Control Theory #31 — Tank System Linearization (Worked Example 8)

Instructor: Dr. Süleyman Burak ÇELİK

In this worked example, we solve a complete nonlinear system analysis problem from start to finish. A cylindrical tank system with a motor-driven valve is modeled, linearized, and its transfer function is computed — all four parts in one video. Topics covered: - Part (a): Nonlinear state space model — states h (water level) and phi (valve angle), motor + gear box + valve + tank dynamics - Part (b): Set-point calculation — given q_in = 50 cm3/s and phi = 4pi, reading the characteristic curve to find a_SP = 0.15 cm2, computing h_SP = 55.6 cm - Part (c): Linearization via Jacobian — computing partial derivatives, reading the slope of the nonlinear characteristic curve (0.06 cm2/rad), building A, b, o matrices - Part (d): Transfer function — applying G(s) = cT(sI-A)^(-1)b to get G(s) = -0.0666 / [s(s+0.03)], identifying it as a first-order lag times an integrator Physical parameters: K = 7.5 rad/(sec·V), g = 10 m/sec2, A = 150 cm2, rat = 15 Every calculation shown step by step — no steps skipped. Playlist: Control Theory - AcEdumy GitHub: https://github.com/acedumy