FEATUREFEATUREAnalog Computers in Academia and IndustryBy Robert M. Howet the end of World War II, the U.S.Air Force recognized that none ofits officers had any academictraining in the emerging field ofguided missiles. To remedy thissituation, the Air Force estab-lished the Guided Missiles Training Programat the University of Michigan. The programconsisted of two years of graduate studies inthe Department of Aeronautical Engineeringfor qualified junior and senior officers, with anemphasis on new courses related to guidedmissile technology. A similar program wassponsored at MIT. At the same time, ownershipof Willow Run airport, a facility 12 miles east ofAnn Arbor that was built during World War II aspart of the Ford plant to mass produce B-24 Libera-tor bombers, was transferred from the U.S. Govern-ment to the University of Michigan. This facilityenabled the University of Michigan to create the Michi-gan Aeronautical Research Center as an organization forconducting large government-funded projects. The initialWillow Run program was Project Wizard, sponsored by the U.S.Air Force, which involved the design of a surface-to-air guided mis-sile to destroy enemy ballistic missiles in flight.With these post-World-War-II developments, the Department of AeronauticalEngineering at the University of Michigan began to add faculty members with backgrounds inphysics, electrical engineering, and applied mathematics to the existing faculty with expertisein the traditional areas of aeronautical engineering (aerodynamics, propulsion, structures, andaircraft design). The new facultymembers were charged with creating and teaching graduatecourses in guided missiles and control systems technology, as well as conducting researchassociated with the Aeronautical Research Center at Willow Run. In 1947, under the auspices ofA history of analog computing at the University of Michigan and the founding of Applied Dynamics International ©DIGITALVISIONJune 2005370272-1708/05/$20.00©2005IEEEIEEE Control Systems MagazineAJune 200538IEEE Control Systems MagazineProject Wizard, the author (then a graduate research assis-tant), the author’s father (C.E. Howe, a physics professorfrom Oberlin College who spent his summers doingresearch at the University of Michigan), and D.W. Hagel-barger (a new faculty member in the Department of Aero-nautical Engineering) initiated a study of the utility ofelectronic analog computers for solving engineering prob-lems [1]. This study led directly to the development anduse of analog computers for simulation in the laboratorycourses associated with the USAF Guided Missiles TrainingProgram. It also spurred a number of follow-on govern-ment-sponsored research efforts and the founding in 1957of the company Applied Dynamics to manufacture andmarket analog computer systems.The Study of the Utility ofElectronic Analog Computersat the University of MichiganThe development and application of electronic analog com-puters in the Aeronautical Engineering Department at theUniversity of Michigan, initiated in 1947, employed opera-tional amplifiers based on a high-gain dc amplifier circuitpublished at that time in an article by Ragazzini et al. [2]. The amplifier circuit utilized two vacuum tubesand exhibited an open-loop gain of approximately 50,000,with an output voltage range that exceeded the ±100-V dcreference. Each operational amplifier was housed in its ownchassis, which included sockets for input and feedbackresistors mounted on twin banana-jack plugs when theamplifier was used as a summer, and a feedback capacitorwhen the amplifier was used as anintegrator. Carbon film resistors with1% accuracy were used as input andfeedback resistors, and a WesternElectric 1-µF polystyrene capacitoraccurate to 1% was used as an integra-tor feedback capacitor. The poly-styrene dielectric was utilized becauseof its low dielectric absorption. Inputand feedback impedances werematched to 0.1% to improve the over-all accuracy of analog solutions. Figure1 shows two summer and two integra-tor operational amplifiers (as constructed in the Universityof Michigan Aeronautical Engineering Laboratories) con-nected to solve a second-order linear differential equation.Thanks to the success of the 1947–1948 study of theutility of analog computers in solving engineering prob-lems, the analog computers constructed for the study wereintroduced into the laboratories of two graduate coursescreated to serve the needs of the Guided Missiles TrainingProgram at the University of Michigan. Specifically, theanalog computer was used to simulate dynamic systems,such as seismic instruments and feedback control sys-tems, in courses on engineering measurements and designof control systems [3].Follow-On Analog ComputerDevelopments in the Departmentof Aeronautical EngineeringIn 1950, the author returned to become a faculty memberin the University of Michigan Department of AeronauticalEngineering following a two-year absence to earn his doc-torate in physics from MIT. At the same time L.L. Rauch,who joined the departmental faculty in 1949 from Princeton, initiated a program to construct new andimproved operational amplifiers based on a circuit devel-oped by the Rand Corporation. One of the problems associated with the dc operational amplifiers used in theoriginal 1947–1948 study was the drift over time in theamplifier output voltage. Partial elimination of the solutionerrors caused by this drift could be achieved by frequentlyrebalancing the amplifiers. An ingenious method for practi-cally eliminating this drift was worked out by RCA andLeeds and Northrup. The scheme involved passing theinput to the dc amplifier through a low-pass filter. Theinput was then converted to an ac signal by means of a 60-Hz Leeds and Northrup chopper, passed through an acFigure 1. Four of the original University of Michigan opera-tional amplifiers connected to solve a second-order linear dif-ferential equation. Input and feedback resistors are mountedon the twin banana-jack plugs in the front of each amplifierchassis. The polystyrene integrating capacitors can be seennext to the vacuum tubes on the right hand pair of amplifierchassis.The initial Willow Run program wasProject Wizard, sponsored by the U.S.Air Force, which involved the design of asurface-to-air guided missile to destroyenemy ballistic missiles in flight.June 200539IEEE Control Systems Magazineamplifier, reconverted to a dc signal, and then added backto the dc amplifier input through a