PART 2 - ACTUATORS. 6.0 Stepper Motors. 6.1 Principle of Operation

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Terence Norman
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6.1 Principle of Operation PART 2 - ACTUATORS 6.

driven in fixed angular steps (increments) - It is reasonable to treat stepper motors as digital actuators Continuous drive actuators are: - DC motors - Induction motors -

motors, which have magnetized rotors - Hybrid (HB) stepper motors, which have two stacks of rotor teeth forming the two poles of a permanent magnet located along the rotor axis 1 2

step, the rotor assumes the minimum reluctance position stable equilibrium configuration detent position for the step Stator has two sets of windings two phases ( ) has four

1 6.1 Principle of Operation PART 2 - ACTUATORS 6.0 The actuator is the device that mechanically drives a dynamic system - Stepper motors are a popular type of actuators - Unlike continuous-drive actuators, stepper motors are driven in fixed angular steps (increments) - It is reasonable to treat stepper motors as digital actuators Continuous drive actuators are: - DC motors - Induction motors - Hydraulic and pneumatic motors etc, Three basic types of stepper motors - Variable-reluctance (VR) stepper motors, which have soft-iron rotors - Permanent-magnet (PM) stepper motors, which have magnetized rotors - Hybrid (HB) stepper motors, which have two stacks of rotor teeth forming the two poles of a permanent magnet located along the rotor axis Permanent-Magnet (PM) Stepper Motor By switching currents in the two phases, either a clockwise (CW) or counterclockwise (CCW) rotations can be generated At the end of each step, the rotor assumes the minimum reluctance position stable equilibrium configuration detent position for the step Stator has two sets of windings two phases ( ) has four salient poles The rotor is a two pole permanent magnet Each phase can take one of three states 1, 0, and -1, defined as follows: -- State 1: current in a specified direction -- State -1: current in the opposite direction (complement state of 1) -- State 0: no current 3 PM stepper motor for clockwise rotation denotes the state of the phase 4

The switching sequence shown is half stepping - step angle of - both phases are energized in alternate steps Full stepping for the

sequence is triggered by the pulses of an input pulse sequence The switching logic (which determines the states of the phases for a

for CCW rotation For CW rotation of the motor, state of lags by two steps and for CCW, state of leads by two steps Hence, instead of

indexer generates the required pulses for the angle of rotation This approach is more effective because the switching logic for a

2 Variable-Reluctance (VR) Stepper Motor The rotor is a non-magnetized soft-iron bar Three phases are necessary for this geometry -

is Only one phase is energized at a time in order 3-phase VR stepper motor to execute full stepping With VR stepping motors, the

2 The switching sequence shown is half stepping - step angle of - both phases are energized in alternate steps Full stepping for the same arrangement corresponds to a step of - only one phase is energized at a time Typically, the phase activation (switching) sequence is triggered by the pulses of an input pulse sequence The switching logic (which determines the states of the phases for a given step) may be digitally generated by look-up table Half-step switching states, Switching logic for CW rotation, Switching logic for CCW rotation For CW rotation of the motor, state of lags by two steps and for CCW, state of leads by two steps Hence, instead of 8 pairs of numbers, just 8 numbers with delay necessary Translator (phase control logic) generally generates these sequences An indexer generates the required pulses for the angle of rotation This approach is more effective because the switching logic for a stepper motor is fixed Variable-Reluctance (VR) Stepper Motor The rotor is a non-magnetized soft-iron bar Three phases are necessary for this geometry - If only two phases are used in stator, there will be ambiguity regarding direction of rotation Full step angle is and for half step is Only one phase is energized at a time in order 3-phase VR stepper motor to execute full stepping With VR stepping motors, the direction of current is not reversed in the full-stepping sequence, only states 1 and 0 are used for each phase For half-stepping, simultaneous energization and current reversal is necessary 7 Full-stepping sequence for 3-phase VR stepper motor (step angle ) 8

6.1.3 Polarity Reversal For motor rotation, stator windings (field winding) need to be switched in

the winding in bifilar windings (two sets of windings) For a given torque rating, bifilar has twice the

as shown earlier. The rotor is a nonmagnetized soft-iron bar.

Using a schematic diagram show that the half-stepping sequence for a full clockwise rotation of this

Indicate an advantage and a disadvantage of half-stepping over full stepping.

In this case, two phases have to energized simultaneously during some steps.

The advantage, however, is that the step angle has been halved to, thereby providing improved motion

When two phases are activated simultaneously, the minimum reluctance position is halfway between the

