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

Figure 7

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_{\text{d}}=0.04\hspace{0.17em}\text{s}\text{,}$$\delta =12$,and $I_{\text{cr}}=24.982$. Periodic orbit occurs at $P_{\text{cr}}=3.5714$ (black); the control is stable at $P=4.1$ (green), unstable at $P=3.3$ (red).