Part 3 complete

Project_2_Speed_Controller/Part_3_Resource_Allocation/part_3_notes.md

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+# Project 2 – Part 3
+
+## Measured values
+
+From Part 2 with the wheel attached:
+
+- Steady-state speed: approximately 77.4 RPM
+- Time constant: τ ≈ 41 ms = 0.041 s
+
+The controller update rate must be at least:
+
+f_update >= 10 / τ
+
+f_update >= 10 / 0.041 ≈ 244 Hz
+
+A controller update frequency of 250 Hz is selected:
+
+T_update = 1 / 250 = 4 ms
+
+This satisfies the requirement because 4 ms < τ / 10 = 4.1 ms.
+
+
+## Timing, methods and resources
+
+| Task | Requirement | Method / Resource |
+|---|---|---|
+| Count encoder pulses | Capture all encoder edges | Pin-change interrupt on D8 |
+| Determine direction | At each encoder edge | Read C2 on D9 |
+| Calculate speed | Fresh value every 4 ms | Encoder count difference + Timer1 |
+| Update controller | At least 244 Hz | Timer1 interrupt at 250 Hz |
+| Generate PWM | Much faster than controller update | Timer2 hardware PWM |
+| Send data to laptop | Not time-critical | Serial in main loop |
+
+At the measured speed of 77.4 RPM and approximately 2100 counts/revolution:
+
+f_encoder = (77.4 / 60) × 2100 ≈ 2709 counts/s
+
+Therefore the time between encoder counts is approximately:
+
+T_encoder = 1 / 2709 ≈ 369 us
+
+The encoder interrupt must therefore execute in much less than 369 us.
+
+
+## Timer and PWM choice
+
+Timer1 will provide the 250 Hz controller time base.
+
+With a 16 MHz clock and prescaler of 64:
+
+OCR1A = (16000000 / (64 × 250)) - 1 = 999
+
+Therefore Timer1 can generate an interrupt every 4 ms.
+
+Timer2 will generate hardware PWM. Using Fast PWM with a prescaler of 8:
+
+f_pwm = 16000000 / (8 × 256) ≈ 7.8 kHz
+
+T_pwm ≈ 128 us
+
+Since:
+
+128 us << 4 ms
+
+the PWM frequency is sufficiently faster than the controller update rate.
+
+
+## Validation
+
+| Requirement | Validation |
+|---|---|
+| Encoder counting | Compare measured count/RPM while rotating motor |
+| 250 Hz controller update | Toggle debug pin and measure 4 ms period with oscilloscope |
+| PWM frequency | Measure PWM output with oscilloscope; expect about 7.8 kHz |
+| Controller execution time | Measure debug pulse around update routine; must be < 4 ms |
+| Serial transmission | Keep Serial outside time-critical interrupt routines |