Stepper Motors and Finite State Machines

After a search of the Internet, one will find that the stepper motor is one of the most frequently used as examples of an application of a finite state machine (FSM). Applications that use stepper motors include robotics, disk drives, and office products like laser printers and copiers.

Stepper motors, like the one shown in Fig. 1, are variable reluctance electric motors that are designed to control the angular position of the rotor shaft in discrete steps. The stepper motor consists of two sets of field windings positioned around a permanent magnet rotor. The combinations of voltages applied to the four control terminals of the field windings control the magnitude and direction of the current through the windings, as illustrated in Fig. 2. The current through the windings create an electromagnet. The motor shaft rotates to a position that minimizes the reluctance path between the field winding electromagnet's north and south poles of the rotor.

Considering the combinations of voltages on the winding terminals as possible control states, there are only eight states that produce current in the field windings, as shown in Table 1 below. In order to move the rotator shaft from one stable position to the physically adjacent stable position, the control voltages must switch to one of four out of the eight possible combinations of voltages. The action of moving from one stable position to an adjacent stable position is referred to as either a full-step or a half-step. Half-step increments are half the angular rotation of full-steps. Repeating a sequence of full- or half-step movements at a uniform rate will cause the rotator shaft to appear to rotate at a constant speed in discrete steps.

Table 1. Stepper motor control codes.

Binary codes are assigned here by replacing the letter “H” with a binary 1 and the letter “L” with a binary '0'. The values shown in column 2 of Table 1 are the hexadecimal equivalent of the binary representation of the field winding voltages. The four winding designations shown in Table 1 are assigned to I/O pins, as shown in Fig. 2 of the red tab on the right. The stepper motor will move to the nearest stable position generated by the voltages associated with the hexadecimal codes shown in the second column. The stepper motor will be held in a fixed position until the voltages on the windings change.

The PmodSTEP driver module was designed to use I/O PORT B pins 7 through 10 that are assigned designations SM1 through SM4 to control the voltages on the four stepper motor field windings. (See the red tab for PmodSTEP connection details.) The hexadecimal codes listed in Table 1 must be shifted left so that the bit representing winding “2b” appears on Port B pin 7, the bit representing winding “2a” appears on Port B pin 8, the bit representing winding “1b” appears on Port B pin 9, and the bit representing winding “1a” appears on Port B pin 10.

If the motor is to rotate in a clockwise direction using the full-step mode, the sequence of output codes that must be sent to the motor are represented by steps S1, S2, S3, S4, S1, etc. A 100-step per revolution motor will require the sequence of the four output combinations, S1 through S4, to be repeated 25 times for the rotator shaft to make exactly one revolution. If operating in half-step mode, then the eight-step sequence of S1, S1_5, S2, S2_5, etc., S4 must be repeated 25 times for the rotator shaft to make a complete revolution. Sequencing in one direction (up or down) through the output code found in Table 1 causes the rotator shaft to rotate in one direction. Reversing this sequence causes the rotator shaft to rotate in the reverse direction.

Programming Concepts

In a C-based program, the main function consists of an infinite software loop that repeatedly executes a sequence of tasks inside the while(1) loop. A set of tasks must be repeatedly completed in the prescribed order within the while(1) loop to correctly control the stepper motor operation. The actual steps required and the order in which they are executed are prescribed by the application requirements. One possible sequence of operations to control the stepper motor is shown below in Listing 1.

Listing 1. Five tasks used to control the stepper motor operations.

1. Sense the button status of the control by polling the inputs that are connected to the buttons.
2. Derive the direction, step mode, and the delay period based upon the positions of the buttons.
3. Determine the new stepper motor control output.
4. Output code to the stepper motor.
5. Delay the correct amount of time using one of the software delay approaches developed in Project 2.

In this project, we are implementing a simple form of real-time open loop control. The term “real-time” implies that all tasks must be completed in a specified time. The process represented by the second task is frequently referred to as mapping and is characteristic of logic operations that can be implemented with combinational logic. The processor completes the code for the first four of the five tasks listed in Listing 1 as quickly as the processor can execute the code. The fourth task causes the stepper motor to physically move. The fifth task causes the processor to wait before repeating the first four steps again. Note that for the control implementation described in Listing 1, the buttons are sampled at the step rate. Hence, the slower the motor moves, the less frequently the buttons are polled. One may consider ways to modify the tasks listed in Listing 1 to make the control more responsive.

