A Paper and Pencil Control System Design

This paper describes an algebraic method of control system design using the system characteristic equation and the Routh array. This technique does not require finding roots of the characteristic equation and therefore is suitable for pencil and paper analysis. In addition, since no graphical steps are required, large system trade-off studies can be easily programmed for digital computer optimization. The method is based on the idea of validating a simple response approximation formed by truncating the characteristic equation. This validation is performed by placing a constraint on the ratio between the integrated square of the system impulse response and the corresponding integral of the approximation. The values of these integrals are obtained quite easily from the Routh array. Additional ratios and a generalized damping ratio are also defined. The design of a hydraulic control system is presented as an example problem illustrating the use of this method.