Control of linear systems in parallel

A technique is presented for the design of optimum linear control laws for systems in parallel: a primary system with a state vector x1, and a secondary system with a state vector x2 which is not weighted in the performance integral. The procedure entails calculating the gain matrix K1 for the primary system alone, using this gain matrix to determine the gain matrix K2 for the secondary system, and finally modifying K1 to obtain the required gain matrix K1 for the primary system with the secondary system present. The procedure is illustrated with the design of a control law for positioning the center of mass of a two-mass, spring connected system.