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Closed loop better than open loop (cruise)

Short answer

Closed-loop cruise measures speed and computes u=Kp·(r-v), reducing slope error from d/b (open-loop) to d/(b+Kp). Adding integral term u=Kp·e+Ki∫e dt forces steady-state error to zero regardless of disturbance or parameter changes. Trade-off: requires speed sensor and gain tuning to avoid oscillation.

How is a closed loop control system better than an open loop controller? Explain with the example of a cruise control system.

A closed-loop controller measures the actual output and corrects the control action, so it can compensate for disturbances and model errors that an open-loop controller never sees.

Cruise control example

Plant: m·dv/dt = -b·v + u + d (u = engine force, d = slope force, v = speed, r = set speed).

 Open loop:
  r --> [K=b] --u--> (+)--> [Car] --> v
                      ^ d
 Closed loop:
  r -->(+)--e--> [Kp] --u--> (+)--> [Car] --+--> v
        ^ -                   ^ d           |
        +------ [speed sensor] <------------+
  • Open loop: u = b·r. In steady state v = r + d/b. On an uphill (d negative) the car slows down and the controller does nothing. If the mass or drag changes, v also drifts.
  • Closed loop (P): u = Kp·(r - v). Steady state: v = (Kp·r + d)/(b + Kp). The error from the slope becomes d/(b + Kp), which is smaller than d/b, and shrinks as Kp grows.
  • With an integral term: u = Kp·e + Ki·∫e dt. In steady state e must be zero, so v = r regardless of slope.

Why closed loop is better

PointOpen loopClosed loop
Road disturbanceSpeed error d/bReduced to d/(b+Kp), or zero with I
Parameter changeSpeed driftsCompensated
Needs accurate modelYesLess so
Needs speed sensorNoYes

Cost: a sensor, and the gain must be limited to avoid overshoot and oscillation.

✓ Answer checked by Claude Opus 5.5 (high effort)

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