Control Theory #29 — Active Suspension Transfer Functions (Worked Example 6)

Instructor: Dr. Süleyman Burak ÇELİK

In this worked example, we continue the active suspension problem from our previous Problem Solving video. Starting from the integrator-based block diagram we built from physics, we replace the integrators with their transfer functions and simplify the diagram into the standard form u → G1 → (Σ+h) → G2 → x. Topics covered: - Recap of the active suspension block diagram (K, A, c, mass m, two integrators) - Step 1: Series combinations — K·A and 1/(ms)·1/s = 1/(ms²) - Step 2: Move summing junction past gain c (Summation Move Type 2) - Step 3: Close inner feedback loop (forward 1/(ms²), feedback c) - Step 4: Identify G1 and G2 from the resulting structure - Final result: G1(s) = K·A/c (constant gain), G2(s) = 1/(1+s²·m/c) (second-order lag) - New transfer function type introduced: undamped second-order lag Every calculation shown step by step — no steps skipped. This builds directly on our Active Suspension Modeling video, transforming the same physical system from time-domain integrators to frequency-domain transfer functions. Playlist: Control Theory - AcEdumy GitHub: https://github.com/acedumy