Two swarm-intelligence algorithms — particle swarm and ant colony — pitted against classical Routh–Hurwitz tuning to control the speed of a separately excited DC motor.
The DC motor's speed loop was first closed with a PID controller whose gains were chosen using the conventional Routh–Hurwitz criterion — picking values that merely satisfy a stability inequality, not ones tuned to minimize error, overshoot, or settling time.
So the tuning problem was reframed as an optimization task — minimize overshoot and settling time directly — and handed to two swarm-intelligence algorithms.
Each algorithm searches the same three-dimensional space of gains — Kp, Ki, and Kd — but explores it the way its namesake swarm does.
Modeled on bird flocking and fish schooling. Each candidate gain-set is a "particle" that remembers its own best result (pbest) and is pulled toward the swarm's best (gbest) at every step.
Modeled on ant foraging. Each "ant" walks a candidate solution and deposits pheromone in proportion to how good it is — over time the colony's trail converges on the shortest path to the optimum.
Each method was run against the same DC motor model in Simulink, with an identical load-torque disturbance at t = 10s.
| Method | Kp | Ki | Kd | Overshoot | Settling time |
|---|---|---|---|---|---|
| Conventional (Routh–Hurwitz) | 2.00 | 15.00 | 0.01 | 0.2680 p.u. | 0.5690 s |
| PSO-tuned | 15.06 | 31.58 | 0.68 | 0.000 p.u. | 0.0460 s |
| ACO-tuned | 4.85 | 9.30 | 0.53 | 0.000 p.u. | 1.4545 s |
Both swarm methods eliminate overshoot entirely; the gap between them shows up in how quickly the speed settles back to reference.
| Metric | PSO | ACO |
|---|---|---|
| Iterations to reach objective | 57 | 120 |
| Objective function value at 250 iterations | 0.070361 | 0.708562 |
| Overshoot | 0.000 p.u. | 0.000 p.u. |
| Settling time | 0.0460 s | 1.4545 s |
Both algorithms converge to a near-zero overshoot, but PSO gets there in roughly half the iterations and settles about thirty times faster than the ant colony method — at comparable computational cost.
Both PSO and ACO reach near-optimal gains with far less trial-and-error than the conventional method, and both hold up cleanly through the load-torque disturbance. But for this plant, particle swarm optimization converges faster, needs fewer iterations, and yields the tighter dynamic response — the better tool for the job.