Find output of system with sinusoidal excitation.
Design system accordingly.
(i.e. Design bridge so this doesn't happen) Pole-Zero Map Vibrations Absorbers Isolators Prevent transmission of vibration from or to object for some frequency range Eliminate vibrations at a given frequency Pick a small mass that vibrates at
systems natural frequency Steps Filters Types Cut-Off Frequency Bandwidth High Pass Low Pass Bandpass Notch Format Components Combining Components The portion of the response that eventually disappears Dependent on the input to the system only Dependent on initial conditions only The portion of the response that remains forever
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