Control Systems by Hand: Open & Closed Loops, First- and Second-Order Responses, Steady-State Error, Dead Time, Stability Checks, Frequency Response in Decibels & Tuning Tables
See why feedback works and when it goes wrong. You will compare open and closed loops, simulate first- and second-order step responses, read overshoot and settling time, compute steady-state error under proportional control, add dead time, check stability from characteristic roots, tabulate magnitude and phase in decibels with margins and apply a tuning table to a toy process, with every cell checked as you go.
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About this course
This course explains feedback control with toy models in a spreadsheet. You compare a heater run open loop and with a P controller, then simulate first-order step responses row by row and check 63 % at one time constant. You compute natural frequency, damping ratio and overshoot of a spring-mounted arm, the steady-state error and speed for four controller gains, and delay the input by a dead time with INDEX. You test stability from characteristic roots with real and imaginary parts in separate columns, tabulate magnitude in decibels and phase, read gain and phase margins with MATCH and finish by comparing P and PI settings from a fictional tuning table.
Lessons
- Open vs Closed Loop: A Toy Heater, a Disturbance Step & Sensitivity to a Gain Change Pro
- First-Order Systems: A Step Table, 63 % at One Time Constant & Settling at About 4τ Pro
- Second-Order Systems: Damping Ratio, Natural Frequency, Overshoot, Peak & Settling Time Pro
- Proportional Control: Closed-Loop Gain, Steady-State Error & Speed vs Error for Four Gains Pro
- Dead Time & Sampling: Delaying the Input by d Steps, Sample Period & When a Loop Starts to Oscillate Pro
- Stability Checks: Characteristic Roots in Real and Imaginary Parts, a Stable Flag & a Gain Sweep Pro
- Frequency Response: Magnitude in Decibels, Phase, Corner Frequency, Parts in Series & Margins Pro
- Capstone – Tuning Table & Comparison: P vs PI Settings, Simulated Responses, Overshoot & Summed Absolute Error Pro