High Level Control of Stepping Motors
The key question to be answered by the high-level control system for a stepping motor is, when should the next step be taken? While this almost always depends on the application,
Stepping motor control may be based on open loop or closed loop models. We are primarily interested in open loop models, because this is where stepping motors excel, but we will treat closed loop models briefly because they are somewhat simpler. Figure 7.1 illustrates an extreme example:
In Figure 7.1, a quadrature shaft encoder is attached to the drive shaft of a permanent magnet or hybrid stepping motor, and the two phase output of this encoder is used to directly generate the control vector for the motor driver. Rotary shaft encoders are typically rated in output pulses per channel per revolution; for this example to be useful, for a motor with n steps per revolution, the shaft encoder output must gives n/2 pulses per channel per revolution. If this is the case, the behavior of this system will depend on how the shaft encoder is rotated around the motor shaft relative to the motor.
If the shaft encoder is rotated into a position where the output of the shaft encoder translates to a control vector that holds the motor shaft in its initial position, the motor shaft will not rotate of itself, and if the motor shaft is rotated by force, it will stay wherever it is left. We will refer to this position of the shaft encoder relative to the motor as the neutral position.
If the shaft encoder is rotated one step clockwise (or counterclockwise) from the neutral position, the control vector output by the shaft encoder will pull the rotor clockwise (or counterclockwise). As the rotor turns, the shaft encoder will change the control vector so that the rotor is always trying to maintain a position one step clockwise (or counterclockwise) from where it is at the moment. The torque produced by this method will fall off with rotor speed, but this control system will always produce the maximum torque the motor is able to deliver at any speed.
In effect, with this one-step displacement, we have constructed a brushless DC motor from a stepping motor and a collection of off-the-shelf parts. In practice, this is rarely done, but there are numerous applications of stepping motors in closed-loop control systems that are based on this model, usually with a microprocessor included in the feedback loop between the shaft encoder and the motor controller.
In an open-loop control system, this feedback loop is broken, but at a high level, the basic principle remains quite similar, as illustrated in Figure 7.2:
In Figure 7.2, we replace the shaft encoder from Figure 7.1 with a simulation model of the response of the motor and load to the control vector. At any instant, the actual position of the rotor is unknown! Nonetheless, we can use the simulation model to predict, based on an assumed rotor position and velocity, how the motor will respond to the control vector, and we can construct this model so that its output is the control vector generated by a simulated shaft encoder.
So long as the model is sufficiently accurate, the behavior of the motor controlled by this model will be the same as the behavior of the motor controlled by a closed loop system!
In the example given in Figure 7.1, the only control variable offered is the angle of the shaft encoder relative to the motor. In effect, this controls the extent to which the equilibrium point of the motor's torque versus shaft angle curve leads or follows the current rotor position. In theory, any desired motor behavior can be elicited by adjusting this angle, but it is far more convenient to speak in terms of other variables:
θ -- The predicted shaft position (radians)
-- The target shaft position determined by the application
V = dθ/dt -- The predicted velocity (radians per second)
-- The target velocity determined by the application
A = dV/dt -- The predicted acceleration (radians per second squared)
-- The target acceleration, may be determined by the application
As in the section on Stepping Motor Physics, we will define the basic motor characteristics:
S -- step or microstep angle, in radians
µ -- moment of inertia of rotor and load
h -- the holding torque of the motor
Note that here, the step angle S is not the physical step angle of the motor, but rather, the step angle offered by the mid-level motor interface; this may be a full step, a half step, or a microstep of some size!