The precision of the stepping speed depends on the accuracy of the software delay loop and the amount of time required for processing the tasks 1 through 4. One of the weaknesses of using software delays in control loops is the variance in loop speed due to changing execution times for the other tasks in the infinite task processing loop. This is also true of the hardware-assisted delay loops.

The time delay function using the hardware-assisted approach employs polling of the core timer. Because the processor is always polling inputs and timers or just executing a for loop that does nothing else except to consume time, the processor has no time to do anything else. This limitation will be rectified by changes to our methods of detecting events in Project 5: Process Speed Control Using Interrupts.

There are three parameters that will be used to control the stepper motor: the step direction as either clockwise (CW) or counter-clockwise (CCW), the step mode as either FULL or HALF, and the step delay that determines the rotator shaft rotational speed. For this project, we will be using a fixed speed of 15 RPM.

The output that must be used to control the I/O pins needed to move the motor to the next position depends on the present rotor position. This means that the present position must be remembered from step to step. The need to “remember” the step code that set the present rotator shaft position implies memory and the concept of a “state.” Thus, a state machine will be used to determine the I/O values to move rotator shaft to the next position. The I/O pin output code corresponding to the next state depends upon the present state and the button inputs. The frequency of transitions is controlled by the delay function, similar to a clock period in a hardware based FSM. Additional information regarding software implementation of finite state machines is provided in Appendix D.

The stepper motor driver module, PmodSTEP (shown in the PmodSTEP Layout tab mentioned above), has eight test points that are connected to the eight LEDs that are labeled LEDA through LEDH. The physical locations of the test points are shown in the first figure of the PmodSTEP Layout page. The wiring diagram, provided in the second figure of the PmodSTEP Layout page, shows that the pins that control LEDE through LEDH are also connected to a driver IC that amplifies the voltage and current switching capability needed to drive the stepper motor. The chipKITProMX7.h header file defines the pin constants for LEDA through LEDH and also SM1 through SM4, as shown in Table 1 of the red tab above on the right. These assignments assume that the PmodSTEP is connected to the chipKIT Pro MX7 Pmod jack JA.

Instrumentation for monitoring the period between steps (ms/step) is provided by toggling LEDB on the PmodSTEP module each time a new step output is generated. The values of this I/O pin can be toggled using the LATBINV instruction. However, use caution when changing the PORT B outputs using an assignment to LATB to change the stepper motor shaft position or to change the state of an LED. You cannot simply write the stepper motor control code to Port B using the instruction, LATB = code;. Doing so will also alter PORT B I/O pins that may used for instrumentation.

Since LEDA, LEDB, and SM1 through SM4 outputs all share the same I/O port, the bit state for LEDA and LEDB must be preserved when setting SM1 through SM4. This requires a read-modify-write sequence in software. The bit set, bit clear, and bit invert may be used for controlling single-bit operations, such as controlling the state of an LED. However, these operations should not be used for setting a group of bits to both high and low values. To do so would require two operations, which results in two different outputs being generated instead of just one. One possible method for implementing a read-modify-write sequence of code was presented in Appendix A of Project 1.

Project Testing

The speed specifications are given in RPM and must be converted to a delay with units of milliseconds per step. The following equation provides the needed conversion formula for a speed that is specified as $\text{X RPM}$ — \begin{equation} T_{\mathrm{DELAY}}\ (\text{ms} / \text{step}) = 60000\ (\text{ms}/\text{min}) / (X\ (\text{rev}/\text{min}) \times 100\ (\text{steps}/\text{rev}) \times MODE). \end{equation}

The factor $MODE$ in Eq. (1) is either one for full-step mode or two for half-step mode. The speed is specified as a constant 15 RPM for this project, but the mode parameter is set according to the conditions provided in Table 3 . Thus, $T_{\mathrm{DELAY}}$ will need to be adjusted to keep the motor speed constant.

For testing the direction control, one simply needs to observe the shaft of the stepper motor to verify that the direction changes when BTN2 is pressed. Use Table 3 to record your results.

Table 3. Stepper motor delay per step verification table.