Direct tuning of the data-driven controller considering closed-loop stability based on a fictitious reference signal

The direct tuning of controller parameters, which is based on data-driven control, has been attracting considerable attention because of the ease of its control system design. In practical use, it is important to consider the stability of the closed-loop system and model matching with few design parameters. In this study, we propose a direct tuning method based on a fictitious reference signal that considers the bounded-input bounded-output (BIBO) and model matching without repeating experiments. The proposed method includes two steps. In the first step, the BIBO stability is satisfied. The pole information is lost in the cost function of the conventional method using a fictitious reference signal. Then, we derive a new cost function that can prevent the loss of the pole information. This provides controller parameters that can stabilize the closed-loop system. The model matching between the reference model and the closed-loop system is considered in the second step. When model matching is achieved, the characteristics of the reference model almost match those of the closed-loop system, including the gain and phase margins. The parameters of the reference model are automatically tuned to realize model matching. Using the two-step method, we can obtain parameters considering BIBO stability and the model matching. In addition, there are no design parameters apart from the dealing noise. Two simulations and an experiment were performed on a system with dead time to verify the effectiveness of the proposed two-step method. The results showed that the proposed method provides BIBO stability and model-matched control parameters from the measured data through a one-time experiment without trial and error.

Sufficient Conditions for Absolute Cesàro Summable Factor

Quasi-f-power increasing sequence has been used for infinite series to establish a theorem on a minimal set of sufficient conditions for absolute Cesàro φ-|〖C,α;δ;l|〗_k summable factor. Further, a set of new and well-known arbitrary results have been obtained by using the main theorem. The presented main result has been validated by the previous result under suitable conditions. In this way, the Bounded Input Bounded Output (BIBO) stability of impulse response has been improved by finding a minimal set of sufficient conditions for absolute summability because absolute summable is the necessary and sufficient condition for BIBO stability.