Practical Aspects of State-Space Methods, Part I-System Formulation and Reduction

Practical methods, suited to digital computers, are presented for the formulation, reduction, and combination of systems in state-space form. Formulation is illustrated in two ways. The coefficients of a linearized set of equations describing a simple superheater are entered directly in the matrices of the state-space equations. Transfer functions of a control system are decomposed into first-order differential equations and put in the same form. Reduction to standard state-space form is accomplished by matrix inversion and by signal-flow graph manipulation that is equivalent to inversion by partitioning. Composite systems are formed from subsystems that are in either reduced or unreduced form. The emphasis is upon the ease of handling large, complex problems afforded by the systematic format of the state-space representation. Key words are combination, composite system, control design, digital computer, formulation, linear, matrix, matrix inversion, reduced system, reduction, signal-flow graph, state-space, superheater, unreduced system.