The balancing arm and one standard

The balancing arm and one standard servomotor are the plant and actuator,respectively.Thesensor is an IR range sensor and provides the feedback signal on the location of the ball relativeto the sensor from which we can compute the offset from the set-point. The commands enterthe control system via the host computer through front panel commands sent over the USBEthernet connection to the myRIO, which hosts the PID controller code.Closed-loopstabilityAstable feedback control system displays a bounded response to a bounded input.Forexample,if the balancing arm feedback control system is stable, then when we place the ball atthe setpoint and gently push it, the actuated arm will rotate according to commands fromthecontroller to return the ball to the setpoint. If the system is unstable, when the ball is pushed,it will not return to the setpoint, but instead will continue to deviate farther and farther awayfrom the setpoint until likely coming to rest against the stop. If the system is marginally stable,the ball will roll away and come rest at some distance from the setpoint in a controlled fashion.Stability is a key objective in the design of feedback control systems. Closed-loop feedbacksystems that are unstable are, in general, particularly undesirable.Disturbance rejection and performanceThe gentle push can be viewed as an external impulsive disturbance. The stable closed-loopbalancing arm control system demonstrates an ability to reject these disturbances by returningthe ball back to the setpoint. A key element of the control design process is not only to achieveclosed-loop stability, but also to have the ball return to the desired setpoint with a specifiedperformance.In other words, we want the feedback control system to meet our designspecifications that typically include settling time, percent overshoot, time to peak,time to rise,and steady-state errors in response to a specific set of test input signals, such as impulses, steps,and ramps