The open-loop transfer function of a plant is given as $$G(s) = {1 \over {{s^2} - 1}}.$$ If the plant is operated in a unity feedback configuration, then the lead compensator that can stabilize this control system is

A double integrator plant, $$G(s) = {K \over {{s^2}}},H(s) = 1$$ is to be compensated to achieve the damping ratio $$\zeta = 0.5$$ and an undamped natural frequency, $${\omega _n} = 5$$ rad/sec. Which one of the following compensator $${G_c}(s)$$ will be suitable?

A process with open-loop model $$G(s) = {{K{e^{ - s{\tau _d}}}} \over {\tau s + 1}},$$ is controlled by a PID controller. For this process

The transfer function of a simple RC network functioning as a controller is: $${G_c}(s) = {{s + {z_1}} \over {s + {p_1}}}$$

The condition for the RC network to act as a phase lead controller is: