PID Controller Design for MIMO Systems by Applying Balanced Truncation to Integral-Type Optimal Servomechanism

A closed-loop balanced truncation technique has been applied to an integral-type optimal servomechanism (IOS) expressed in graph-operator form of normalized right coprime factorization to produce a reduced-size state-feedback gain matrix, which is then converted into proportional-derivative (PD) gain matrices. On the other hand, the states of the integral of control error in the IOS are not truncated, so that the feedback gain matrix of the IOS for the states becomes the integral (I) gain matrix. All the design procedure is completed with the state-space approach, which is convenient especially in dealing with multiple-input multiple-output (MIMO) systems. Application of the proposed method to the boiler system of the PID '12 benchmark problem demonstrates the effectiveness of the design method.