📘 control systems

1. The problem is to understand and solve for the Bode plot of a given transfer function. 2. A Bode plot consists of two plots: magnitude (in dB) vs frequency (log scale) and phase

1. The problem asks to discuss the type of the family of second order systems (SOS) in terms of the parameter $k$. 2. Typically, the type of a second order system depends on the ch

1. **Problem Statement:** We have a control system with forward path transfer function $G(s) = \frac{s+1}{s(s+2)}$ and feedback path transfer function $H(s) = \frac{s+3}{s+4}$. The

1. The problem is to write the state-space equations for the plant given by the differential equation $$\frac{d^2 y(t)}{dt^2} + 3 \frac{d y(t)}{dt} + y(t) = r(t)$$. 2. Define the s