Analysis of a nonlinear control system for stabilizing a missile

An autopilot with attitude and rate feedback, representative system lags, and a two-way relay servo with inherent hysteresis is considered for roll control of a missile with peripheral, tangentially operating jets. This type of control system is shown to produce a steady-state oscillation. Missile dynamics in the presence of this hunting are developed and the relationships governing angular position and rates are found to be functions of the oscillation frequency, control force magnitude, and missile constants (geometry and weight). The describing function technique is utilized to determine graphically the relationship among frequency, hysteresis band, and system time delays. A comparison is made between the root locus and amplitude-phase presentation. An analog computer study of system behavior is presented to illustrate the agreement between the analysis and system performance.