Astronaut Bruce McCandless II took the first un-tethered walk in space on February 7, 1984, using the gas-jet propulsion device illustrated in Figure P5.7(a). The controller can be represented by a gain K2, as shown in Figure P5.7(b). The moment of inertia of the equipment and man is 25 kg m2.
(a) Determine the necessary gain K3 to maintain a steady-state error equal to 1 cm when the input is a ramp r(t) = t (meters).
(b) With this gain K3, determine the necessary gain K1K2 in order to restrict the percent overshoot to 10%.
(c) Determine analytically the gain K1K2 in order to minimize the ISE performance index for a step input.
Figure P5.7
(a) Astronaut Bruce McCandless II is shown a few meters away from the earth-orbiting space shuttle. He used a nitrogen-propelled hand-controlled device called the manned maneuvering unit.
(b) Block diagram of controller.

Transcribed Image Text:

Gas jet controller Astronaut R(s) Desired position Force Veloeity Position meters) x.