Control Systems Lab Composed

Explore PID, LQR, MPC, and Bang-Bang controllers on various plants. See how different control strategies handle the same challenge.

PID Controller

u(t) = Kp*e + Ki*integral(e) + Kd*de/dt
Classic three-term controller. Kp=proportional (speed), Ki=integral (steady-state), Kd=derivative (damping).

Kp 8 Ki 1.5 Kd 4 Setpoint 60

Overshoot: --
Settling: --
SS Error: --

LQR Controller

u = -K*x where K minimizes J=integral(x'Qx + u'Ru)
Optimal control — balances state error (Q) vs control effort (R).

Q (state cost) 10 R (control cost) 1 Setpoint 60

Gain K: --
Overshoot: --
Settling: --

Model Predictive Control

Optimize u[0..N] to minimize predicted cost
Looks N steps ahead, picks best action, re-plans each step. Handles constraints naturally.

Horizon N 10 u_max (max control) 15 Setpoint 60

Overshoot: --
Settling: --
Constraint violations: 0

Bang-Bang Controller

u = u_max if e>0, u = -u_max if e<0
Simplest controller — full power on/off. Fast but oscillates. Add deadband to reduce chatter.

u_max 10 Deadband 2 Setpoint 60

Oscillations: --
Avg Error: --

Side-by-Side Comparison

All four controllers on the same plant with the same setpoint. Which one wins?

Setpoint 60 Disturbance at t=150 0