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Mechatronics · Module 7 of 10

Electrical Actuation Systems

Electric motors are the default mechatronic actuator. A DC motor's speed follows its average voltage set by PWM, while a stepper motor moves in fixed angular steps counted open loop.

Readiness check

This module drives the load electrically. Tick only what you can do closed-notes.

Divide a full circle by a number of steps.
Take a percentage of a voltage.
Convert steps per second to revolutions per minute.
Recall that a DC motor speeds up with more voltage.
Recall that a duty cycle is an on-time fraction.

0 or 1 weak itemsContinue with this module.

2 weak itemsRevisit the DC motor model in System Dynamics, Module 3.

3 or more weak itemsRevisit control basics in Control Systems.

The core idea

A DC motor's speed is set by its average applied voltage, which PWM controls through the duty cycle: average = duty × supply. A stepper motor moves a fixed step angle of 360 degrees over its steps per revolution, so a pulse train positions it open loop, and its speed is the step rate divided by the steps per revolution.

step angle = 360° / steps per revspeed (rpm) = (pulses/s ÷ steps per rev) × 60PWM average = duty × V_supply

Electric motors turn current into torque and voltage into speed, and the two dominant mechatronic choices are the DC motor and the stepper. A DC motor produces torque proportional to current and spins at a speed that rises with the average voltage across it. Rather than waste power in a resistor, we set that average voltage by pulse-width modulation: the supply is switched fully on and off fast, and the average is the duty cycle times the supply, so 60 percent duty on 24 volts is 14.4 volts. An H-bridge adds direction by reversing the connection. A stepper motor is different: its rotor advances one fixed step per input pulse, a step angle of 360 degrees divided by the steps per revolution, so simply counting pulses sets the position without any sensor, which is why steppers dominate open-loop positioning like printers and small machine axes. The step rate sets the speed, pulses per second divided by steps per revolution giving revolutions per second. When a task needs guaranteed accuracy under load, a servo motor closes the loop with an encoder, combining a DC or brushless motor with the feedback of the earlier modules.

The skill works when: you take duty times supply for PWM and 360 over steps for a stepper.

The skill breaks down when: PWM is thought to vary frequency, or a stepper is assumed to need feedback.

The concept. PWM switches the supply fully on and off; the fraction of on-time, the duty cycle, sets the average voltage the motor responds to.

The skills, taught in order

Five skills cover the motors a mechatronic system reaches for first.

7.1 The DC motor

Torque is proportional to armature current and the speed rises with applied voltage, opposed by a back-emf that grows with speed. It is simple, cheap, and easy to control, the default for continuous rotary motion.

7.2 PWM speed control

Switching the supply on and off quickly and varying the on-fraction sets an average voltage of duty × supply, with almost no loss in the switch. An H-bridge of four switches lets the same drive run the motor in either direction.

7.3 The stepper motor

A stepper advances a fixed step angle of 360 degrees over its steps per revolution for every pulse, so counting pulses positions it open loop. Half-stepping and micro-stepping subdivide the step for finer resolution and smoother motion.

Motor	Control	Best for
DC	PWM average voltage	continuous speed
Stepper	pulse counting, open loop	indexed positioning
Servo	closed loop with encoder	accurate motion under load

The three common actuators and the control style each uses. The task decides the choice.

7.4 The servo motor

A servo is a motor plus an encoder and a controller that closes the position or speed loop. It guarantees accuracy under disturbance, at the cost of the sensor and control the open-loop stepper avoids.

7.5 AC motors and choosing

AC induction motors driven by variable-frequency drives handle high-power continuous loads. Choosing an actuator weighs power, accuracy, whether feedback is needed, and cost, matching the motor to the duty.

Engineering connection: a 3D printer moves its axes with steppers counted open loop for cheap repeatable positioning, while an industrial robot uses servos to hold accuracy under varying load.

Worked example 1: a stepper motor

A stepper motor has 200 steps per revolution. Find the step angle, the steps for a 90 degree move, and the speed at 500 pulses per second.

Figure 1. With 200 steps per revolution each pulse turns the rotor 1.8 degrees, so 50 pulses make a quarter turn, and 500 pulses per second is 150 rpm.

ProblemFind the step angle, steps for 90 degrees, and speed at 500 pps for the stepper in Figure 1.
Given / find200 steps/rev, move 90 degrees, rate 500 pulses/s. Find step angle, step count, and rpm.
AssumptionsFull-step operation, no missed steps, load within the pull-in torque.
Modelstep angle = 360/steps; steps = angle/step angle; rpm = (pps/steps) × 60.
Equationsstep = 360/200 = 1.8°rpm = (500/200) × 60
Solvestep angle 1.8°; 90/1.8 = 50 steps; (500/200) × 60 = 150 rpm.
Check50 steps of 1.8 degrees is 90 degrees; 500 pulses per second is 2.5 rev/s, which is 150 rpm, both consistent.
ConclusionCounting 50 pulses commands a precise quarter turn with no sensor, the open-loop strength of the stepper.

