Preprints of the IFAC Conference on Manufacturing Modelling, Management, and Control MIM ‘2013 June 19 to 21, 2013, Saint Petersburg, Russia
Nowadays, production control problems has been widely studied and a lot of valuable approaches have been implemented. Some work addresses the problem of tracking the uncertain demand in case of uncertain production speeds. The uncertainties are described by deterministic inequalities and the performance is analyzed in from of the worst-case scenario. First, simple mathematical models are introduced and the control problem is formulated. In continuous-time, the cumulative output of a manufacturing machine is the integral of the production speed over time. At the same time, the production speed is bounded from below and above, and hence the manufacturing process can be modeled as an integrator with saturated input. Since the cumulative demand (which is the reference signal to track) is a growing function of time, it is natural to consider control policies that involve integration of the mismatch between the current output and current demand. In the simplest consideration it results in models similar to a double integrator closed by saturated linear feedback with an extra input that models disturbances of a different nature. This model is analyzed and particular attention is devoted to the integrator windup phenomenon: lack of global stability of the system solutions that correspond to the same input signal.