Question: Consider the group of five pendulums shown in the diagram. Each pendulum oscillates with the same natural frequency. Its motion is rep-resented by two state variable components (angle and angular rate); hence the total state vector has dimension 10. Each pendulum could be affected by a control force, but it is desired to provide a control vector of minimum dimension. What is the smallest dimension control vector that provides complete controllability? Would the answer be different if the pendulums had different natural frequencies?
