13.3 Uncertain Plant Variables

Core idea¶

Uncertain Plant Variables must be treated as a system-level decision rather than an isolated technique. For a suspension with uncertain mass, road, damping, measurement noise, and actuator efficiency, state what is fixed, what is optimized, what information is available, and what equations define feasibility.

The relevant quantities are $\theta$, design $p,c$, random trajectories, failure events, and risk $\alpha$. The chapter-level formulation is

For this section, trace how the choice changes risk formulation, the active constraints, and the implementable engineering design. A method is useful only when its assumptions are explicit and its result answers the same system question as the baseline.

Engineering interpretation¶

Ask three questions:

1. Which physical, informational, computational, or economic resource changed?

2. Which objective component or active constraint made the change valuable?

3. Does the conclusion survive model, disturbance, initialization, uncertainty, and implementation checks?

A practical action is to propagate. Record units and assumptions before optimization, report component objectives and margins afterward, and verify the result using an independent calculation or higher-fidelity model.

Activity 13.3: quantify uncertain plant variables¶