Trends in the Field of Automatic Control in the Last Two Decades

T lecture is given in memory of Theodore von Karman. There are two reason which make me happy to be this year's lecturer. I have known Dr. von Karman personally. I met him the first time at a conference in England in 1934. The other reason is the admiration I have had for his work since I started working in Gb'ttingen's Aerodynamics Research Institute in 1929, where von Karman spent time working with L. Prandtl and where he was well remembered. In 1940 von Karman delivered the fifteenth J. W. Gibbs lecture at a meeting of the American Mathematical Society, titled "The engineer grapples with nonlinear problems." He explained that in many fields of engineering nonlinearities could no longer be neglected, and that a deeper mathematical treatment of some problems had led to particularly interesting results. Since in my lecture nonlinear control theory and its growth will play a role, it seems to me that this topic is fit to remind us of von Karman and his far-reaching ideas. Speaking before an audience of aeronautical engineers, I cannot forget those times when "control" meant stabilization of an airplane with the help of control surfaces at the tail or ailerons at the wing. The pilot used them to fly a desired path and to counteract gusts, or adverse winds. There came a step forward when the pilot's task was eased by building the "automatic pilot" to which the human pilot would essentially give commands. My talk today shall not be restricted to this specific task, but consider "automatic control" in general, built to relieve the human being from any dull and repetitive operation, may be to supervise a chemical process or may be to determine the path of a rocket, a missile and finally to let satellites fulfill their task without manual interference. After World War II automatic controls have spread into many regions of technology. The consequence was that barely an engineer in any field could escape coming in contact with them. Some mechanisms and regulators were a long time in use, (for instance, the centrifugal regulator of steam engines), but complicated automatic control systems were still little used. Beginning with the 1950s, the mathematicians' interest awoke and this was the start of a tremendously fast development surpassing the linear control theory which was presented in a number of books written for engineers with relatively minor mathematical background. Let us go back to the airplane. One understood the basic behavior of the dynamic system, and the controls tended to keep the plane on its desired path and in its desired attitude by removing the undesired deviations which could be described by linear differential equations. Linear control elements were mostly used, however, at the same time the airplane was a wonderful example to show that linearization was not always suitable for describing the behavior of the system, and controls designed on that assumption could not be satisfactory. Maybe nonlinear controls had to be introduced. Among others, Kochenburger and MacCollhad attacked the problem of designing stable nonlinear control systems. I remember a conference at which two wind tunnel designers were enthusiastic about their success in designing a wind tunnel with special flow characteristics. After linear controls did not yield the desired airstream quality, they finally used Kochenburger's paper and, with the help of the describing function they designed a suitable control of the propulsion system. I could not agree only with their conclusions that Kochenburger's rule had solved all nonlinear control problems. The describing function allows us to handle certain nonlinear controls in the same manner as linear ones by way of approximation. J. G. Truxal's book on Control System Synthesis contains many historically interesting details. The essential assumptions for its use is: the system contains only one nonlinear element; the output of this element depends only on the present value and the past history of the input; if the input is sinusoidal only the fundamental output of the nonlinear element influences the system. One particular nonlinear type of control used was the discontinuous control; often designed with the help of the describing function, or by trial and error method. In this case, each of the control inputs has only two or three settings. In wartime, the controls were employed for steering missiles. Such controls are simple from the design standpoint, they are rugged and inexpensive. These qualities are appreciated in controlling objects which