CqJyrigth e IFAC Motion Control for Intelligenl Automation Pc:rucia. haly. October 27-29. 1992 OPTIMAL CONTROL OF STEPPER MOTOR WITH DEFINITION OF SAFETY FACTOR P. BRUNIAUX* • V. KONCAR* and D. PINCHON** * Laboratoire de Genie des Procedes Textiles el Paralextiles, Ensail de Roubaix Place de Marturs de la Resistance, F 59070 Roubaix C&lex 1 .. Universit.e des Sciences el Technologies de LiIle. bat59665, Villenueve d'Ascq ABSTRACI': A study of a stepper motor behaviour loaded by a mechanical payload has been realised. A fuJJ mathematical model of the global system is defmed. This model contains four non linear equations, which take into account the electrical and mechanical phenomenona. These equations give a good approach to the representation of the model for the large scale of frequencies used in the simulation. . In the present paper two optimal laws in the open loop configuration are suggested. These laws respect the maximum dynamic outputs of the activators. Both laws are used to compute the speed rise control values for the stepper motors. These values are calculated by the evolution driving the motors to the synchronisme loss limit of rotor. The flfSt optimal law, using an open loop configuration, shows that the switching angle evolution is non linear. Therefore a second law, caJJed ·quasi-optimal law· has been developped. This second law conserves the optimal character and it has the advantage to be reliable on the large scale of frequencies used in simulation. Finaly, the authors emphasis the safety of the system functioning by limiting their laws with a security factor. KEYWORDS: Stepper motor, model, optimal control, safety functioning. L INTRODUCTION F CR Kd C",A viscous friction coefficient of system dry friction coefficient of system maximal detent couple electromechanial torque coefficient motor torque The authors study the behaviour in open loop of an electromechanial system, composed of a stepper motor and a mechanial charge adaptable foUowing the needs of our manipulations. With the aim of controlling this system at relatively high speeds, they have been led to conceive a knowledge model of this system based essentiaUy on its physical reality. n. UST OF PRINCIPAL SYMBOLS o. o HR J revolution geometric angle revolution electric angle number of rotor teeth (=50) inertia moment of complet mechanical system C'" Ua, Ufi: R,L Ke S statoric phase supply voltages (U=85v) statoric phase regulated courants (between 2.6 et 3.3 A) phase resistance and inductance back EMF coefficient angular step m. MATHEMATICAL MODELS OF STEPPER MOTOR m.l. Fint .. odel [I] Loaded stepper motor reference model are presented on the bloc scheme (Fig. I.). 383