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Week 11-2: Manual Control

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**1. **1 Week 11-2: Manual Control This module will provide you with a general overview of the needs assessment process. Later modules will provide more detail on the steps involved. This module will provide you with a general overview of the needs assessment process. Later modules will provide more detail on the steps involved.

**2. **2 Week 11 Topics Lecture 11-1
Open Loop vs. Closed-loop systems
Modeling movement time: Fitt’s law
Elements of the Tracking loop
Lecture 11-2
Revisting Fitt’s Law as a feedback system
Tracking capabilities of the human operator
Multi-axis control
Spectral Analysis and the cross-over model

**3. **Transfer Functions and Control Order transfer function: function that relates system input to system output
control order: the number of integrations performed by the transfer function
Two important parameters
Gain: ratio of system output to system input
Lag
pure time delay
exponential lag 3

**4. **Continuous Tracking of Dynamic Systems Transfer Functions and Control Order (cont.)
Zero-order: displacement controller, no integration
Example: computer mouse
Types
Pure gain
Pure time delay
exponential lag
Good for
systems designed to control position precisely
controllers without a natural zero point 4

**5. **Continuous Tracking of Dynamic Systems Transfer Functions and Control Order (cont.)
First-order: velocity controller, single integration
Example: car steering wheel
Output equals integral (sum) of input
input displacement is proportional to output velocity
Good for
systems designed to control velocity precisely
controllers with a natural zero point (joysticks)
Similar response to zero-order controller with exponential lag 5

**6. **Continuous Tracking of Dynamic Systems Transfer Functions and Control Order (cont.)
Second-order: acceleration controller, double integration
Example: car breaks and gas pedals
Output equals double-integral of input
input displacement is proportional to output acceleration
operator must move to negative position to slow down
overcorrection can lead to instability and oscillatory behavior 6

**7. **Continuous Tracking of Dynamic Systems Transfer Functions and Control Order (cont.)
Minus-first-order: differentiator
output is proportional to rate of change of the input (derivative)
can be used in series with first and second-order controllers to reduce control order 7

**8. **Human Operator Limits in Tracking Lags generated by perceptual-motor processing time
effective time delay
zero- and first-order systems: 150-300 ms
second-order systems: 400-500 ms
Bandwidth in information transmission
Elkind & Sprague (1961): upper frequency limit for human tracking of unpredictable signals is between 0.5-1.0 Hz (2 corrective decisions per second)
if signals are predictable then bandwidth increases to 2-3 Hz-->motor limit 8

**9. **Human Operator Limits in Tracking Difficulty in predicting or anticipating movement
large system lags require operator to predict future states based on the system’s current trajectory --> velocity and acceleration
humans are poor at perceiving changes in velocity and acceleration, thus poor at predicting
Anticipation requires mental resources for calculations --> increases mental workload
S-R compatibility: misaligned axes of controls and displays increase error and control reversals 9

**10. **Human Operator Limits in Tracking System Dynamics and Tracking Performance
Gain: intermediate is best, inverted “U-shaped” function
Time delay: directly related to magnitude of error
System Order
zero and first are roughly equal
Why? Successful tracking requires both position and velocity to be matched
If space is constrained, first order offers better economy of movement
Second-order and higher are much more difficult
can lead to instability 10

**11. **Instability and Feedback Negative feedback – feedback that tends to reduce error – self-correcting systems
Most systems typically have negative feedback
Purposeful control means trying to minimize error
Positive feedback – feedback that tends to increase error
Not common in purposeful control, but possible in some physical systems
If left unattended, small errors inevitably lead to larger errors 11

**12. **Displays & Closed-loop Control Goal: eliminate effects of lags or higher-order systems
Input prediction: preview displays
Output Prediction:
predictive displays: computer estimates future position and adds a second symbol to the display representing this future position (predictive span)
quickened displays: same as predictive except no symbol representing current position, only future position is displayed 12

**13. **Input Devices Constraints on Input devices supporting continuous closed-loop control
Physical constraints
space, fatigue, vibration, G-forces
Control-order compatibility
Speed-accuracy trade-off
Voice control? 13

**14. **Multi-axis Control Many tasks require the operator to control more than one dimension of a dynamic system
Independent vs. Cross-coupled axes
Example of independent: speed and steering
Example of Cross-coupled: aircraft pitch and roll
Hierarchical cross-coupled (Fig. 10.13)
e.g., heading and lateral position, yaw and roll, thrust and speed
operator sets goal based on highest order system but controls a lower order system 14 After Abbott and Costello
High HT: very consistent stimulus-response mappings, but although information was conveyed (“back to third again”), misunderstandings perpetuated.
Costello’s conceptual model of the team was inaccurate
Why was the misunderstanding not corrected?
Ineffective feedbackAfter Abbott and Costello
High HT: very consistent stimulus-response mappings, but although information was conveyed (“back to third again”), misunderstandings perpetuated.
Costello’s conceptual model of the team was inaccurate
Why was the misunderstanding not corrected?
Ineffective feedback

**15. **Factors Affecting Multi-axis Control Display Separation: multi-axis control is impeded by spatially separated displays--increases visual scanning
Integrated vs. Separated Displays and Controls
Advantage for integrated displays: object perception
Smaller advantage for integrated controls: cross-talk
Integral vs. Separable Axes: Proximity compatibility
Resource Demand: Higher control orders more difficult
Similarity of Control Dynamics: best to require only a single mental model of control dynamics for all axes 15 After Abbott and Costello
High HT: very consistent stimulus-response mappings, but although information was conveyed (“back to third again”), misunderstandings perpetuated.
Costello’s conceptual model of the team was inaccurate
Why was the misunderstanding not corrected?
Ineffective feedbackAfter Abbott and Costello
High HT: very consistent stimulus-response mappings, but although information was conveyed (“back to third again”), misunderstandings perpetuated.
Costello’s conceptual model of the team was inaccurate
Why was the misunderstanding not corrected?
Ineffective feedback

**16. **Modeling Human Operator in Manual Control Frequency vs. Time domain
Bode plots (Figures 10.16-10.19)
Y-axes
Gain: log10(output/input amplitude ratio), expressed in units of decibels (dB)
Phase Lag: expressed in units of degrees
X-axis: log10(frequency)
Representations of 0, 1st, and 2nd order systems
16

**17. **The Cross-over Model Good control achieved by
Low error
High degree of stability
Cross-over model states that human adapts to controller and system dynamics such that the total open-loop transfer function e(t)?o(t) is first-order
Operator compensates for higher-order control and system dynamics by differentiating
Gain is adjusted to balance error and stability 17