Classical and Modern Control with Worked Examples by Jean-Pierre Elloy

By Jean-Pierre Elloy

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2 curve K F(ju) in the servo control system of the : rd/s Black of terms aircraft. 5s diagram. 15 K voltages shown makes of manoeuvre. set we identified aerodynamic numerical which angle is c s(l in the as . regulate F(s) geometric angle turning the and loop) control. 6 and whose which the its adjustable gives aircraft order3 with natural gain an electric and gain pulsation K is whose signal propor­ transfer function K„ = 8 V/rd3 equal independent to with 50 of rd/s. the fre- CLASSICAL AND MODERN CONTROL WITH WORKED EXAMPLES 54 quenoy in the pass band of the - A control part which activates function of this activator, once a first order function with gain followed by a simple integrator, system, the horizontal rudder.

Otherwise N = O, P = O, >o Z = O and the system is stable. 9 So if K < Ko the system is stable if not, it is unstable. 9 (b> 0 ) . 11K b = K K closed loop. G(s) V(s) a) Using the Routh test, determine the values of K for which the closed loop system is stable. b) Find the preceding result again by the Nyquist test. For this, trace from the transfer curve in the Black diagram (see figure), the shape of the Nyquist curve in the complex plane ; then calculate the pulsation ω- for which the Nyquist curves crosses the real negative axis ; and finally, apply the Nyquist test and determine the values of K for which the servo system is stable.

3 STUDY OF THE AUTOMATIC PILOT OF AN AIRCRAFT The automatic tant altitude. e. of the of statement. 2 curve K F(ju) in the servo control system of the : rd/s Black of terms aircraft. 5s diagram. 15 K voltages shown makes of manoeuvre. set we identified aerodynamic numerical which angle is c s(l in the as . regulate F(s) geometric angle turning the and loop) control. 6 and whose which the its adjustable gives aircraft order3 with natural gain an electric and gain pulsation K is whose signal propor­ transfer function K„ = 8 V/rd3 equal independent to with 50 of rd/s.

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