4.4 Environmental Inputs and Disturbances

Prescribed inputs are not design decisions¶

The function $d(t)$ represents exogenous quantities that influence system behavior but are not selected by the optimizer in the nominal problem. External loads, wind, waves, road elevation, ambient temperature, payload motion, and reference commands may appear here. For the positioner,

where $r$ is the commanded motion, $\tau_d$ an external joint disturbance, and $T_a$ ambient temperature.

The role of an input depends on the study. A reference trajectory may be prescribed when evaluating tracking, optimized when planning motion, or uncertain when representing user behavior. State the role explicitly rather than relying on a variable name.

Disturbance knowledge is part of the controller model¶

The optimizer may know the entire disturbance history offline, while a real controller knows only past and present measurements. Open-loop optimal control with full $d(t)$ uses complete information. Preview control uses a finite future segment. Reactive feedback observes consequences after they occur. These assumptions change achievable performance and may change the optimal plant.

Multiple operating conditions¶

A credible CCD design is rarely based on one trajectory. Let $s\in\mathcal S$ index duty cycles, payloads, load cases, or environments. The system objective may aggregate them:

while safety constraints may be required for every case. Scenario weights should represent frequency or design preference, and extreme cases should not be assigned tiny probability merely to remove their influence.

Activity 4.4: specify information availability¶