Feedback Control Fundamentals

Feedback control compares what a system should do with what it actually does, then changes the actuator command to reduce the error. It is the reason a servo reaches position, a heater holds temperature, a pump maintains pressure, and a balancing robot rejects disturbances.

The important point for mechatronics is that a feedback loop is not only software. It includes the controller, sensor, actuator, mechanics, power supply, sampling, filtering, cable routing, and safety limits. A mathematically correct controller can still behave badly if the measurement is delayed, the actuator saturates, the mechanism has backlash, or the sensor is mounted at the wrong point.

Learning Objectives

By the end of this lesson, you should be able to:

• Define setpoint, output, feedback, error, plant, actuator, disturbance, and controller.
• Explain why closed-loop control improves accuracy but can become unstable.
• Read step-response terms such as rise time, overshoot, settling time, and steady-state error.
• Recognize how sensor delay, actuator saturation, friction, backlash, and sample time affect control.
• Plan a safe first tuning test for a real mechatronic axis.

Closed-Loop Blocks

The controller acts on error:

$$
e(t)=r(t)-y(t)
$$

where r(t) is the reference or setpoint and y(t) is the measured output. If a speed loop should hold 1200 rev/min and the encoder reports 1120 rev/min, the error is:

$$
e=1200-1120=80\ \text{rev/min}
$$

The controller output might be motor voltage, PWM duty cycle, torque command, valve position, heater power, or another actuator command.

Open Loop vs Closed Loop

Open-loop control commands an actuator without measuring the result. A simple timed motor move is open loop: apply power for two seconds and assume the load moved far enough. Closed-loop control measures the result and corrects the command.

Closed loop does not automatically mean safe. A broken sensor, reversed feedback sign, saturated actuator, or runaway integral term can make the loop command full power in the wrong direction.

Time Response Terms

When the setpoint changes suddenly, the output response gives useful tuning information.

For a position axis, a common acceptance target might be: overshoot below 10%, final error below 0.02 mm, and settling inside the tolerance band within 0.5 s. Those numbers are application requirements, not universal control rules.

Sensor, Actuator, and Plant Limits

Control quality is limited by hardware:

• Saturation: the actuator cannot exceed its voltage, current, force, torque, pressure, or travel limit.
• Deadband: small commands produce no motion because of friction, valve overlap, backlash, or PWM threshold.
• Quantization: an ADC, encoder, or timer has finite resolution.
• Delay: filtering, communication, computation, and sampling all add phase lag.
• Noise: derivative action and high gain can amplify measurement noise.
• Compliance: belts, shafts, couplings, and frames deflect under load.
• Backlash: direction reversal produces lost motion before the load responds.

If the actuator is saturated most of the time, changing controller gains cannot create more force. If the sensor measures the motor shaft but the requirement is load position after a flexible belt, the controller may report success while the load is still moving.

Stability and Feedback Sign

Negative feedback reduces error. Positive feedback increases error. A reversed motor polarity, reversed encoder direction, inverted valve command, or sign error in software can turn a stabilizing loop into a runaway loop.

A safe first test uses low power and a small setpoint step:

1. Confirm sensor direction manually.
2. Confirm actuator direction manually.
3. Apply a small command with the loop disabled.
4. Enable the loop with low gain and a current or force limit.
5. Verify that error decreases when the actuator moves.

Stop immediately if the actuator drives away from the setpoint.

Sampling and Discrete Control

Most mechatronic controllers run in firmware at a fixed sample time Ts. The sample frequency should be much higher than the desired loop bandwidth. A common practical starting rule is:

$$
f_s \ge 10 f_\text{bandwidth}
$$

Faster sampling is not automatically better if the sensor is noisy, the computation jitters, or the actuator cannot respond. Keep the loop period deterministic and log actual timing during tests.

Practical Design Rules

• Measure the variable you actually need to control, as close to the load as practical.
• Use limits, fault states, and emergency stop behavior before aggressive tuning.
• Keep actuator commands inside continuous and peak ratings.
• Tune with recorded plots, not only by feel or sound.
• Plot setpoint, feedback, error, actuator command, saturation flag, and fault status.
• Test both directions, different loads, startup, shutdown, and blocked-load behavior.

Common Mistakes

• Tuning by feel without recording response data.
• Ignoring delay and filtering phase lag.
• Letting the controller command impossible actuator output.
• Measuring the wrong point in the mechanism.
• Reversing feedback sign during wiring or software integration.
• Assuming a stable unloaded test is stable with payload.
• Hiding oscillation with a slow display update instead of logging the control loop.

Summary

Feedback control reduces error by measuring output and correcting actuator command. Stability and performance depend on the controller, sensor, actuator, plant dynamics, sampling, delay, saturation, mechanical stiffness, friction, and safety limits. A good loop is designed and verified as a complete electromechanical system.

Further Reading

• Karl Astrom and Richard Murray, Feedback Systems.
• Control Tutorials for MATLAB and Simulink, system response basics.
• National Instruments, PID and closed-loop control fundamentals.
• Franklin, Powell, and Emami-Naeini, Feedback Control of Dynamic Systems.

Mind Map