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Lecture 9 – ‘Clever Tricks’ in Frequency-Domain Control Design

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A ‘good’ controls joke (credited to Dr. Douglas Bristow)

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An even better controls joke…

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Common Feedforward Control Methods: Synchronous AC Motors (Wikipedia.org) Baldor AC Motor (e.g. 1740 rpm motor) (Wikipedia.org)

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Common Feedforward Control Methods: Stepper Motors (Wikipedia.org) Applied Motion Stepper Motor

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Common Feedforward Control Methods: Nanopositioning (S. Devasia, et al., IEEE TCST, 2007)

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Common Feedforward Control Methods: Chemical Processes (large.stanford.edu)

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Motor position control example with 5V saturation limit Integral Windup Input saturates, preventing response from reaching steady- state Integral term of PID continues to integrate error (winds up). Falling step behavior is much different from rising step.

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Anti-Windup Control Anti-windup prevents integral term from continually building Results in a more consistent response without artifact from windup

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Gain Scheduling and Bumpless Transfer: Boeing 767 autopilot design Landing Conditions Cruise Conditions Elevator angle to pitch transfer functions (Gangsaas, et al., IEEE TAC, 1986) Mean Aerodynamic Chord (MAC) (wikipedia.org) It may be beneficial to build different controllers for different operating conditions. But how would you switch between the two? Compare these transfer functions

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Gain Scheduling and Bumpless Transfer: HVAC System Different behaviors depending on valve opening ratios (Rasmussen, Chang, ASME JDSMC, 2010)

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Gain Scheduling Two controllers, a and b, designed for operating points λ a and λ b. For an operation at an intermediate operating point λ’ select controller weightings k a and k b that are a weighted average of the two. This example gives a Gaussian weighing scheme. (Hoelzle, Barton, IEEE CDC, 2012)

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Bumpless Transfer Different controllers have different objectives, hence different input magnitudes. Naively switching between the two controllers causes an instantaneous ‘bump’ in the input signal magnitude. This input signal ‘bump’ is felt in the system output. (Cheong, Safonov, IFAC World Congress, 2008)

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