This brief considers the problem of designing second-order controllers for model matching of interval plants. This task is theoretically challenging and important for practical applications due to the widespread use of low-order control. In this brief, the second-order controller structure is chosen to encompass most of the classical control structures, such as proportional-integral-derivative (PID) controllers and lead/lag compensators. Based on results from parametric robust control and an extension of complex PID stabilization, a synthesis method for model matching of the interval plant is proposed. The obtained results are applied to the design of a controller for the speed control of a servo motor in the presence of load inertia variation and a sudden load change. To capture uncertainty due to load inertia variation, the system model is constructed as an interval system family from the experimental data. The performance specifications are translated into a model matching and load disturbance attenuation problem. The proposed approach is then used to design a robust second-order controller to meet performance specifications. The effectiveness of the proposed method is verified through simulation and experimental studies.

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