Spreadsheet analysis of position extrapolation

	A	B	C	D
1	Introduction
2	This spreadsheet tool allows simulation of several control models tracking a moving target (pursuit tracking)
3	Position control
4	Position control with target extrapolation
5	Position control with target and cursor extrapolation
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7	These models are simplified versions of those found in the following paper, and serve as an illustrative demonstration.
8	Parker, Weightman, Tyson, Abbott, & Mansell (XXXX). Sensorimotor delays in tracking may be compensated by negative feedback control of motion-extrapolated position. XXXX
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10	Instructions
11	The tool comprises two simulation sheets. Thef irst runs the models on a ramp target (constant velocity), the second runs the models on a sinusoid target
12	The sheets are of the same format. At the top of the page are the model parameters. These can be altered manually.
13	Below the parameters is the table of computed values for the target signals and model simulated cursor positions
14	To the right is a graph displaying the target path over time and the simuated cursor paths
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16	All models have been simulated with a loop delay of 100 ms. This means that they act on outdated input, as is the case for humans manually tracking targets.
17	Note that the loop delay value is fixed and cannot be changed (it can be changed but this will have no effect on the data)
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19	The default parameters are:
20		Position control	Target extrapolation	Cursor and target extrapolation
21	Input Delay	100 ms	100 ms	100 ms
22	Output Gain	3	3	3
23	Target Velocity Gain		6	3
24	Cursor Velocity Gain			3
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26	Position control model
27	If the models are set to these parameters it can be observed that the position control model will always lag behind the target by a fixed amount due to the Input Delay
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29	Target extrapolation model
30	In contrast, the position extrapolation model will quickly eliminate most of the lag.
31	In the case of sinusoid target tracking, the cursor will overshoot the target when the target switches direction and then slightly lag behind the target as the target accelerates.
32	As the target begins to decelerate, the cursor will overtake the target,causing an overshoot.
33	This occurs as a result of acting on outdated velocity information.This characteristic pattern is commonly observed when human participants track sinusoid targets.
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35	Target and cursor extrapolation model
36	If both the target and cursor are extrapolated equally (same velocity gain parameter values), the model will behave similarly to the position control model.
37	If the target velocity gain is larger than the cursor velocity gain then the model will behave similarly to the position extrapolation model
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