| The problem considered in this thesis is that of designing optimal compensation for the weapon positioning system of a surface to air fire control system that has to respond to stochastic inputs. The object of the design is to minimize the mean square sampled error between 'where the gun is' and 'where the gun ought to be'. It is assumed that the input or some derivative of the input can be described as a stationary random process.Three different input profiles have been considered. For a range of values for the statistical properties of the input, the optimal K(,g)(z) has been found for each case. Finally, the objective function has been evaluated for the K(,g)(z) designed by the mathematical programming approach and by two other design methods. A comparison of the three values of the objective function showed that it was minimum for the K(,g)(z) designed by the mathematical programming approach.The development presented in this thesis provides a new approach to the design of a fire control system. A new method has been described to deal with situations in which a derivative of the input, and not the input itself, can be described as a stationary random process.The mean square sampled error is expressed as a quadratic function of the system variables. The system variables are the coefficients of the series expansion of K(,g)(z), the overall pulse transfer function of the weapon positioning system. The coefficients of the quadratic objective function are derived from the statistical properties of the input to the system. Linear constraints can be imposed on the system variables based on considerations of physical realizability, stability, transient response and steady state response specifications. The quadratic objective function and the linear constraints are then used in a quadratic programming algorithm to find the optimal value of K(,g)(z). |
