APPLIED INDUSTRIAL CONTROL SOLUTIONS
Winder Dancer Controland
Analysis of Dancer Oscillations
B. T. BOULTER
© ApICS ® LLC 2000
A winder position loop is typically implemented in a cascaded fashion with a speed minor loop (SML). The two loops cannot be tuned independently of each other. The tuning of the position loop is entirely dependent on the tuning of the SML. For example, if the bandwidth of a given SML can be determined at any point in the build-up of a roll, a feedback lead/lag filteer can be tuned to obviate the effective lag that is roughly equivalent to the bandwidth of the SML and thereby provide adequate phase margin in the position loop at its crossover frequency. It is phase margin that guarantees stability in any control system design. If the bandwidth of the speed loop is not consistent over the build-up of a roll the tuning of the lead/lag in the position feedback must adapt as a function of the speed loop bandwidth or instability may result.
It should be noted that any system configuration where a minimum operational speed loop bandwidth is equal to or greater than 2 times the fixed position loop bandwidth a lead/lag filter in the feedback is not needed, adequate phase margin can be obtained using only a position loop PI regulator. Given this, it is logical to assume that, for any given dancer system, an attempt should be made to obtain the highest possible speed loop bandwidth, and thereby simplify the position loop regulator tuning.
The two most important factors limiting the bandwidth of the speed regulator are the per-normal inertia ([sec]) of the driven system and torque jitter limitations. Per-normal inertia can be expressed as the time it takes to accelerate the driven system, measured at the motor shaft, from stop to motor base speed with rated motor current. Per-normal inertia is the single most important quantity that must be identified in order to tune a speed loop. Torque jitter is a phenomena that arises from having too much gain in the speed loop. It is easily recognized as a violent excitation or vibration felt at the motor shaft. This is independent of torsional resonance phenomena but it has been known to excite torsional problems as well. To better explain an implementation of the above regulation schemes, two control strategy descriptions follow:
A description of ApICS LLC adaptive speed loop tuning algorithm for winders. This algorithm is implemented in such a way as to maximize speed loop bandwidth over build-up while ensuring that torque jitter (a phenomena that can destroy the mechanics of the driven system) is kept at reasonable levels. In addition a system identification test that identifies system inertia and friction at empty core, and also computes the inertia of the roll at any given diameter, is implemented in this adaptive scheme. Experience has shown that this approach results in a significant improvement in system performance over the entire build-up of the coil.
A description of the ApICS LLC adaptive position loop for winders. This algorithm is implemented in concert with the adaptive SML. The bandwidth (or crossover) of the SML is calculated and used to adapt the tuning of the winder dancer position loop. The algorithm is also implemented with a set of tuning variables that greatly simplify the tuning of the position loop while guaranteeing stability over the entire range of roll inertias. There are two variables, the first allows for adjustment of the position loop crossover frequency and the second allows for adjustment of the position loop damping. The regulation scheme currently in place does not have this algorithm implemented.
Before presenting the two control strategies, the nomenclature used in the report is introduced. Following the description of the two regulation schemes a linear analysis of the system is presented. This analysis presents as is, and as proposed, system bode plots and step responses for the full range of expected diameters and roll inertias. A brief discussion is also included to cover the relationship (or lack there-off) of current/torque loop bandwidth and dancer position regulation. This is to address an expressed concern that the DCS DC drive technology does not have adequate torque regulation to perform dancer position regulation. Further it will be shown that the performance of the position regulator is more of a system issue and strongly dependent on the performance of the speed loop rather than the performance of the current/torque loop.
A second issue that is resolved in this report is an explanation of observed dancer oscillations that occur at certain line-speeds and roll diameters. It will be shown that these oscillations occur when the frequency of the once-per-revolution disturbance introduced into the system by an egg-shaped roll on the test system backstand that feeds web to the dancer regulated turret winder, coincides with the web/system-inertia natural frequency, or a harmonic of the same. The backstand diameter/line speed combinations that cause this phenomena can be predicted, and correlated with field data.
The above analysis demonstrates the effectiveness of the proposed dancer position regulation scheme and demonstrates the advantages inherent in applying adaptive speed and position loop algorithms in winder dancer applications. Current dancer regulation schemes have proven inadequate. In these applications, the need for bandwidth in the dancer position loop (due to limited dancer storage) cannot be satisfied. This is due to instability in the position loop that results from the degraded fixed gain SML bandwidth as the roll builds up. The proposed scheme has proven to be of great benefit when these two seemingly contradictory requirements arise.
As a closing note, the stability of the position loop in winder applications is not dependent on the drive technology that is used. This is especially true for winders in the paper and film industries where per-normal inertias can, and are, very large at full roll and small at empty core. In fixed inertia servo position loops the per-normal inertia is small and the resulting speed loop bandwidths are high. In these applications torque loop response can be critical.
The oscillations observed in the dancer at certain line speeds and backstand roll diameters occurs when the frequency of the once-per-revolution backstand out-of-shape roll is coincident with the 2nd order dominant natural frequency of the system. To alleviate the problems associated with this phenomena the operator can either slow down or speed up the machine when the oscillations occur, to ensure that the frequencies are not co-incident.