1. This section illustrates how the above procedure can be applied to the design of an autopilot for a particular missile concept. The concept selected for this demonstration is a medium range air-to-air missile. The aerodynamic coefficients have been determined with the semi-empirical aerodynamic prediction code Missile Datcom6,7. It's also difficult to make a single choice of specification because missile capability is dependent on flight conditions such as altitude and velocity. Low altitude, high velocity missiles can achieve faster dynamics than high altitude, low speed missiles. A good choice for the specification remains dependent of these conditions. A suggested specification is to use a value of µ and ω equal to the natural frequency of the missile ωN,plusacriticaldamping ζandaunitarygain K: Coefficients Processing
2. δ + δ = δ Figure 3 gives an overview of the closed-loop step response of the proportional-integral autopilot connected to the linearized airframe model. The figure presents the time response of Equation 33 that includes the effect of the coefficient Zδeven if it has been neglected in the tuning. Forreference, the responsewith exact gains computed with Zδare shown. For this example, neglecting this coefficient for the tuning still gives an acceptable step response. As expected fromthe specification, lower altitude and high Mach number results in faster time response. The differences between simulation results and the specification come from the numerator termof the closed-looptransfer function. Non-dimensional linear coefficients determination From the raw coefficients, linear coefficients must be determined. The proposed approach is to use a finite difference approach to estimate the partial derivatives of eq. 10-12. For each Mach number, the coefficients variations are evaluated for small variations α∆ and
3. Based on transfer functions models, autopilot gains are computed for lateral proportional, lateral proportionalintegral and roll autopilots. Gains are computed according to a tuning specification given in frequency domain. A recommend specification based on the airframe natural frequency is given as a starting point (eqs. 46-48), and further refinements are possible for specific operating points on a case-by-case basis. For the lateral autopilots, a simplification of the linear model is possible, yielding a simpler expression for the autopilots gains. These gains are obtained for each linear airframe model derived from a specified Mach and altitude operation point. During missile flight, gain-scheduling is used where lookup of the gain table interpolation yields the desired gain values for the currentflightcondition.
4. Deshpande, P.B. and Ash, R.H. (1988) Computer Process Control with Advanced Control Applications. 2nded.Instrument Society of America. p509.