Result. 1.8° per step, 50 steps for 90°, 150 rpm at 500 pps.

Worked example 2: PWM speed control

A DC motor on a 24 V supply is driven at 60 percent PWM duty. It turns at 125 rpm per volt. Find the average voltage and the speed.

Figure 2. Sixty percent duty on a 24 V supply averages 14.4 V; at 125 rpm per volt the motor runs at 1800 rpm.

ProblemFind the average voltage and speed for the PWM drive in Figure 2.
Given / findV_supply = 24 V, duty 60 percent, 125 rpm/V. Find average voltage and speed.
AssumptionsSpeed proportional to average voltage, light steady load, fast switching.
Modelaverage = duty × supply; speed = average × (rpm per volt).
EquationsV_avg = 0.60 × 24N = V_avg × 125
SolveV_avg = 14.4 V; N = 14.4 × 125 = 1800 rpm.
CheckFull duty would give 24 V and 3000 rpm; 60 percent of 3000 is 1800 rpm, matching.
ConclusionDuty cycle sets speed with almost no wasted power, the reason PWM drives nearly every DC motor.

Result. Average 14.4 V; speed 1800 rpm.

Misconceptions and diagnostics

Mistake	Symptom	Diagnostic question	Correction
PWM varies frequency	Speed unchanged with duty	"Am I changing on-time or rate?"	PWM fixes frequency and varies the duty.
Stepper needs feedback	Adding a sensor a stepper does not use	"Am I counting pulses?"	A stepper positions open loop by pulse count.
Confusing pps and rpm	Speed off by steps per rev	"Did I divide by steps per rev?"	rpm = (pps/steps) × 60.
Duty as percent left in the product	Voltage 100 times too high	"Is duty a fraction?"	Use 0.60, not 60, in duty × supply.

Practice ladder

Level 1 · Direct skill

A stepper has 400 steps per revolution. Find the step angle and the steps for a 180 degree move.

Show answer

Step angle = 360/400 = 0.9 degrees; steps = 180/0.9 = 200 steps.

Level 2 · Mixed concept

A DC motor on 12 V is driven at 75 percent duty. Find the average voltage.

Show answer

Average = 0.75 × 12 = 9 V.

Level 3 · Independent problem

A 200 step per revolution stepper is driven at 1000 pulses per second. Find its speed in rpm.

Show answer

rpm = (1000/200) × 60 = 5 × 60 = 300 rpm.

Transfer task | Real engineering

Choose an actuator for (a) an indexing turntable that must stop at exact angles, (b) a high-power conveyor, and (c) a robot joint that must hold angle under load.

What good work looks like

(a) Stepper, for open-loop indexed positioning; (b) AC induction motor with a variable-frequency drive, for continuous high power; (c) servo motor, closing the loop with an encoder to hold accuracy under disturbance.

Working with AI, and proving it yourself

Use AI as an examiner, not a solver

"Check that I converted pulses per second to rpm using steps per revolution."

"Give me three PWM settings; I will compute each average voltage."

"Which motor should I use?" Match power, accuracy, and feedback yourself.

"Set my duty cycle." Solve for it from the target speed.

Portfolio task

Pick a motion task and select a motor: give the step angle or PWM duty and the resulting speed, and say whether feedback is needed.

Must include: a motor type, a computed speed or step count, and an open versus closed loop decision.

Retrieval and spaced review

Closed notes. Answer out loud, then reveal.

1. Write the stepper step angle.

360 degrees divided by the steps per revolution.

2. Write the PWM average voltage.

Average = duty × supply voltage.

3. Convert pulses per second to rpm.

rpm = (pulses per second / steps per rev) × 60.

4. Why can a stepper run open loop?

Each pulse is a fixed known step, so counting pulses gives position.

5. What does a servo add?

An encoder and controller that close the loop for accuracy under load.

TodayFinish this quiz and Levels 1 and 2 of the ladder.

+1 dayRe-derive a stepper speed and a PWM average.

+3 daysSelect a motor for one real task.

+7 daysMove on to microcontrollers in Module 8.

+30 daysReuse duty × supply and 360 over steps on any drive.

Textbook mapping

This module follows William Bolton, Mechatronics, 6th edition. Use these references to read further.

Topic in this module	Where to read more
DC motors and PWM	Bolton, Chapter 9, DC motors
Stepper motors	Bolton, Chapter 9, Stepper motors
AC motors and drives	Bolton, Chapter 9, AC motors

Chapter numbers refer to Bolton's Mechatronics, 6th edition. Any edition with the same chapter titles is equivalent for study.