Control ideas, after the textbook.
Practical design questions, model limits and experiments worth repeating. Each note starts with a practical question and states clearly what the current lab can demonstrate.
A smaller z-pole is not always a faster machine
Two logs use different sampling periods. Comparing pole magnitudes without their clocks can reverse your engineering conclusion.
Read the noteRead one question, then try a related run when the lab supports it.
A smaller z-pole is not always a faster machine
Two logs use different sampling periods. Comparing pole magnitudes without their clocks can reverse your engineering conclusion.
Your sensor log can hide an oscillation
A smooth trace can be a sampling artifact. Before retuning a controller, check how the trace was measured.
Feedforward does not replace feedback
A model can supply an expected command before error develops. The remaining question is what happens when that expectation is wrong.
Which error is your feedback actually reducing?
A sensor gain can make a small summing-junction error coexist with a large physical tracking error.
A moving target needs a different tracking test
Zero step error does not guarantee zero ramp error. Use the input your application actually needs.
Positive coefficients are not a stability certificate
A cubic with positive coefficients can still have two growing modes.
Why the fastest observer is not always the best
If the observer trusts each noisy position reading more strongly, what happens to the control effort?
One tank, many linear models
Does the water level return on the same time scale at low and high operating heights?
Which RLC resonance did you measure?
Must the largest capacitor-voltage response occur exactly at ωn = 1/√(LC)?
A heater cannot cool: check authority before tuning
Use a thermal example to separate slow dynamics, impossible targets and integral windup. A better gain cannot create an actuator you do not have.
Why more damping can make a system slower
Use a mass–spring–damper to separate overshoot, settling and energy loss. Compare underdamped, critical and overdamped responses before treating damping as a universal speed knob.
Do you need feedback if a voltage already gives the right speed?
Compare a held voltage with speed feedback under the same load. Learn when open-loop control is useful, what feedback changes, and why an open-loop Bode plot is a different idea.
Can you tune PID without a plant model?
Yes—but model-free does not mean evidence-free. A safe experiment still needs measured signals, limits and repeatable conditions.
PID or state-space? First fix the question.
PID is a controller family. State-space is a model representation. LQR is one design method built on that representation.
Lead or lag? Read the Bode plot, then check the motor.
Phase near crossover and low-frequency accuracy are different goals. A good frequency plot can still hide actuator saturation.
A smooth Kalman estimate is not yet a good controller.
Separate state estimation from feedback, test your noise assumptions, then compare LQG with ideal full-state LQR.
Why does a motor overshoot with a healthy phase margin?
A linear margin describes one loop model near an operating condition; a limited actuator can tell a different time-domain story.
Lead, lag or PI: which problem are you solving?
Compare phase, persistent error and actuator effort under the same motor target and load before choosing a compensator.
One good step fit does not validate a motor model.
Parameter fitting and held-out prediction answer different questions; use a second target or load trial before trusting a design model.
Why a spring and an RLC circuit share an equation
Match mass, damping and stiffness to inductance, resistance and inverse capacitance—without confusing an analogy with an actual motor circuit.
When does a linearized cart-pole model stop helping?
A controller designed near upright may fail after a larger tilt, but a failed run alone does not measure the approximation error.
A calm-looking trace is not proof of stability
A short simulation checks one input and one initial condition; BIBO and internal stability make broader claims.
Write a control specification before tuning gains
Turn 'fast and stable' into observable requirements for tracking, load rejection, actuator effort and limits.
Why delay and right-half-plane zeros resist faster control
Two different mechanisms—late information and an initial wrong-way response—can limit useful bandwidth and make aggressive tuning backfire.
Lecture Room follows the path from feedback and models to state estimation and robust design.
Go to Lecture Room