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Mechatronics Engineering DISCUSSION
My control course moved from PID to state-space methods (pole placement, LQR, observers), and the lecturer presents them as the modern approach. For my project I have a DC motor with an encoder positioning a rotary arm, and every industrial drive I look at still seems to use PID loops.
Is PID simply the older, inferior method that survives out of habit, or is there a technical reason to prefer it here? When does state-space control actually give a better result?
The two are not really rivals at the same level. State space is a way of modelling a system and designing feedback from all of its states; PID is one fixed controller structure. For your plant they largely coincide. A motor with a rigid load is close to a double integrator, J × θ'' = T, whose states are position and velocity. Full state feedback is T = -k1 × θ - k2 × ω, which is exactly a PD controller on position.
With J = 1 × 10^-4 kg·m², placing the closed-loop poles at ω_n = 50 rad/s and ζ = 0.7 gives k1 = J × ω_n² = 0.25 N·m/rad and k2 = 2 × ζ × ω_n × J = 0.007 N·m·s/rad. Those are your Kp and Kd.
State-space design earns its place when one loop per output is not enough. Typical cases: a flexible coupling or belt between motor and load (a two-mass system has four states and a resonance that a plain PID cannot damp well), an inverted pendulum where one motor must control both cart position and pendulum angle, or several axes that are strongly coupled. LQR then gives a consistent set of gains for all states from one cost function, and an observer estimates the states you cannot measure.
The cost is that everything depends on the model. Pole placement and LQR are only as good as your values for inertia, friction and torque constant, and an observer built on a wrong model gives wrong state estimates. Plain state feedback also has no integral action, so a constant disturbance such as gravity on the arm or friction leaves a steady error until you add an integrator state, at which point you are back to something very like PID.
PID can be tuned on the real machine with no model at all, and it comes with well-understood practical additions such as anti-windup and derivative filtering.
Industrial drives are not using a single textbook PID either. The usual structure is a cascade: a current (torque) loop inside a velocity loop inside a position loop, each inner loop roughly five to ten times faster than the one around it, with velocity and acceleration feedforward doing most of the tracking work. Feeding back current, velocity and position is state feedback in all but name, arranged so that each loop can be tuned and limited separately. That is a technical reason for its survival, not habit: current and speed limits are trivial to enforce in a cascade.
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