3.3 Feasible Design Space

Feasibility comes before preference¶

The feasible set is the collection of designs satisfying every constraint:

Optimization searches for the preferred point inside $\mathcal F$. A low objective value outside this set is not a candidate design. This distinction is especially important in CCD because stability, saturation, displacement, temperature, and stress constraints can carve out a narrow or disconnected feasible region.

For the suspension, small $k$ may violate displacement limits, large $k$ may degrade ride response, and small $F_{\max}$ may make the required feedback action impossible. The controller changes the location of these boundaries; the feasible plant set is therefore not fixed independently of control design.

Constraint violation as a diagnostic¶

Define the nonnegative violation measure

A value $V=0$ indicates feasibility under the chosen scaling and tolerances. During debugging, reporting each contribution is more informative than reporting only a solver’s success flag.

import numpy as np

# Illustrative algebraic screening model, not a suspension simulation.
def screen_design(k, fmax):
    ride = (k / 18_000.0) ** 2 + (2200.0 / fmax) ** 2
    travel = 0.11 * (12_000.0 / k) + 35.0 / fmax
    g = {
        "travel": travel - 0.13,
        "authority": 1800.0 + 0.03 * k - fmax,
    }
    feasible = all(value <= 0 for value in g.values())
    return ride, g, feasible

for design in [(12_000, 1800), (15_000, 2800), (24_000, 3000)]:
    print(design, screen_design(*design))