Control Systems

Douglas Delorenzi Schons, Nov 10, 2020

This geobook is being produced focused on Control Systems lectures.

Table of Contents

  1. First Order systems
    1. first order dirac
    2. first order unitary degree
    3. first order ramp [T k]
    4. first order ramp [c1 c2]
    5. first order delayed system
  2. Second Order systems
    1. Introduction
    2. underdamped system [m k c]
    3. underdamped system [zeta c k]
    4. underdamped system [zeta c m]

1.

First Order systems

In this chapter we gonna study first order systems. Described in: - time domain as ODE of first order. [math]c_1 \frac{dy(t)}{dt}+c_2\ y(t)= \ u(t) [/math] -s domain as transfer function of a single pole. [math]G(s)=\frac{K_g}{Γs+1} [/math]

  • 1. first order dirac
  • 2. first order unitary degree
  • 3. first order ramp [T k]
  • 4. first order ramp [c1 c2]
  • 5. first order delayed system

1.1.

first order dirac

first order
This graph shows the system response in time domain.[br]The function in red is:[br][math]y\left(t\right)=K_ge^{\left(-\frac{t}{\tau}\right)}[/math][br]The time function came from the inverse Laplace Transform of s domain function G(s):[br][math]G\left(s\right)=\frac{K_g}{\tau s+1}[/math][br](standard form)[br]where:[br]a,c and c and a are polynomial coef[br][math]K_g=\frac{1}{c_2}[/math] [br]is the system gain[br][math]\tau=\frac{c_1}{c_2}[/math] [br]is the time constant
– Douglas Delorenzi Schons

1.2.

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1.3.

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1.4.

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1.5.

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2.

Second Order systems

This chapter is based on the mass spring damper mechanical model.

  • 1. Introduction
  • 2. underdamped system [m k c]
  • 3. underdamped system [zeta c k]
  • 4. underdamped system [zeta c m]

2.1.

Introduction

This system is described in time domain by the ODE:[br]m\ddot{x} +c\dot{x}+kx=F(t)[br][math]m.x''+c.x'+k.x=F[/math]
– Juan Carlos Ponce Campuzano, Douglas Delorenzi Schons

2.2.

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2.3.

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2.4.

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