## Modern Stability and Control Teaching Methods

The digital computer has revolutionized the teaching of airplane stability and control, just as it has its practice. In precomputer times, flight dynamics students had to learn numerical techniques for factoring high-degree polynomials and producing linearized transient responses. Eigenvalues or roots of the equations of airplane motion were extracted by factorization, and the flight modes of motion were found.

Computer programs for root extraction and a great deal more are at the modern engineer’s fingertips, and present-day teachers of flight dynamics have found ways to use the digital computer to improve their courses. A few instances follow. Stanford University Professor Arthur Bryson’s book Control of Aircraft and Spacecraft uses Matlab® computer routines in many examples and problem assignments. For example, pages 199-201 show a student how to synthesize an optimal climb-rate/airspeed stability augmentation system using Matlab. As with other mathematics computer packages, Matlab is available in a low-cost student edition.

The State University of New York at Buffalo Professor William J. Rae assigns exercises that use a 6-degree-of-freedom computer program called SIXDOF to explore in detail the solutions of the nonlinear equations of airplane motion. This supplements normal instruction in the modes of motion and control theory using linearized equations. Still another approach has beenpursuedby University ofFlorida Professor Peter H. Zipfel. He makes available to his students a CADAC CD-ROM disk, with which to build modular aerodynamics, propulsion, and guidance and control computer models. As in the previous cases, students are able to solve realistic stability and control problems without getting lost in routine mathematical detail.

In France, Professor Jean-Claude Wanner, on the staffs of several universities, is developing an advanced flight mechanics teaching tool, in the form of a CD-ROM. A stability volume computes the time response of an airplane specified by the user to control and throttle inputs, presenting results in the form of conventional strip charts, but also in real time as viewed from the cockpit or the ground. There are preliminary interactive chapters, including text and exercises, on subjects such as phugoid motion and accelerometer instruments.

The only cautions that might be applied to these modern approaches are the same ones that must be observed in the practice of engineering, using powerful digital computers. Both student and working engineer must keep in mind the assumptions that lie behind flight dynamics computer programs, their limitations as well as their capabilities. Good practice also requires reasonableness checks on computer output using independent simple methods.