STATE ESTIMATION
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STATE ESTIMATION
State estimation is a method of estimating some of the states in a system based on measurements of other states and knowledge of how the system behaves. The estimates of some of the states together with the measurement
MOTION IN A STABILITY REGION (PART I)
4
MOTION IN A STABILITY REGION (PART I) When motion is confined to one independent degree-of-freedom, the linearized equation that governs the motion is of the form (4 1)
& m& + cx + kx = f x
In this section, we analy
MOTION IN A STABILITY REGION (PART II)
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MOTION IN A STABILITY REGION (PART II)
Figure 5 1
MAE 461: DYNAMICS AND CONTROLS
MOTION IN A STABILITY REGION (PART II)
This section begins by showing how to find the steady-state response of a one degree-of-freedo
TRACKING THE REFERENCE PATH
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TRACKING THE REFERENCE PATH
As stated earlier, the problem of controlling a dynamical system is customarily divided into two basic problems tracking and regulation. The former is associated with moving a component from one eq
REGULATING THE REFERENCE PATH
7
REGULATING THE REFERENCE PATH (CONTINUOUSLY-ACTING ACTUATORS)
This Chapter considers the regulation problem restricted to the case in which the control force is produced by a continuously-acting actuator. The control force
REGULATING THE REFERENCE PATH (DISCRETELY-ACTING ACTUATORS)
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REGULATING THE REFERENCE PATH (DISCRETELY-ACTING ACTUATORS)
This chapter considers the regulation problem restricted to the case in which the control force is produced by discretely-acting actu
SYSTEM CONCEPTS
9
SYSTEM CONCEPTS
Automotive vehicles, building structures and aircraft vehicles are dynamical systems but so too are actuators and sensors. Actuators and sensors have their own dynamical behavior, as well. For example, when we say that a
TREATING MULTI-DIMENSIONAL SYSTEMS
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TREATING MULTIDIMENSIONAL SYSTEMS
Chapter 1 through Chapter 9 developed basic principles of dynamics and control of single degree-of-freedom systems. The interacting parameters were composed of physical parameters, dy
REGULATING MULTI-DIMENSIONAL SYSTEMS
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REGULATING MULTIDIMENSIONAL SYSTEMS
This chapter considers the regulation problem restricted to the case in which the actuators are continuously-acting. We'll consider two types of regulation problems; full regulati
REGULATING STEADY-STATE BEHAVIOR
12
REGULATING STEADY-STATE BEHAVIOR
This section treats the regulation problem associated with a two degree-of-freedom system acted on by a persistent excitation. For simplicity we'll assume that the persistent excitation
SENSITIVITY ANALYSES
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SENSITIVITY ANALYSES
The previous chapters hinted at the importance of the sensitivity of a system to its parameters. As mentioned in Section 4 of Chapter 3, in the absence of feedback, control forces do not really move a system in
TYPES OF SYSTEMS, PROBLEMS, AND STRATEGIES
3
TYPES OF DYNAMICAL SYSTEMS, CONTROL PROBLEMS AND CONTROL STRATEGIES
The field of controls is very broad. Even when it's restricted to dynamical systems, it still applies to a very wide range of problems. It app
CONVERTING TO THE STATE SPACE
2
CONVERTING TO THE STATE SPACE
Differential equations can be solved analytically when the equations are linear and when the nonlinearities are relatively simple. Otherwise, the equations need to be solved numerically. To sol
COMPLEX DYNAMICS SIMPLIFIED
1
COMPLEX DYNAMICS SIMPLIFIED
To develop a control system for a dynamical system one must first understand precisely how the system behaves. One can arrive at this understanding using mathematics by performing a dynamic analysi
MAE 461 Dynamics & Controls FALL 2009
Instructor L. Silverberg [email protected] 919 515 5665 BR 1402, MW 1:30 2:45 BR 4219, MW 2:45 4:00
Class Office Hours Grading
Homework Test 1 (in class) Test 2 (in class) Test 3 (in class) Exam (in class) Computer Re
The assignment & The system When assignment Day when needed material was completed in class being treated is due* PROBLEMS 1-1, 1-2 System 1 4 3 Aug 26 1 Aug 19 PROBLEMS 1-3 System 1 4 4 Aug 31 1 Aug 19 PROBLEMS 2-1, 2-2 System 1 4 6 Sept 9 3 Aug 26 PROBL
MONDAY
2 Aug 24 CONVERTING TO THE STATE SPACE: NONLINEAR STATE EQUATIONS; EQUILIBRIUM; LINEARIZATION 4 Aug 31 TYPES OF DYNAMICAL SYSTEMS, CONTROL PROBLEMS AND CONTROL STRATEGIES: APPLICATIONS;PROPERTIES OF DYNAMICAL SYSTEMS; CONTROL, PROBLEMS; CONTROL STR
0ame.m %This program determines the state variables of the 0ollowing mass-spring-damper system: % %m(d2x/dt2)+c(dx/dt)+kx=0 %x(0) = 1; dx/dt(0) = 0, %m = 1; c = 2, k = 5 % %This program graphs x(t). %The state equations are contained in the M-file %called
function f = name_state(x,t) % function f = name_state(x,t) % This M-file lists the state equations % INPUTS % x(t) n x 1 vector of state variables at time t % t time % OUTPUTS % f(x,t) n x 1 vector of time derivatves of state variables % % Free mass-spri
function xnew = step1(filex,t,deltaT) % function xnew = step1(filex,t,deltaT) % This M-file performs a 1st-order numerical integration step. % INPUTS % file name of the file that contains the state equations % x n x 1 vector of state variables at time t %
function xnew = step2(filex,t,deltaT) % function xnew = step2(filex,t,deltaT) % This M-file performs a 2nd-order numerical integration step. % INPUTS % file name of the file that contains the state equations % x n x 1 vector of state variables at time t %
% Simulation : Comparing the Runge Kutta 2nd order method of % solving ODEs % Language : Matlab 2007a % Authors : Autar Kaw % Last Revised : July 12, 2008 % Abstract: This program compares results from the % exact solution to 2nd order RungeKutta methods
MAE 461 DYNAMICS AND CONTROLS CONTENTS 1. Complex Dynamics Simplified 1. Equations 2. Equilibrium 3. Linearization 2. Converting to the State Space 1. Nonlinear State Equations 2. Equilibrium 3. Linearization 4. The Euler Method 5. The 2ndOrder Runga-Kutt
PREFACE
MAE 461 Dynamics and Controls is an introductory course designed to provide you with a strong background in control of dynamical systems. In the aerospace curriculum you will later learn about flight systems; they're covered in MAE 462 and in your
LINEAR ALGEBRAIC EQUATIONS
14
LINEAR ALGEBRAIC EQUATIONS
Systems of linear algebraic equations arise in all walks of life. They represent the most basic type of system of equations and they're taught to everyone as far back as 8-th grade. Yet, the complet