NASA has identified the need for large deployable space structures which

will be constructed of lightweight materials and will contain large numbers

of joints or structural connections. This need is evident for programs such

as space station. These deployable space structures may have precision

shape requirements and a need for vibration suppression during in$-$orbit

operations. One such structure is the mast flight system which is shown in

Figure $1($a$).$ The intent of the system is to provide an experimental test bed

for controls and dynamics. The basic element in the mast flight system is

a $60\mathrm{.}7$ m long truss beam structure, which is attached to the shuttle

orbiter. Included at the tip of the truss structure are the primary actuators

and collocated sensors$.$

A deployment$/$retraction subsystem, which also secures the stowed beam

package during launch and landing is provided. The system uses a large

motor to move the structure and has the block diagram shown in Figure

$1($b$).$ Design lead and$/$or lag controllers using the Root Locus or Frequency

Response methods so that the system overshoot for a step input is less

than $10\%,$ the settling time is less than $3$ seconds. Using MATLAB, show

the performance of the compensated system. Discuss the characteristics

of the designed controller.

$($a$)$

$($b$)$

Figure $1$ please solve with detail anationsed