I was reading about controller design from the book Control System Design, An Introduction by Bernard Friedland.
In one of the examples of controller design for an inverted pendulum, the author considered two state variables (e.g. angular position and velocity) as shown in the figure.
But to my knowledge for controller design, we have to select minimum number of independent state variables and then connect the gains via feedback to input of motor.
So in my understanding, there should be only one gain (that is connected to gain via feedback to input of motor) because system is a pendulum of some mass so we have only one energy storing element (e.g. mass of pendulum) so we need only one state variable to design controller.
So why does the author take two state variables instead of one for controller design?