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Unformatted text preview: Comparison of Open-Loop & Closed-Loop Control Example: Disk Drive Head Objective: precise control over the velocity of the head ME575 Session 3 – Open-Loop and Closed-Loop Control Comparison School of Mechanical Engineering Purdue University Slide 1 Comparison of Open-Loop & Closed-Loop Control Model: V (s) Km τms + 1 ω(s) where and 0.9K m ≤ K m ≤ 1.1K m K m is the nominal value based on motor data sheet Objective: make output ω(t) follow specified reference ωd(t) with uncertainty in Km ME575 Session 3 – Open-Loop and Closed-Loop Control Comparison School of Mechanical Engineering Purdue University Slide 2 1 Open-Loop Control ωd(s) Controller ME575 Session 3 – Open-Loop and Closed-Loop Control Comparison C V (s) Motor Km τms + 1 ω(s) School of Mechanical Engineering Purdue University Slide 3 Open-Loop Control - Problems • Controller is usually unrealizable • Unstable plant cannot be stabilized • Right-half-plane plant zeros cause unstable controller ME575 Session 3 – Open-Loop and Closed-Loop Control Comparison School of Mechanical Engineering Purdue University Slide 4 2 Open-Loop Control Relax objective so that ω(t) → ωd(t) at steady-state. Assume setpoint is constant, i.e., ωd = ωdss. Apply the Final Value Theorem (FVT): ωss = lim sω ( s ) = s →0 e ss open = ωdss − ωss = ωdss − loop ME575 Session 3 – Open-Loop and Closed-Loop Control Comparison Km K⎞ ⎛ ωdss = ⎜ 1 − m ⎟ ωdss Km Km ⎠ ⎝ School of Mechanical Engineering Purdue University Slide 5 Open-Loop Control (cont.) e ss open = ωdss − ωss = ωdss − loop ME575 Session 3 – Open-Loop and Closed-Loop Control Comparison Km K⎞ ⎛ ωdss = ⎜ 1 − m ⎟ ωdss Km Km ⎠ ⎝ School of Mechanical Engineering Purdue University Slide 6 3 Closed-Loop Control ωd(s) Pre-filter K0 Controller + − K / Km V (s) Motor Km τms + 1 ω(s) Sensor K0 Convert to a unity feedback block diagram. ME575 Session 3 – Open-Loop and Closed-Loop Control Comparison School of Mechanical Engineering Purdue University Slide 7 Closed-Loop Control Controller ωd(s) + − K0 ω(s) = K / Km V (s) Motor Km τms + 1 ω(s) K 0KK m / K m ωd ( s ) τms + 1 + K 0KK m / K m ME575 Session 3 – Open-Loop and Closed-Loop Control Comparison School of Mechanical Engineering Purdue University Slide 8 4 Closed-Loop Control (cont.) E ( s ) = ωd ( s ) − ω ( s ) = e ss = lim sE ( s ) = s →0 τms + 1 ωdss τms + 1 + K 0KK m / K m s 1 ωdss 1 + K 0KK m / K m For K0 = 1 (no loss of generality): e ss closed = loop 1 ωdss 1 + KK m / K m ME575 Session 3 – Open-Loop and Closed-Loop Control Comparison School of Mechanical Engineering Purdue University Slide 9 Closed-Loop Control (cont.) e ss closed = loop 1 ωdss 1 + KK m / K m ME575 Session 3 – Open-Loop and Closed-Loop Control Comparison School of Mechanical Engineering Purdue University Slide 10 5 Comparison of Open-Loop & Closed-Loop Control • Closed-loop (feedback) control can reduce steady-state errors with modeling uncertainty for high enough gain, relative to open-loop control. • High-gain feedback control also reduces errors to unknown disturbance inputs. • Feedback control can be destabilizing. ME575 Session 3 – Open-Loop and Closed-Loop Control Comparison School of Mechanical Engineering Purdue University Slide 11 6 ...
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