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

Figure 10

Three optional periodic orbits, both orbits step through $x_n=1$ and $y_n=1$, and have $t_{\text{s}}=0.1\hspace{0.17em}\text{s}$ sampling time, $t_d=0.04\hspace{0.17em}\text{s}$ time delay, and $\delta =12$ dead zone width. Black colored orbit is produced with $P_{\text{cr}}=3.5714$ and $I=24.982$, red one is with parameters $P_{\text{cr}}=3.1859\text{,}$$I=22.968$, green one is with parameters $P_{\text{cr}}=4.6586$ and $I=32.259$.