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Chapter 4 • Theory & Derivations

Embedded Computing and Industrial Interfaces

Comprehensive university textbook unit covering fundamental principles, governing relationships, and engineering applications of Embedded Computing and Industrial Interfaces.

§4.1 Scheduling, interrupts and execution budgets

**OpenSTEM Mechanical Engineering · Book 11: Mechatronics Engineering · Unit 4: Embedded Computing and Industrial Interfaces.** Educational draft for university study; no hardware-specific safety certification is implied.

§4.2 PWM, H-bridges and current measurement

**OpenSTEM Mechanical Engineering · Book 11: Mechatronics Engineering · Unit 4: Embedded Computing and Industrial Interfaces.** Educational draft for university study; no hardware-specific safety certification is implied.

§4.3 SPI, I2C, CAN and communication diagnostics

**OpenSTEM Mechanical Engineering · Book 11: Mechatronics Engineering · Unit 4: Embedded Computing and Industrial Interfaces.** Educational draft for university study; no hardware-specific safety certification is implied.

§4.4 ADC quantization, references and ground design

**OpenSTEM Mechanical Engineering · Book 11: Mechatronics Engineering · Unit 4: Embedded Computing and Industrial Interfaces.** Educational draft for university study; no hardware-specific safety certification is implied.

§4.5 State machines, watchdogs and fault recovery

**OpenSTEM Mechanical Engineering · Book 11: Mechatronics Engineering · Unit 4: Embedded Computing and Industrial Interfaces.** Educational draft for university study; no hardware-specific safety certification is implied.

THREE WORKED QUESTIONS

Step-by-Step Mechatronics Engineering Solutions

Three original questions connect calculations, definitions and interpretation. Open each solution to follow the reasoning.

Solved Problem Example 4.1: Calculation & Verification: Scheduling, interrupts and execution budgets

Problem Statement: Tasks using 1 ms every 5 ms and 2 ms every 10 ms contribute a combined utilization of 0.40. Rewrite the given numbers before substitution; explicitly carry their units through the equation. Compare the answer to a rough mental estimate and state a sensible number of significant figures. Do not interpret the displayed precision as measured accuracy. The calculation is synthetic unless independently verified against a particular device.

Worked Engineering Derivation:

**Sensitivity experiment.** Repeat the calculation after changing one controlling quantity by +10% while keeping other stated inputs fixed. For a linear relationship, expect a proportional response in the appropriate variable; for a nonlinear one, compute the actual change and compare it with the local slope. Explain whether the chosen perturbation is realistic for the application. **Dimensional audit.** Convert angles, voltages, forces, lengths and time to an explicitly declared convention before putting them in code. A numerical answer with the wrong units is not a small editorial error: it can change the actual machine motion or power demands by large factors. Record the conversion and the numerical rounding separately.

Solved Problem Example 4.2: Calculation & Verification: PWM, H-bridges and current measurement

Problem Statement: For duty ratio 0.35 and a 24 V bus, the idealized average is 8.4 V. Rewrite the given numbers before substitution; explicitly carry their units through the equation. Compare the answer to a rough mental estimate and state a sensible number of significant figures. Do not interpret the displayed precision as measured accuracy. The calculation is synthetic unless independently verified against a particular device.

Worked Engineering Derivation:

**Sensitivity experiment.** Repeat the calculation after changing one controlling quantity by +10% while keeping other stated inputs fixed. For a linear relationship, expect a proportional response in the appropriate variable; for a nonlinear one, compute the actual change and compare it with the local slope. Explain whether the chosen perturbation is realistic for the application. **Dimensional audit.** Convert angles, voltages, forces, lengths and time to an explicitly declared convention before putting them in code. A numerical answer with the wrong units is not a small editorial error: it can change the actual machine motion or power demands by large factors. Record the conversion and the numerical rounding separately.

Solved Problem Example 4.3: Calculation & Verification: SPI, I2C, CAN and communication diagnostics

Problem Statement: A 128-bit payload at an ideal 500 kbit/s occupies at least 0.256 ms before framing and bus arbitration. Rewrite the given numbers before substitution; explicitly carry their units through the equation. Compare the answer to a rough mental estimate and state a sensible number of significant figures. Do not interpret the displayed precision as measured accuracy. The calculation is synthetic unless independently verified against a particular device.

Worked Engineering Derivation:

**Sensitivity experiment.** Repeat the calculation after changing one controlling quantity by +10% while keeping other stated inputs fixed. For a linear relationship, expect a proportional response in the appropriate variable; for a nonlinear one, compute the actual change and compare it with the local slope. Explain whether the chosen perturbation is realistic for the application. **Dimensional audit.** Convert angles, voltages, forces, lengths and time to an explicitly declared convention before putting them in code. A numerical answer with the wrong units is not a small editorial error: it can change the actual machine motion or power demands by large factors. Record the conversion and the numerical rounding separately.

Solved Problem Example 4.4: Calculation & Verification: ADC quantization, references and ground design

Problem Statement: For a 12-bit converter with 3.3 V reference, the nominal ideal step is about 0.806 mV. Rewrite the given numbers before substitution; explicitly carry their units through the equation. Compare the answer to a rough mental estimate and state a sensible number of significant figures. Do not interpret the displayed precision as measured accuracy. The calculation is synthetic unless independently verified against a particular device.

Worked Engineering Derivation:

**Sensitivity experiment.** Repeat the calculation after changing one controlling quantity by +10% while keeping other stated inputs fixed. For a linear relationship, expect a proportional response in the appropriate variable; for a nonlinear one, compute the actual change and compare it with the local slope. Explain whether the chosen perturbation is realistic for the application. **Dimensional audit.** Convert angles, voltages, forces, lengths and time to an explicitly declared convention before putting them in code. A numerical answer with the wrong units is not a small editorial error: it can change the actual machine motion or power demands by large factors. Record the conversion and the numerical rounding separately.

Solved Problem Example 4.5: Calculation & Verification: State machines, watchdogs and fault recovery

Problem Statement: If detection takes 12 ms and output disable takes 8 ms, fault command latency is 20 ms, excluding mechanical stopping. Rewrite the given numbers before substitution; explicitly carry their units through the equation. Compare the answer to a rough mental estimate and state a sensible number of significant figures. Do not interpret the displayed precision as measured accuracy. The calculation is synthetic unless independently verified against a particular device.

Worked Engineering Derivation:

**Sensitivity experiment.** Repeat the calculation after changing one controlling quantity by +10% while keeping other stated inputs fixed. For a linear relationship, expect a proportional response in the appropriate variable; for a nonlinear one, compute the actual change and compare it with the local slope. Explain whether the chosen perturbation is realistic for the application. **Dimensional audit.** Convert angles, voltages, forces, lengths and time to an explicitly declared convention before putting them in code. A numerical answer with the wrong units is not a small editorial error: it can change the actual machine motion or power demands by large factors. Record the conversion and the numerical rounding separately.