Control Systems: Closed-Loop & Open-Loop, Block Diagrams, and PID Controllers - Prof. Amy , Study notes of Aerospace Engineering

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AE-

Lecture Notes

09 Mar 2012 1

Overview

Closed-loop / open-loop

Block diagrams

Feedback

P, I, D controllers

PID design 2

Closed-loop Systems

4

Add feedback to ‘close the loop’

Can compensate for disturbances

Greater accuracy but more complex Section 1.

Block Diagram Algebra

• Blocks in series: • Blocks in parallel with their outputs added: 1 2 1 2 GG U ( s ) Y (s ) = € Y ( s ) U ( s ) = G 1

• G 2 5 Section 5. Can reduce complex systems into single transfer functions!

Negative Feedback

Ge(s) is closed- loop transfer function

G(s)H(s) is the open-loop transfer function 7 Section 5.

Example:

8 Reduces to: Section 5.

Unity Feedback

The closed-loop transfer function becomes:

Notice that the characteristic equation for the above system becomes:

The controller has an effect on the system’s poles 10 ( ) ( ) 1 + Gc(s)Gp(s) = 0 Section 5.

P, I, D Controllers

Proportional controllers

• pure gain or attenuation

Integral controllers

• integrate error

Derivative controllers

• differentiate error 11 Chapter 9

Integral Controller

Integral of error with a constant gain

Increase system type by 1

• Infinity steady-state gain
• Eliminate steady-state error for a unit step input u=Ki ∫edt 13

Derivative Control

Differentiation of error with a constant gain

Reduce overshoot and oscillation

Do not affect steady-state response

Sensitive to noise u=Kd de/dt t 14

PID Controller

PI controller

PD controller

PID controller 16

PID Controller

17

P Controller

Increase in gain

• upgrade both steady-state and transient responses
• reduce steady-state error
• reduce stability! 19

P Controller

20