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

Figure 11

Left: linear stability chart at $t_{\text{s}}=0.1\hspace{0.17em}\text{s}\text{,}$$t_{\text{d}}=0.04\mathrm{\hspace{0.17em}\hspace{0.17em}}\text{s}$. Black colored point shows $P_{\text{cr}}=3.5714$ and $I=24.982$; blue one shows parameters $P_{\text{cr}}=3.1859$,$\mathrm{\hspace{0.17em}\hspace{0.17em}}I=22.968$; red one shows parameters $P_{\text{cr}}=4.6586$ and $I=32.259$, both with $\delta =12$. Right: one point is picked on the boundary of linear stability, one inside the stable, one in the unstable region: (a) $P=3.3\text{,}$$I=24.982$, (b) $P=3.5714\text{,}$$I=24.982$, (c) $P=3.9\text{,}$$I=24.982$.

(a)

(b)