DC Motor — Robotics/Actuators And Drivetrain

DC Motor

Robotics / Actuators and Drivetrain

The brushed DC motor as a two-state linear plant, from its nameplate constants:

• L·di/dt = V − R·i − Ke·ω – the electrical loop.
• J·dω/dt = Kt·i − b·ω − τ_load – the mechanical one.

With the state x = [i; ω] and the input u = [V; τ_load] that is the state space A = [−R/L, −Ke/L; Kt/J, −b/J], B = [1/L, 0; 0, −1/J], C = [0 1; 1 0], D = 0 – which the block carries as a real state space rather than as a hand-written recursion, so model reduction can absorb it into a neighbouring plant and code export discretizes it by whichever method the model selects.

Ports

• V – terminal voltage in volts, a scalar [1,1]: the command, usually a controller output or a PWM duty times the bus voltage.
• tau_load – load torque in N·m, a scalar [1,1], opposing motion: a positive value slows the motor. Tie it to a Constant of 0 for the unloaded case.
• w – shaft speed in rad/s, a scalar [1,1].
• i – armature current in amperes, a scalar [1,1]: what a current loop closes on, and what says whether the motor is near its thermal limit.

Parameters

• Resistance (ohm) – armature resistance R, > 0.
• Inductance (H) – armature inductance L, > 0. It sets the fast electrical pole at −R/L; a very small L makes the plant stiff, which matters for the sampling rate and for fixed-point export (see Code export).
• Torque Constant (N.m/A) – Kt, the torque produced per ampere.
• Back-EMF Constant (V.s/rad) – Ke, the voltage generated per rad/s. In SI units an ideal motor has Ke = Kt; they are separate parameters here so a datasheet's own two numbers can be entered as given.
• Rotor Inertia (kg.m^2) – J, > 0, including whatever is bolted to the shaft.
• Viscous Damping (N.m.s) – b, ≥ 0: the speed-proportional loss. Coulomb friction is not part of a linear plant – put a Stribeck Friction or a Coulomb and Viscous Friction block in the load path for that.
• Initial Current (A) and Initial Speed (rad/s) – the state at t = 0.
• Sampling Time (s) – zero or less inherits the solver's rate; a positive value runs the block at that period.

Code export

All ten targets: Python, MATLAB, Java, Rust, C, C++, VHDL, Verilog, SystemVerilog and PLC Structured Text. The block exports the discretized state space x[k+1] = Ad·x + Bd·u, y = Cd·x + Dd·u, with every coefficient folded to a constant at export time – so no generated core contains R, L, J or a matrix inverse, and the discretization follows the model's method (ZOH, FOH, Tustin, Matched, Impulse or either Euler) rather than a rule frozen into the generators. There is no tunable parameter object.

The three HDL targets are genuine synthesizable Q16.16: the emitted body is multiply-accumulate on those constants, with no division and nothing transcendental. Check the discretized coefficients if the motor is an aggressive one – a very small inductance drives 1/L, and with it the entries of Bd, up by orders of magnitude, and Q16.16 saturates beyond ±32768.

Simulink bridge

None. Simulink's motor blocks live in Simscape Electrical, which is not installed on this machine, so there is no block whose parameters this one could be mapped onto or verified against. A model that must cross can carry the same plant as a State-Space block with the A/B/C/D above. The entry reports the block with that reason rather than dropping it silently, and no parity testbench is owed – the documented consequence of Support::None. Code export verification still covers all ten languages.

Notes

• It carries a real continuous state space, seeded in the constructor and re-derived whenever the configuration changes – so it is a first-class citizen of model reduction and of every discretization method, which a block that only wrote its own recursion would not be.
• States are (current, speed); ports are (speed, current). The output matrix is the permutation that reconciles the two, so the equations keep their natural order and the ports keep theirs.
• Linear only. No saturation of the voltage, no Coulomb friction, no cogging, and no thermal model: those are separate blocks in the path, which is what keeps this one mergeable.
• τ_load opposes motion – a positive load torque decelerates the motor. That is the sign convention in B, and it is the one worth checking first when a model runs backwards.
• The electrical pole is the fast one. At the shipped defaults it sits at −R/L = −2 rad/s against the mechanical −b/J = −10; with a real motor's millihenry inductance it is thousands, and the model's sampling rate has to respect it.