# Documentation

## Absolute Time Temporal Logic Using the DURATION Operator

This example models an automotive transmission system using the Stateflow® duration operator. The Stateflow chart uses duration to automatically shift gears based on the vehicle's throttle requirements and speed.

### Model Description

There are five major blocks in this model.

• User Inputs: Provides two inputs to the model viz. brake and throttle.

• Engine: Calculates engine RPM based on impeller torque value and throttle.

• Gear_logic: Calculates next gear based on current gear, throttle, and current vehicle speed.

• Transmission: Calculates impeller and output torque based on RPM, gear and transmission speed.

• Vehicle: Calculates vehicle and transmission speed based on output torque and brake.

### Chart Description

The Stateflow chart models the shifting of gears based on throttle and speed of the vehicle. The down_threshold and up_threshold outputs represent minimum and maximum speed values that throttle and current gear are able to handle. The Simulink function 'calculate_thresholds' calculates these two values using throttle and current gear as inputs. If the actual speed is higher than up_threshold value for longer than TWAIT then chart transitions to higher gear. Conversely, if the actual speed is lower than the down_threshold for longer than TWAIT then the chart transitions to a lower gear. At each time step, duration operator is called to get the amount of time for which speed is higher than up_threshold. If this time exceeds TWAIT then boolean variable 'up' is set which in turn transitions chart from current gear to a higher gear. Conversely the chart transitions to a lower gear based on the value of 'down_threshold'.

### Active State Data

Active State Data is the enumerated data that represents the current active state during simulation. For more information, see: Active State Data. In this chart, the output data 'gear' maintains the current active state which in turn represents the current gear. This data automatically updates when a transition is taken. The data is used by downstream blocks as well as the Simulink® function calculate_thresholds.

### Simulation

To visualize these changes, simulate the model and open the scope.