Actuators, drivers and interactions with physical systems

Follow both paths through the interface

An actuator converts supplied energy into a physical action. A driver connects a low-power control signal to an energy source in a controlled way. Motor, valve and heater interfaces have different output quantities and stored-energy effects. The control pin is not itself the mechanical or thermal energy supply.

A requested position or speed is not a directly imposed physical state. A motor first develops electromagnetic torque, while inertia, resistance and external load influence motion. A position sensor can observe the resulting movement. The later control chapter uses that observation to revise a command; here we establish the physical relationships a controller must respect.

Electrical and mechanical states interact

For a simplified permanent-magnet DC motor, electromagnetic torque is τ=KtI and rotation generates back emf E=Keω. Here I is current, ω angular speed and the constants carry units relating each pair. A resistive steady electrical model gives V=RI+Keω. Inductance and changing current require an additional dynamic term that this limited model omits.

Mechanical output at the conversion port is τω, while electrical input is VI. A winding resistance dissipates I²R. Friction, other losses and driver consumption add further terms in a fuller model. These equations describe relationships, not a guarantee that a chosen motor can sustain their computed current, torque or temperature.

A command waveform is not a complete output rating

A switching driver may vary its command duty fraction rather than a continuous voltage. The resulting current depends on electrical storage, switching behavior, back emf and load. Duty fraction alone therefore does not establish torque or speed. Mechanical stops, clearance, friction and supply limitations can also change the response.

Integration records should connect command, supplied voltage, current and relevant motion or force over compatible times. A stalled output can still consume energy and heat the actuator. A decreasing current can indicate increasing back emf rather than a reduced command. These alternatives help distinguish a physical load change from a driver, sensing or software problem without proposing unverified operating procedures.

Reconcile power for a supplied steady state

Use fictional V=6 V, R=2 Ω, Kt=.05 N·m/A and Ke=.05 V·s/rad. At ω=80 rad/s, the back emf is 4 V and current (6−4)/2=1 A. Torque is .05 N·m. Electrical input 6 W splits into I²R=2 W and τω=4 W under the stated omissions. The equal numerical constants use compatible SI units.

The plotted ideal relation decreases from .15 N·m at zero speed to zero at 120 rad/s. At zero speed the algebra gives 3 A and no mechanical power, so all 18 W input becomes winding dissipation in this simplified steady electrical account. It supplies no permissible stall duration or actual driver/motor rating; dynamics and thermal limits require separate evidence.

Try the reasoning

1. Does a speed command directly impose speed on any load?

   Show the answer and reasoning

   No. Available torque, supply, inertia and opposing loads determine the response.

2. Why does the example current fall as speed rises?

   Show the answer and reasoning

   Increasing back emf leaves less voltage across the winding resistance at the fixed supplied voltage.

3. Can zero mechanical output coexist with electrical power input?

   Show the answer and reasoning

   Yes. Energy can accumulate or be dissipated while the output is stationary.

What to carry forward

Measure the physical output and energy path rather than equating command value with delivered action.