Setup and tuning
Studies conducted on the compressibility of hydraulic oil must have had this hydraulic system in mind. Each of the four lift cylinders requires almost 400 gal of oil to fully retract when starting in the extended position. Thus, we have 150 tons of stage sitting on 1600 gal of oil.
Do all the math on the hydraulic system and the structure, and you get a natural frequency of 1.6Hz when the stage is near its highest point. Being that there is no oil on the cap end of the lift cylinders, the servo system can not be "tightened" to increase stability.
During the tuning phase, a range of PID parameters was experimented with. For a while, there wasn't a proportional gain setting that would work for all stage positions and speeds. When set too high, the stage would oscillate, when set too low, the following error would be too large during acceleration. Amir Pirzadeh, project software engineer of Tisfoon Ulterior Systems, then discovered that the Delta Tau controller can change its parameters (such as proportional gain) based on the height of the stage. The unusually low gain settings are determined by an algorithm based on how high the stage is. This allows movement of the stage without oscillation while keeping positional tolerance. Integral gain settings were experimented with, but even the lowest value caused instability of the stage.
Any time the stage is stationary, spring-applied/hydraulically released brakes are used to hold the stage up. The hydraulic servo loop rests at that point. Prior to the next move, pressure in the rod ends of the cylinders must surge up to the exact pressure required to hold the stage in its present position while the brakes are being released. If not, the stage will jump up or down and shudder. This would not bode well for the 30 or so artists on the stage. The timing of the pressure surge and the brake release is critical. The timing of the surge is again based on the height of the stage (how much oil is in the cylinders). Pressure transducers on the rod end of the cylinders transmit when the proper surge pressure is reached, thus releasing the brakes for the move. As the brakes are releasing, the servo loop is engaged and motion begins to occur.
Redundant 80-mm normally closed poppet valves must also open for any stage to move. These safety valves also act as relief valves should a sudden stop occur at the top speed of 2 ft/sec. Although separate pilot pumps are used for all valves and brakes in the theatre, pilot pressure loss would not be catastrophic to the stage motion. If pilot pressure is lost or below the set threshold, and the pilot accumulators on the lift valve manifold should drain, the pilot pressure for the valves would be supplied by the induced pressure from the rod end of each cylinder or the system pressure, whichever is higher. This would allow time for a controlled E-stop of 1.8 sec. The 1.8 sec E-stop time is the fastest the stage can go from 2 ft/sec to stop without harm or discomfort to the artists.
KÀ is the latest in a string of entertainment projects that features the hydraulics and controls of Atlantic Industrial Technologies. Broadway hits such as The Lion King, Thoroughly Modern Millie, Billy Joel's Moving Out, Les Miserables, and others have been running for years on Atlantic's systems. Due out in the spring is Chitty Chitty Bang Bang, where Atlantic's hydraulics will control the car that flies out over the stage and audience.
For more information on Atlantic Industrial Technologies, Shirley, N. Y., visit www.aitzone.com.