Systems goal: to quickly modulate brake pressure.

Automatic Water Dispenser in First Order System, transfer function with gain.

G(s) =K /(s+a)

Effect of settling time

Settling time in this case is how long the dispenser takes to reach and stay near the desired temperature.The temperature increases smoothly over time until it reaches the set value. If the heater size is small, more settling time are required.

2nd Order Response

The speed of the response increase and even overshoot the target temperature a bit before it stable. The curve goes above the target, then comes back down.

Therefore, if instructed to give warm water it should not produce hot water in the bathroom.

It should follow instructions correctly without overstretching itself. Therefore, an underdamped approach is best considered in the settling time.

Secondly it's data input for transient communication will involve sensors, temperature, sound sensor, voice recognition and image recognition. The second order would involve adding speed in task execution, and the settling time will be swift enabling a smooth transition to a steady state.

The speed and smoothness with which the car reaches near-its new steady cornering or turning rate is a measure of transient response.

Factors influencing the transient response of a car:

Mass and Moment of Inertia

Tire

Suspension and Roll Dynamics

Weight Distribution.

Settling time is the time required for a system’s response to a disturbance (or input change) to reach and then stay within a specified tolerance band around its final steady-value.

In vehicle dynamics, this often means after a maneuver (steering input, hit a bump, etc.), how long until the car stops oscillating and returns to a stable state.

A shorter or longer settling time has practical consequences for both performance and comfort. In other words, it varies depending on the type of a car.

Different types of rising time in terms of car's behaviour:

What a faster (shorter) rise time means:

- The vehicle starts responding quickly to driver inputs. If you turn the wheel, the yaw/lateral acceleration increases almost immediately.

- Better agility and responsiveness. Useful for sharp cornering, sudden avoidance maneuvers, or when driving dynamically.

- More “nervous” feel: faster rise time can lead to overshoot or oscillation if the system (suspension, tires, steering, control systems) isn’t well damped.

So, we can conclude that it fits more for sport cars.

What a slower (longer) rise time means:

- The car feels more gradual. Inputs lead to more subdued or delayed changes.

- More comfortable ride: less abrupt responses reduce jerk or sudden lateral acceleration felt by driver and passengers.

- Possibly safer in everyday driving because responses are less surprising, more prpredictable.

So, it fits more for family cars where comfort is way more important than sharp behaviour on a road.

Different orders of Transient response have different behaviour:

1st-order systems respond to a step input with a simple exponential approach to the final value. No oscillations, no overshoot (assuming stable).

2nd-order systems Overdamped – slow approach, no oscillation but slower than first order.

2nd-order systems Critically damped – fastest approach without overshoot.

2nd-order systems Underdamped – you get oscillations / overshoot before settling.

Input : the temperature of the object

Bloc: mechanical machine

Output : the temperature desired  

The dynamic behaviour of a thermocouple can be modelled as a first-order system:

H(s) = K/(1+T(s))

With :

K: the propotionality constant (gain, in V/°C)

T: The thermal time constant