EDNE June 2012 - (Page 50)

AU I TO TIVE MO AERO SP A CE M N G CE Control Systems Digital Control Systems E D S IC S A L M AT E R IALS PR O Control Electronics RAPHY ROG XE MECHATRONICS IN DESIGN The significance of poles and zeros Software mechatronics Mechanical CAD Electromechanics Electronic Systems FRESH IDEAS ON INTEGRATING MECHANICAL SYSTEMS, ELECTRONICS, CONTROL SYSTEMS, AND SOFTWARE IN DESIGN T E Mechanical Systems M S M CO A S CT NSU MER PRODU Emulate Wilbur Wright and learn the significance of poles and zeros. W ilbur Wright’s understanding of complex, dynamic problems contributed to his and his brother Orville’s successful first airplane flight. Wilbur understood, for example, that, to turn a bicycle to the left, you must first turn the handlebars a little to the right and then, as the bicycle inclines to the left, you must turn them a little to the left. He understood countersteering. In mathematical language, the transfer function between the steer torque applied to the handlebars and the straight-line-path deviation has a right-half-plane zero, which imposes a limit on maneuverability. The path deviation has an inverse-response behavior; that is, in response to a positive step-torque input you apply to the handlebars, the path deviation is initially positive and then becomes negative. This effect has contributed to numerous motorcycle accidents, but countersteering could prevent these accidents. To better understand the physical significance of the poles and zeros of a transfer function, consider a simpler system, comprising two rigid links and a torsional spring (see Figure 1). Assume small displacements. The equations of motion, shown adjacent to the graphic in the diagram below, are in matrix form, along with two transfer functions, G 0 (s) and G 1 (s). A pole of a transfer function is a value of s that makes the denominator equal to zero, and a zero of a transfer function is a value of s that makes the numerator equal to zero. Systems that have no poles or zeros in the right half of the complex plane are minimum- Figure 1 This system comprises two rigid links and a torsional spring. 50 EDN EUROPE | JUNE 2012 www.edn-europe.com U N FA C TU S NS FE DE RI NG E Y S http://www.edn-europe.com

Table of Contents for the Digital Edition of EDNE June 2012

Cover
Agilent Technologies
Contents
International Rectifier
RS Components
International Rectifier
Comment
Pulse
Analog Devices
Digi-Key
Farnell
NXP
Test & Measurement
Silicon Labs
Digi-Key
Test-driven development for embedded C: why debug?
Digi-Key
Baker’s best
Cover story
Rohde & Schwarz
Rohde & Schwarz
Rohde & Schwarz
Rohde & Schwarz
Rohde & Schwarz
Pico-projector design uses color LEDs
Digital isolation in smart energy metering applications
Mechatronics in design
Teardown
Design Idea
Product Roundup
Tales from the cube