Feedback Control and Estimation
Comprehensive university textbook unit covering fundamental principles, governing relationships, and engineering applications of Feedback Control and Estimation.
§5.1 First-order identification and actuator response
**OpenSTEM Mechanical Engineering · Book 11: Mechatronics Engineering · Unit 5: Feedback Control and Estimation.** Educational draft for university study; no hardware-specific safety certification is implied.
§5.2 Cascade position, velocity and current loops
**OpenSTEM Mechanical Engineering · Book 11: Mechatronics Engineering · Unit 5: Feedback Control and Estimation.** Educational draft for university study; no hardware-specific safety certification is implied.
§5.3 PID tuning and anti-windup
**OpenSTEM Mechanical Engineering · Book 11: Mechatronics Engineering · Unit 5: Feedback Control and Estimation.** Educational draft for university study; no hardware-specific safety certification is implied.
§5.4 Complementary filters and observer limitations
**OpenSTEM Mechanical Engineering · Book 11: Mechatronics Engineering · Unit 5: Feedback Control and Estimation.** Educational draft for university study; no hardware-specific safety certification is implied.
§5.5 Discrete-time stability and saturation tests
**OpenSTEM Mechanical Engineering · Book 11: Mechatronics Engineering · Unit 5: Feedback Control and Estimation.** Educational draft for university study; no hardware-specific safety certification is implied.
Step-by-Step Mechatronics Engineering Solutions
Three original questions connect calculations, definitions and interpretation. Open each solution to follow the reasoning.
Problem Statement: With K=2, u=1.5 and tau=0.20 s, the predicted response at 0.20 s is about 1.896 units. 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.
Problem Statement: For a 0.010 m position error and proportional conversion 25 (rad/s)/m, the velocity request is 0.25 rad/s. 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.
Problem Statement: With Kp=3, e=0.2, Ki=0.8 and integral 0.5, the PI command before saturation is 1.0 units. 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.
Problem Statement: For alpha=0.98, prior tilt 10 degrees, rate 1 degree/s, dt=0.01 s and accelerometer tilt 8 degrees, estimate is about 9.970 degrees. 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.
Problem Statement: For a=20 s^-1 and dt=0.020 s, the linear update multiplier is 0.60; dt=0.12 s yields -1.4 and instability. 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.