Influence of Control Valve Delay and Dead Zone on the Stability of a Simple Hydraulic Positioning System

Figure 8

Three simulation results, both with initial conditions ${\mathbf{z}}_2={(1\hspace{0.17em}1\hspace{0.17em}1\hspace{0.17em}1)}^T\text{,}$$t_s=0.1\hspace{0.17em}\text{s}\text{,}$$t_d=0.04\hspace{0.17em}\text{s}\text{,}$$I_{\text{cr}}=24.982$ and $P_{\text{cr}}=3.5714$. Periodic orbit occurs at $\delta =12$ (black), dense orbits with increased period length at different dead zone sizes, $\delta =20$ (green) and $\delta =4$ (red).