---
title: "Open-loop cruise control using P control"
subject: "Embedded System"
chapter: 7
key: "semester_6/embedded_system:open-loop-cruise-p-control"
source: https://www.bctengineer.com/q/semester_6/embedded_system/open-loop-cruise-p-control
site: BCT Engineering
---

# Open-loop cruise control using P control

Embedded System · Chapter 7: Control System

- Asked in: 2078 Chaitra
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/embedded_system/open-loop-cruise-p-control
- Whole chapter: https://www.bctengineer.com/md/semester_6/embedded_system/chapter-7

## Question

Design control system for an automobile cruise control in open-loop control system using P control.

## Short answer

In open-loop cruise P control, set engine force u = Kp·r with Kp = b to obtain v = r. The discrete model v[k+1] = (1-bT/m)v[k] + (T/m)(u+d). Stability requires T < 2m/b, no oscillation T < m/b. Performance: time constant m/b, settling time ~4m/b, zero overshoot, steady-state error d/b.

## Answer

In an open-loop cruise controller the "P control" is a proportional gain applied to the reference speed: the engine force is u = Kp·r. Nothing is measured, so there is no error signal; the gain Kp is set from the car model.

#### Plant model

m·dv/dt = -b·v + u + d, where m = mass, b = drag/friction coefficient, v = speed, u = engine force, d = road disturbance (slope, wind), r = desired speed.

```text
 r --> [ Kp ] --u--> (+) --> [ 1/(m s + b) ] --> v
                      ^
                      d
```

#### Design steps

1. **Choose Kp.** With d = 0 the steady state is v = Kp·r/b. To get v = r choose Kp = b.
2. **Discretise** (sampling period T, Euler): v[k+1] = a·v[k] + c·(u[k] + d[k]), with a = 1 - b·T/m and c = T/m.
3. **No unbounded output:** |a| < 1, so T < 2m/b.
4. **No oscillation:** 0 < a < 1, so T < m/b. The speed then rises smoothly like a first-order exponential.
5. **Implementation:** the microcontroller reads the set speed r, computes u = Kp·r every T, and writes it to the throttle actuator (DAC/PWM).

#### Performance

| Parameter | Value |
|---|---|
| Time constant | m/b |
| Settling time (2 %) | about 4·m/b |
| Overshoot | none |
| Steady-state error | d/b from road disturbance, plus error from wrong b or m |

The controller is simple and stable, but it cannot reject road disturbance or compensate for changes in mass or drag; for that, feedback (closed loop) is required.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. In open-loop P control, u equals?
   A. Kp*(r - v)
   B. Kp*r
   C. Kp*v
   D. Kp*d
   Answer: B. No error signal. (Key point: Open-loop P)

2. Kp for v = r with d = 0?
   A. Kp = b
   B. Kp = m
   C. Kp = 1
   D. Kp = m/b
   Answer: A. v = Kp r / b. (Key point: Kp value)

3. What can it not do?
   A. Reach any speed
   B. Be implemented
   C. Reject road disturbance or compensate for mass changes
   D. Be stable
   Answer: C. Needs feedback. (Key point: Limitation)

## Related in Embedded System

- [Open-loop automobile cruise controller design](https://www.bctengineer.com/question.md?key=semester_6%2Fembedded_system%3Aopen-loop-cruise-controller) — Embedded System, chapter 7, asked 3×
- [Closed loop better than open loop (cruise)](https://www.bctengineer.com/question.md?key=semester_6%2Fembedded_system%3Aclosed-loop-better-cruise-integral) — Embedded System, chapter 7
- [Open loop versus closed loop control](https://www.bctengineer.com/question.md?key=semester_6%2Fembedded_system%3Aopen-vs-closed-loop) — Embedded System, chapter 7, asked 6×
- [Steps to design closed loop control system](https://www.bctengineer.com/question.md?key=semester_6%2Fembedded_system%3Aclosed-loop-design-steps) — Embedded System, chapter 7
- [Closed loop speed control design conditions](https://www.bctengineer.com/question.md?key=semester_6%2Fembedded_system%3Aclosed-loop-speed-control-conditions) — Embedded System, chapter 7

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- [Traffic light system of Kathmandu: open or closed loop](https://www.bctengineer.com/question.md?key=semester_3%2Fcontrol_systems%3Atraffic-light-justify) — Control Systems, chapter 1
- [Control system block diagram and closed loop advantages](https://www.bctengineer.com/question.md?key=semester_3%2Fcontrol_systems%3Awhat-is-cs-bd-cl-advantages) — Control Systems, chapter 1
- [Define control system and closed loop block roles](https://www.bctengineer.com/question.md?key=semester_3%2Fcontrol_systems%3Adefine-cs-bd-role) — Control Systems, chapter 1, asked 5×
- [Closed loop control system block diagram explained](https://www.bctengineer.com/question.md?key=semester_3%2Fcontrol_systems%3Awhat-is-cs-bd-closed-loop) — Control Systems, chapter 1, asked 4×