Time Response System & Control Engineering Lab.

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Presentation transcript:

Time Response System & Control Engineering Lab. School of Mechanical Engineering

CHAPTER OBJECTIVES How to find the time response from the transfer function How to use poles and zeros to determine the response of a control system How to describe quantitatively the transient response of first- and second-order systems How to approximate higher-order systems as first or second order

POLES, ZEROS, AND SYSTEM RESPONSE POLES OF A TRANSFER FUNCTION ZEROS OF A TRANSFER FUNCTION FIRST-ORDER SYSTEMS SECOND-ORDER SYSTEMS: INTRODUCTION THE GENERAL SECOND-ORDER SYSTEM SYSTEM RESPONSE WITH ADDITIONAL POLES SYSTEM RESPONSE WITH ZEROS

The Performance of Control Systems Test input signals Transient response and Steady-state response Absolute stability, relative stability Steady-state error

Typical Test Signal Step functions Ramp functions Acceleration functions Impulse functions Sinusoidal functions White noise signals

Typical Test Signal Step functions Ramp functions

Typical Test Signal Sinusoidal functions Impulse functions

POLES AND ZEROS OF A FIRST-ORDER SYSTEM: AN EXAMPLE

POLES AND ZEROS OF A FIRST-ORDER SYSTEM: AN EXAMPLE

POLES AND ZEROS OF A FIRST-ORDER SYSTEM: AN EXAMPLE

POLES AND ZEROS OF A FIRST-ORDER SYSTEM: AN EXAMPLE

FIRST-ORDER SYSTEMS

FIRST-ORDER SYSTEMS

FIRST-ORDER SYSTEMS

FIRST-ORDER SYSTEMS TIME CONSTANT RISE TIME, Tr SETTLING TIME, Ts

Unit-Step Response of First-Order Systems Transfer function of the first-order system For unit-step function

Unit-Step Response of First-Order Systems Inverse Laplace transform C (t) = Force response + Free response and t=T

Unit-Step Response of First-Order Systems

Second-Order Systems In transfer function (Laplace Transform)

Second-Order Systems

Second-Order Systems

Second-Order Systems

Second-Order Systems

Second-Order Systems

Second-Order Systems

Second-Order Systems

Second-Order Systems

Second-Order Systems

Second-Order Systems

Undamped Second-Order Systems Response

Undamped Second-Order Systems Response

Undamped Second-Order Systems Response

Undamped Second-Order Systems Response

Undamped Second-Order Systems Response

Undamped Second-Order Systems Response

Undamped Second-Order Systems Response

Undamped Second-Order Systems Response

Undamped Second-Order Systems Response

Undamped Second-Order Systems Response

Undamped Second-Order Systems Response

Undamped Second-Order Systems Response

fig_04_18 SYSTEM RESPONSE WITH ADDITIONAL POLES

fig_04_18 SYSTEM RESPONSE WITH ADDITIONAL ZEROS