LINEAR MODEL EVALUATION OF COMMAND GUIDANCE SYSTEM

The primary design of a missile control system is commonly derived from a linearized model of that system. Gain selection is accomplished by examining both the performance and the relative stability of the linear representation of the system at various operating conditions given by incidence angles, mach number and flight altitude. Most often, classical phase and gain margins are used as measures of relative stability. The linearized model assumes the linearity of hardware comprising the guidance loop and the missile dynamics. The reliability of the linearization assumptions determines the robustness and performance of the primary design. This paper is devoted for the study of the linearization assumptions evaluation. A typical command guidance system is considered as a case study. In spite of the nonlinear behavior of the various subsystems comprising the guidance system, the guidance-commands limiters are assumed the only nonlinear elements in the guidance loop due to their obvious direct effect on the guidance process. Computation analysis shows that the effect of these limiters appears only during the early guidance period which does not exceed 5 percent of the entire flight time. The missile dynamics nonlinearities are also studied. A comparison between the results of the six-degree-of-freedom nonlinear model and the linearized model is carried out. Comparison shows that the linear dynamical model can be relied-on in cases where sudden target maneuver or sudden variation of flight environmental conditions are not considered. However, during steady guidance periods, the linear model results can be fairly adopted. INTRODUCTION Guided missile systems are generally nonlinear systems. The nonlinear behavior is caused by the nonlinearity of parts of the hardware and the nonlinearity of the equations of the missile motion [1][3]. For nonlinear systems, the concept of the transfer function is not valid. Thus, most of the linear control system design and analysis techniques are not applicable. Therefore; the theoretical design and analysis of missile control systems require certain assumptions. A traditional assumption is one of the hardware linearity i.e.; electronic systems, missile servos, measuring devices, and equations of motion. Indeed, linearity is a necessary constraint for one to use Laplace operator method to analyze the system response [1]. * Ass. Prof., Radar and Guidance Dpt. , Military Technical College, Cairo, Egypt. Proceedings of the 8th ASAT Conference, 4-6 May 1999 Paper GC-01 1002 The general method of designing a missile control system is to consider a typical speed or mach number and flight height. A set of aerodynamic derivatives for zero incidence can be considered in the system design with the assumption that the missile is exercised through small perturbations about zero incidence. Obviously, the control system is designed to meet a specific steady state and transient behavior. A small incidence is then assumed and all the calculations are repeated. The calculations are repeated many times for different combinations of incidence angle, mach number, and height. If the design is satisfactory at all these points, then it is satisfactory at all the intermediate points. The effect of varying C.G. position, mass, and inertia is finally considered [1], [6], [8] and [9]. After the theoretical design of the control system is established, accurate theoretical analysis of that system is initiated. For large nonlinear systems, the analytical analysis is an elaborate task. computer numerical simulation is thus considered the practical tool for the designed system evaluation, analysis, and development[1]. For an accurate estimation of the complete system behavior , the six-degree-of -freedom motion for the missile has to be considered. As well, accurate representation of the individual components that comprises the guidance loop should be involved. In situations where the practical experimentation is an expensive process, extreme accuracy in the system simulation is required. In this case, parts of the system that are hard to model mathematically, are physically inserted in the simulation model. The simulation model-in that caseis known as hardware-in-the-loop model [7]. On the other hand, the design of lateral autopilot is based on lateral channels decoupling (yaw and pitch). Then, the roll channel is designed separately [11. This decoupling facilitates dynamical equations linearization procedure. However, in a very recent work , a linearization procedure of the time invariant model for fully coupled, high angle of attack six-degree-of-freedom symmethcal missile in trim is presented [9]. The definition of trim is that the moments acting on the missile are zero and the time-rate of change of the incidc;nce angles is zero. In this paper, the linarization assumptions cited before are analyzed. The analysis is carried out on a command guidance system. The analysis of the present guidance system covers the system hardware and the dynamical equations of the missile flight. The system hardware involves many level-limitation nonlinearities. The effect of these nonlinearities is studied. As well, lineariztion of the equations of motion is considered. A comparison between the linear and nonlinear models is carried out. Except for the initial period, analysis reveals that, ignoring the nonlinear limitation of the guidance error signals is of minor importance since the error signals rarely exceed their limit level throughout the flight. This result is particular for the considered system and may not be valid for other systems. In the mean time, the linearized dynamical model of the missile motion can effectively be adopted in the prediction of the missile flight behavior as Target _0_, coordinates Guidance Station \ r guidance channel computer, —0 coding, and receiver Angular