Laboratory Automation (LA) has the potential to accelerate solid-state materials discovery by enabling continuous robotic operation without human intervention. While robotic systems have been developed for tasks such as powder grinding and X-ray diffraction (XRD) analysis, fully automating powder handling at the milligram scale remains a significant challenge due to the complex flow dynamics of powders and the diversity of laboratory tasks. To address this challenge, this study proposes the SCU-Hand-SV (Soft Conical Universal Robotic Hand with Single-sheet Valve), which preserves the softness and conical sheet designs in prior work while incorporating a controllable valve at the cone apex to enable precise, incremental dispensing of milligram-scale powder quantities. The SCU-Hand-SV is integrated with an external balance through a feedback control system based on a model of powder flow and online parameter identification. Experimental evaluations with glass beads, monosodium glutamate, and titanium dioxide demonstrated that 80% of the trials achieved an error within -2 mg to +2 mg, and the maximum error observed was approximately 20 mg across a target range of 20 mg to 3 g. In addition, by incorporating flow prediction models commonly used for hoppers and performing online parameter identification, the system is able to adapt to variations in powder dynamics. Compared to direct PID control, the proposed model-based control significantly improved both accuracy and convergence speed. These results highlight the potential of the proposed system to enable efficient and flexible powder weighing, with scalability toward larger quantities and applicability to a broad range of laboratory automation tasks.