ABSTRACTThe design of a linear feedback control system normally implies a compromise choice of loop gain between the conflicting requirements of (a) high gain for good steady-state accuracy and bandwidth, and (b) low gain for satisfactory stability and damping. The optimum gain would be that which leads to a system with the best possible step-response as indicated by the minimization of a suitably chosen index of optimization. The paper presents the results of an attempt to develop a frequency-domain approach to the direct determination of optimum gain for linear systems. A figure of merit for linear systems in the form: gm. sinφm.v−1mis suggested, where gm,φm, Vm are respectively the gain-margin, the phase-margin and the frequency-margin (ωcp/ωcg) for the system. The value of loop gain which maximizes this figure of merit is also found to correspond to the minimization of chosen optimization indices of step-response for several typical systems.The above figure merit is identified as the imaginary part of the normalized complex-gain margin defined for any system asThe polar plot ofmn is directly obtainable from the complex gain plot for the system, for which a generalized Cartesian formulation has been developed along with a programme for digital computation. A single straightforward frequency-domain computation is thus made available for the determination of optimum gain for any linear feedback-control system.