Root Locus sketching rules
Wednesday Rule 1: # branches = # poles Rule 2: symmetrical about the real axis Rule 3: real-axis segments are to the left of an odd number of realaxis finite poles/zeros Rule 4: RL begins at poles, ends at zeros Today Rule 5: As
This week's goals
Today Physical realization of compensators Wednesday Proportional-Derivative compensator Lead/Lag compensators Friday Introduction to state space
2.004 Fall '07
Lecture 22 Monday, Oct. 29
Differential amplifier as proportional controlle
Today's goals
So far Feedback as a means for specifying the dynamic response of a system Root Locus: from the open-loop poles/zeros to the closed-loop poles "Moving the closed-loop poles around" Proportional control: moving on the original Root Locus Pro
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Mechanical Engineering
2.004 Dynamics and Control II Fall 2007 Lecture 25 Laplacedomain solution of the State equations In the previous lecture, we derived the following statespace model for the uncomp
Summary: Compensator design using the Root Locus; State Space
controller / plant
R (s) +
G c (s )
/ compensator sensor / / transducer
G p (s)
C (s)
Proportional (P)
K
choice of compensators Proportional-Derivative (PD)
H ( s)
(usually, H (s) = 1).
G c (s
Today's goals
State space so far Definition of state variables Writing the state equations Solution of the state equations in the Laplace domain Phase space and phase diagrams Today Stability in state space State feedback control
2.004 Fall '07
Lecture 2
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Mechanical Engineering
2.004 Dynamics and Control II
Fall 2007
Lecture 38
Overview of the frequency response and Bode plots In this lecture, we'll practice on the topic of frequency response and Bod
2.004: overview
Modeling of systems Mechanical Electrical Electro-mechanical In addition: fluidic, thermal, acoustic, pneumatic, biological, chemical, optical, . Control of systems Feedback control of transients (speed, overshoot, steady-state error) Fre
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2.007 Design and Manufacturing I
Spring 2009
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2.007 Design and Manufacturing I
Draft Exam on Gears, Spring
Undamped DC motor system: complete response
V0 1 - cos (n t) . (t) = Kv
ve (t) = Kv (t).
Electro-mechanical equations of motion (time domain) L di + Ri + Kv = vs dt J
J d(t) . Km dt
i(t) =
vL (t) = L
d + b = Km i dt Step-function source vs (t) = V0 u(t).
Summary from previous lecture
Electrical dynamical variables and elements
Charge q(t), Q(s). Current i(t) = q(t), I(s) = sQ(s). Voltage v(t), V (s) = Z(s)I(s). Resistor v(t) = Ri(t), ZR (s) = R. Capacitor i(t) = C v(t), ZC (s) = 1/Cs. Inductor v(t) = Ldi
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Mechanical Engineering
2.004 Dynamics and Control II Fall 2007 Lecture 2 Solving the Equation of Motion Goals for today Modeling of the 2.004 Lab's rotational system Analytical solution of the equation
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Mechanical Engineering
2.004 Dynamics and Control II Fall 2007 Problem Set #1
Posted: Friday, Sept. 7, '07 Due: Friday, Sept. 14, '07
1. For each one of the following systems, argue if in your opinion
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Mechanical Engineering
2.004 Dynamics and Control II Fall 2007 Problem Set #2
Posted: Friday, Sept. 14, '07 Due: Friday, Sept. 21, '07
1. In class, we showed in two different ways that the torque cons
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Mechanical Engineering 2.004 Dynamics and Control II Fall 2007 Problem Set #3 Posted: Friday, Sept. 21, '07 Due: Friday, Sept. 28, '07
1. A secondorder system has the step response shown below.1 Determin
2.004 Dynamics and Control II
Problem Set 9
Due: 11/20/2015 recitation
Problem 1 (5 points)
P(S)
Figure 1: Block diagram for Problem 1
Consider the block diagram above. We have P( s )
( s 9)
( s 1)( s 2)( s 10)
1. Draw the root locus for the system.
2. D
2.004 Dynamics and Control II
Problem Set 1
Due: 09/18/2015 (at the beginning of the class)
Readings: Franklin Feedback Control of Dynamic Systems, section 2.2-2.3
Prelab: Please be sure to complete Prelab Assignment 1 before your Lab 1 session. You will
2.004 Dynamics and Control II
Problem Set 8
Due: 11/13/2015 recitation
Readings: Franklin Feedback Control of Dynamic Systems, chapter 5.
Problem 1
A system described by the block diagram shown in Figure 1 below. P(s) is the plant transfer
function. C ( s
2.004 Dynamics and Control II
Problem Set 10
Due: 12/04/2015 recitation
Problem 1 (6 points)
Draw Bode plots for the following transfer functions:
s
( s 10)
s 0.1
2. T ( s ) 100
s( s 10)( s 100)
s
3. T ( s ) 200
2
( s 1)( s 20s 200)
1. T ( s ) 20
Problem