Mathematical model

As explained in the Principle of DP, the mathematical model plays a big role in the system. It is important that the Operator understands fully how this feature works, and the difference between it and the older DP systems.
 
In fact, the DP system in the earlier days, was simply a analogue system directly controlled by direct measurement.

This might be also the case in modern DP system, where a Proportional/Integral/Derivative (PID) control algorithm can be used ,for example, to control the surge, sway and yaw.
 
Doing so, there might be the possibilities to set limits for measurements, but the main issue here is that the forces not directly measured won’t be taken in account.  

Using a mathematical modelling, as briefly explained in the principle of DP, the model itself controls the process, for example the thrusters, and the model is updated by the measurements.

There are necessary inputs  to a DP system, these are the forces, namely the external forces and thrusters, and positions (position and heading).

There’s a real need to find an efficient way of “mixing” or “blending” all this data, keeping in mind that measurements from position reference systems are noisy and that calculated data from the vessel model is only as good as your model and is only an approximation of the real world.

So it is necessary to  weigh all these parameters to determine the best possible estimate of the vessel position and heading.

A filter is then necessary to re-construct the vessel state based on noisy position and heading measurements.

 
separate the Low Frequency components of motion (which we want to counteract) from the High Frequency components of motion.
 
estimate the state of the vessel (including velocity [not measured directly] and current)
 
Based on the estimated position and heading of the vessel, the difference (or offset) between the desired values for position and heading, (Wanted Position) and the estimated position and heading is calculated. The control system then calculates the appropriate forces required to bring these offsets to zero and determines the proper command to be sent to the actuators (thrusters).

The problem is now to send the  appropriate  signal to the thrusters based on sensor input and reference signals, through the control.

Proportional Integral Derivative (PID) Controllers were used originally for DP application.

Optimal Controllers combined with Kalman Filters are used today.