System Identification

1 Prescribing the Input Force

Seven types of input force can be used in System Identification Toolbox (with longer description available for each):

Impulse - a sudden, brief applied force
Step - a steady, maintained force
Ramp - a gradually increasing force
Sinusoid - a smoothly oscillating force of sinusoidal shape
Square wave - a sudden oscillating force of a given magnitude that switches between two directions
White Noise - a random force
Pseudo White Noise - a random set of force pulses (usually more functionally useful than white noise)

This Toolbox allows users to combine multiple input forces together, which could be the same type (e.g., two impulses at different times) or different type (e.g., a sequence with an impulse, step and sinusoid). The maximum number of input forces that a user can apply is 10.

The general properties which apply to all input include (with a longer description available for each):

Direction: The direction of an effect can be expressed in polar or Cartesian coordinates. By default, polar coordinates are used, and the direction is specified in the x, with y always 0. Polar coordinates are expressed as a single angle, in hundredths of a degree clockwise from the zero-point (true north, which is the negative y-axis, that is away from the user). For a device (such as a driving wheel) that only supports 1 degree-of-freedom, this property is set to 27000 and is read-only.
Duration: The total duration of the effect, in microseconds. If this value is INFINITE, the effect has infinite duration.
Magnitude: The magnitude of the effect, in the range from -10,000 through 10,000, with -10000 having the same magnitude as 10000 but opposite direction.
Start Delay: Time (in microseconds) that the device should wait after the start of the task before implementing the effect. If this value is 0, the effect begins at the start of the task. For this Toolbox, this start delay can be up to 10 seconds.

Among seven inputs, White Noise and Pseudo White Noise are noise data, which means their signal magnitude randomly generated all the time.

Force	Description	Properties List	Example
Impulse	Constant effect in DirectX. According to the definition of Impulse, “instantaneously large but brief phenomena” [1], System Identification Toolbox set the duration of impulse input to 20ms.	Direction: [Default = {27000, 0}, which is X direction pushing to the right of the user] Duration: [Default, read-only = 20000, which equals 20ms] Magnitude: [Default = 10000] Start Delay: [Default = 106, which equals one second]
Step	Constant effect in DirectX. According to the definition of Impulse, “equal zero before t=0 and one afterwards” [2], System Identification Toolbox set the duration of step input to infinity by default.	Direction: [Default = {27000, 0}, which is X direction pushing to the right of the user] Duration: [Default = (int) DI.Infinite, which equals -1; it represents a infinitive time period] Magnitude: [Default = 10000] Start Delay: [Default = 106, which equals one second]
Ramp	Ramp effect in DirectX. According to DirectX, a ramp force is a force with defined starting and ending magnitudes and a finite duration. A ramp force can continue in a single direction, or it can start as a strong push in one direction, weaken, stop, and then strengthen in the opposite direction.	Direction: [Default = {27000, 0}, which is X direction pushing to the right of the user] Duration: [Default = 5000,000, which equals 5 seconds; the duration can not be set to Infinity.] End: The magnitude at the end of the ramp effect.[Default = 100] Start: The magnitude at the start of the ramp effect.[Default = 0] Start Delay:[Default = 1000,000, which equals one second]
Sinusoid	Sinusoid effect in DirectX	Direction:[Default = {27000, 0}, which is X direction pushing to the right of the user] Duration:[Default = (int) DI.Infinite, which equals -1; it represents a infinitive time period] Magnitude:[Default = 10000] Offset: Offset of the effect. The range of forces generated by the sinusoid effect is offset minus magnitude to offset plus magnitude. Another rule implemented by System Identification Toolbox here is the sum of absolute value of Offset plus magnitude should not be over 10000, which is the maximum value of the force.[Default = 10000] Period: Period of the sinusoid effect, in microseconds. [Default = 1000,000, which equals one second] Start Delay:[Default = 1000,000, which equals one second]
Square Wave	Square effect in DirectX	Direction:[Default = {27000, 0}, which is X direction pushing to the right of the user] Duration:[Default = (int) DI.Infinite, which equals -1; it represents a infinitive time period] Magnitude:[Default = 10000] Offset: The same with Sinusoid Input, please refer to “Sinusoid Input” [Default = 0] Period: [Default = 1000,000, which equals one second] Start Delay: [Default = 1000,000, which equals one second]
White Noise	Derived from Constant effect in DirectX. White Noise is defined as “A random noise that contains an equal amount of energy per frequency band.” System Identification Toolbox uses a random generator to generate a random integer in the range [lowNoise, highNoise], which set as the new magnitude of constant effect in every sampling event.	Direction: [Default = {27000, 0}, which is X direction pushing to the right of the user] Duration: [Default = (int) DI.Infinite, which equals -1; it represents a infinitive time period] highNoise: The upper range the magnitude of the noise may reach. [Default = 100] lowNoise: The lower range the magnitude of the noise may reach. [Default = -100] Start Delay: [Default = 1000,000, which equals one second]
Pseudo White Noise	Pseudo White Noise uses a random generator to generate a random integer too, but it will only assign a value among {lowNoise, 0, highNoise} to magnitude of constant effect in every sampling event. The algorithm may guarantee that chances to fall into these three values are equally. The advantage of using Pseudo White Noise over White Noise is that it provides a much stronger input to the human subjects.

2. Displaying the Input Force Pattern

When users configure input force properties, System Identification Toolbox display Force-Time graph in real-time, which means, any change to input properties, such as magnitude, duration, startDelay and so on, will show in the graph instantly.

In a Force-Time graph, x-axis would be time passed since the input starts, y-axis would be the magnitude of the force.
- There are two Force-Time graphs, showning in X direction and Y direction separately.
Force magnitude ranges from -10000 to 10000, where -10000 represents a input force which has the same magnitude but opposite direction with 10000.
If only one input force applied, the duration would be the one of this input force; otherwise, when multiple input forces applied, the duration would determined by the one which has the longest duration.
When input duration is for the whole task time, System Identification Toolbox will only display 10 seconds duration of Force-Time graph at a time.
For Noise inputs, it is impossible to show the actual magnitude, which changes all of the time. By convention, the System Identification Toolbox uses symbols instead to display the actual magnitude of Noise input. The symbols representating these types of input signals are hatches, as shown below.

Input Force	Display
Square Wave input
White Noise input
Pseudo White Noise Input

3. Position Output Response Data

The position of the device, which is the response of input force, will be collected in every sample period.

For Joystick, both X and Y data could be used as output.
For Driving Wheel, only X data could be used as output; in most case, Y axis data represented the brake and acceleration pedal position.

There are two conditions that will cause the System Identification Tool to stop its running process:

The duration of all the input force has expired.
User stops the running process manually by clicking Stop button.

When the identification process stops, System Identification Toolbox will display the input force and output position graph by X and Y axis separately.

This is an example when a White Noised Sinusoid force, the direction of both equals 27000, applied. Note in the graph, White Noise is not represented by dotted grid symbol any more, instead, the magnitude of the White Noise sum the magnitude of Sinusoid, which is the actual input, will be used.