In this article, a new full-and reduced-order proportional-integral (PI) controller is developed such that the target-tracking or commandfollowing problems become generic for a wide range of frequency inputs. The

This study presents a novel digital control algorithm with state estimator technique for semi-active control of structures with magneto-rheological (MR) damper. The proposed control strategy is based on servomechanism (popularly known as command-following or tracking system), where the measured output of a system pursues the command of reference input. This is achieved through a hybrid proportional-integral (PI) controller, different from the conventional output or state-based feedback design, where the control force is proportional to the feedback of internal state (i.e., displacement and velocity) as well as the integral state (i.e., integral of output error signal) of the system. In this approach, optimal observer technique through Kalman filter is modified to estimate the full state and integral state vector of the system for feedback from the measured absolute acceleration output. Optimal gains of the proposed regulator (i.e., both proportional and integrator gains) and estimator are formulated by minimizing a desired performance index in discrete time. In addition, the present study proposes a direct algorithm, where the applied voltage to the MR damper varies continuously between the maximum and minimum range instead of being restricted to only maximum and minimum values. The adequacy of the proposed strategy is studied in terms of reduction in the following: (a) structural responses, (b) optimal control force, (c) sensor noise and process noise covariance of the filter output, and (d) applied voltage (as compared to clipped on-off case). Finally, it has been demonstrated that the proposed control algorithm provides superior performance and stability in comparison to the conventional proportional (state)based techniques.

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