EE3530-4-1 - Chapter 4 Basic Properties of Feedback...

Unformatted text preview: Chapter 4: Basic Properties of Feedback Sensitivity of Open Loop Control Systems An open loop control system operates without feedback and gen- erates the actuating signal in response of an input signal. y Controller D ol Plant G Input shaping H r U W R If the plant G ( s ) involves variations Δ G , then it induces a relative error of the overall system T ( s ) = G ( s ) D ol ( s ) H r ( s ) Δ T ( s ) = Δ G ( s ) D ol ( s ) H r ( s ) Δ T T = Δ G ( s ) D ol ( s ) H r ( s ) G ( s ) D ol ( s ) H r ( s ) = Δ G ( s ) G ( s ) that is the same as the relative error of the original plant. 1 Why Use Feedback? • Under modeling: The mathematical model can not describe com- plete dynamics of the process, or it is too complex to be useful. • Uncertain parameters: Some physical parameters may change with respect to operating conditions, or difficult to measure ac- curately. • External disturbance: Physical process can’t be insolated com- pletely from outside world, and disturbance may affect the output performance. • The use of feedback suppresses uncertainties due to modeling, parameter variations, and external disturbances. • The price: feedback devices. 2 Example: Operational amplifier. R R 1 2 V V i o V e A +- I I 1 2 Usually A >> 1 and is very uncertain: V o =- AV e . With connection of R 1 and R 2 we have a feedback system. Since A >> 1, V i- V e R 1 ≈ V e- V o R 2 . Solving V e gives V e = V i R 1 + V o R 2 1 R 1 + 1 R 2 - 1 = R 1 R 2 R 1 + R 2 V i R 1 + V o R 2 ....
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