1. List of symbols ki = input filter gain to be adapted (s 1) Pc = pilots' command signal (°/s) Po = amplitude of p~(t) ('/s) q = pitch rate of aircraft (°/s) qm = pitch rate of model (°/s) rc = input command to auto-loop (°/s) w = vertical velocity of aircraft (m/s) x = aircraft response Z, Z 1. z2, z3, = switching functions A = gain of adaptive loop (s-') A (s) = auto-loop transfer function D(s) = denominator polynomial of A (s) DA(s) = denominator polynomial of FA (s) FA(s) = overall transfer function of actuator and aircraft dynamics GA(s) = transfer function of auto-loop controller ' Gq, Gq, G4 = gains of auto-loop (s ') KA = gain of aircraft (s-') M(s) = model transfer function Mw', My;,', Mq', MZ' = pitching motion stability derivatives N(s) = numerator polynomial of A (s) NA(S) = numerator polynomial of FA (s) P,(s), P2(s) = input filter transfer functions TA = aircraft time constant (s) Zy;,', Zq', Zz' = heave motion stability derivatives e = error between commanded and achieved responses 17 = elevator deflection (°) x = input filter inverse time constant (s-1) rc c = time constant of lagged command (s) rL = leaky integrator time constant (s) = damping ratio of auto-loop = damping ratio of uncontrolled aircraft Wi = damped natural frequency of autoloop w, = damped natural frequency of uncontrolled aircraft
IntroductionSince about 1950 there has been strong interest in providing a type of control system to operate in conjunction with a dynamic process in a manner to cause the overall response of the combination to be essentially the same for every operating condition, even though a number of the parameters of the process may have changed considerably as the operating conditions changed. One method used to attain this desirable performance, in situations where the process parameters change, is to arrange to use a measure of the departure of the system response from its desired form to adjust the changed parameters back to their nominal values. Such systems are called adaptive controls. Although the earliest work was concerned with the use of an adaptive control scheme applied to an internal combustion enginel, many other schemes, concerned with how adaptive control could be applied successfully to automatic flight control systems (AFCS) for aircraft, were considered in the USA about 1958 ~ 3, 4, s. By 1959 two bibliographies6, ~ and the proceedings of a symposium concerned with such systems had already been published. A comprehensive statement of the reasons for the need for adaptive flight control was published in 19629 and, of the considerable number of papers which followed, the most relevant included a number 10,11,12 concerned with the model-reference type of system, first proposed in 19584. A comprehensive survey of the design of such modelreference systems was published in 197313 and an account of the development of such systems was printed recently 14, although the justification put forward in that paper for the use of such adaptive control on AFCS is inadequate, as will be demonstrated later in th...