Control Theory #30 — State Space to Transfer Function (Worked Example 7)

Instructor: Dr. Süleyman Burak ÇELİK

In this worked example, we revisit the active suspension system one more time — but with a completely different technique. After modeling it from physics and simplifying its block diagram in earlier videos, we now derive its transfer functions G1 and G2 using state space and matrix algebra. Same physical system, same final answer, brand new method. Topics covered: - Choosing states from integrator outputs (position x and velocity x_dot) - Writing the state equations directly from the block diagram - Building the system matrix A, input vector b, disturbance vector o, and output vector cT - The state-space-to-transfer-function formula: G(s) = cT (sI − A)^(-1) b - Computing (sI − A)^(-1) step by step - Separating G1 and G2 by using the disturbance path (o vector) - Final result: G1 = K·A/c, G2 = 1/(1 + s²·m/c) - Side-by-side comparison with the previous block-diagram simplification result This is the third installment of our active suspension trilogy: physics modeling → block diagram simplification → state space verification. Three views of the same system, one consistent answer. Every calculation shown step by step — no steps skipped. Playlist: Control Theory - AcEdumy GitHub: https://github.com/acedumy