Engineering system design -- whether mechatronic, control, or embedded -- often proceeds in an ad hoc manner, with requirements left implicit and traceability from intent to parameters largely absent. Existing specification-driven and systematic design methods mostly target software, and AI-assisted tools tend to enter the workflow at solution generation rather than at problem framing. Human--AI collaboration in the design of physical systems remains underexplored. This paper presents Design-OS, a lightweight, specification-driven workflow for engineering system design organized in five stages: concept definition, literature survey, conceptual design, requirements definition, and design definition. Specifications serve as the shared contract between human designers and AI agents; each stage produces structured artifacts that maintain traceability and support agent-augmented execution. We position Design-OS relative to requirements-driven design, systematic design frameworks, and AI-assisted design pipelines, and demonstrate it on a control systems design case using two rotary inverted pendulum platforms -- an open-source SimpleFOC reaction wheel and a commercial Quanser Furuta pendulum -- showing how the same specification-driven workflow accommodates fundamentally different implementations. A blank template and the full design-case artifacts are shared in a public repository to support reproducibility and reuse. The workflow makes the design process visible and auditable, and extends specification-driven orchestration of AI from software to physical engineering system design.

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