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To obtain an analytical expression for the miss step that can be used for analysis and design of missile guidance systems. The zero and single lag guidance systems are convenient analytical models, but they do not quite match reality. The binomial representation 1/(1 + sT/n)n, where T is the effective guidance system time constant and n the system order, used for more accurate high-order guidance system models in [5], still does not accurately reflect flight control system dynamics. The binomial units are usually used to approximate delay units [3] and, therefore, they cannot be considered a reliable tool for guidance system design.

Division by range (closing velocity vcl multiplied by time-to-go tgo until intercept) yields the geometric LOS angle λ, where the time-to-go is defined as tgo = tF – t. The missile seeker is presented formally as a perfect differentiator that effectively provides a measurement of the rotation rate of LOS from the interceptor to the target. The filter and seeker dynamics are represented by a transfer function G1 (s) = τzs + 1 , τ 2s + 1 where τz and τ2 are constant coefficients. An estimation of the LOS rate generates a guidance command ac based on the proportional navigation law with the effective navigation ratio N > 2.

14) 1 z3 τ1 z4 = z2 with the initial condition zT(0) = (1, 0,…,0). 8). 8) and by changing time t in the arguments of all time-varying coefficients by tF – t. Changing inputs by outputs is equivalent to the following structural changes: nodes of the original system become summation units of the modified adjoint system; summation units of the original system become nodes of the modified adjoint system; Analysis of Proportional Navigation Guided Missile Systems in the Time Domain 25 the direction of all signal flow is reversed.

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