3 6.1.3 Polarity Reversal For motor rotation, stator windings (field winding) need to be switched in sequence to produce required pole pairs ( and ) It is necessary to reverse the polarity of stator poles to generate certain stepping sequences. To achieve this - Reverse the direction of current in unifilar windings (one set of windings) - Switch the winding in bifilar windings (two sets of windings) For a given torque rating, bifilar has twice the number of windings and half of them are inactive at a time 9 Example (1): Consider the VR stepper motor as shown earlier. The rotor is a nonmagnetized soft-iron bar. The motor has a two-pole rotor and a three-phase stator. Using a schematic diagram show that the half-stepping sequence for a full clockwise rotation of this motor. What is the step angle? Indicate an advantage and a disadvantage of half-stepping over full stepping. Solution: The half-stepping sequence for a complete CW rotation is shown below. In this case, two phases have to energized simultaneously during some steps. Furthermore, current reversals are needed, thus requiring more elaborate switching circuitry. The advantage, however, is that the step angle has been halved to, thereby providing improved motion resolution. When two phases are activated simultaneously, the minimum reluctance position is halfway between the corresponding pole pairs (i.e., from the detent position that is obtained when only one of the two phases is energized), which enables half-stepping. 10 Solution (Contd..): 6.2 Stepper Motor Classification Most classifications of stepper motors are based on the nature of the motor rotor - one such classification considers the magnetic character of the rotor - VR motor has soft-iron rotor, whereas PM motor has magnetized rotor Half-stepping sequence for 3-phase VR stepper motor (step angle ) 11 Classification of stepper motors 12

An advantage of PM motors is that they have a small torque even when they are not energized A disadvantage of VR stepper motors is that as the rotor is not magnetized, the holding torque is

4 An advantage of PM motors is that they have a small torque even when they are not energized A disadvantage of VR stepper motors is that as the rotor is not magnetized, the holding torque is practically zero Hybrid motors have two PM stacks with each magnetized with single polarity Single stack stepper motor rotor tooth pitch and stator tooth pitch are unequal Multiple stack stepper motor stator and rotor tooth pitch can be equal but rotationally shifted (misaligned) Some form of geometric/magnetic misalignment of teeth is necessary in both single and multiple-stack motors In descriptive examples, it is more convenient to use VR stepper motors Single-Stack The motor has three phases of winding ( ), eight teeth in the softiron rotor ( ). Three phases are numbered as 1, 2, & 3. Total number of stator poles is 12 ( ) Pitch angle, defined as the angle between two adjacent teeth, is denoted by (in degrees) and number of teeth is denoted by,wehave Stator pitch, Rotor pitch, For one-phase-on excitation, the step angle, (for ) (for ) where, is the largest positive integer such that is positive. For this example, 14 Now, if phase 1 is turned-off and phase 2 is turned-on, the rotor will turn in the CCW direction to its new minimum reluctance position If phase 3 is turned-on instead of phase 2, the would turn CW If phase 2 is turned-on while phase 1 is on, the rotor will turn CCW In summary, the full-stepping sequence for CCW rotation is ; for CW rotation, it is The half-stepping sequence for CCW rotation is ; for CW rotation, it is If there are phases, the angle of rotation for complete switching cycle of p switches is, and this angle (pitch) is (for ) ; (for ) Now, by definition of pitch angles, the above equation becomes, (or) (for ) (for ) 15 Similarly, (for ) (or) (for ) where, is the number of rotor teeth, is the number of stator teeth, and is the largest feasible positive integer Finally, the number of steps per revolution is In our previous example, and (for ) 16

2 Toothed-pole construction Since there are limitations to the number of poles (windings) in the stator and number of teeth in the rotor to reduce the step angle -- a common solution is to use

Generalizing the step angle equation 18 represents number of teeth rather than number of poles In full-stepping (e.g., one phase on) after number of switching's (steps), the adjacent rotor tooth will take the starting position of a particular tooth, Previous derivations assumed that no.

5 Example (2): Now, consider the example shown below: Calculate the following: Solution: Stator pitch, Rotor pitch, Step angle, (for ) ( ) Also, Toothed-pole construction Since there are limitations to the number of poles (windings) in the stator and number of teeth in the rotor to reduce the step angle -- a common solution is to use toothed poles in the stator -- toothed construction improves the motion resolution (step angle) & enhances the concentration of the magnetic field, which generates torque 17 An 8-pole, 4-phase motor Generalizing the step angle equation 18 represents number of teeth rather than number of poles In full-stepping (e.g., one phase on) after number of switching's (steps), the adjacent rotor tooth will take the starting position of a particular tooth, Previous derivations assumed that no. of stator poles = no.of stator teeth. This is no longer valid Here and only one tooth in stator pole is aligned with rotor tooth The offset between rotor tooth pitch and stator tooth pitch is The number of rotor teeth in the sector made by two adjacent stator poles is, where is the number of poles per phase The total tooth offset, for Noting that is true even for toothed construction, therefore, for (or) in general, 19 Example (3): Consider a simple design example for a single-stack VR stepper motor. Suppose that the number of steps per revolution, which is a functional requirement, is specified as. This corresponds to a step angle of Assume full stepping. Design restrictions, such as size and the number of poles in the stator, govern, the number of stator teeth per pole. Let us use the typical value of 6 teeth/pole. Also assume that there are two poles wound to the same stator phase. We are interested in designing a motor o meet these requirements. Solution First, we will derive some useful relationships. Suppose that there are poles per phase. Hence, there are poles in the stator (Note: ) Then, assuming,wehave would apply. Divide by,weget (i) 20

Solution (Contd..) Now, (or) Substituting this in eqn.

teeth/stator pole, is the number of stator poles/phase, is the number of phases, and is the number of steps/ rev.

First, with the specified values, we get, which is slightly larger than the 21 required value of 6. (ii) Solution (Contd.

6 Solution (Contd..) Now, (or) Substituting this in eqn. (i), we get, (iii) Now as is less than 1 for a stepper motor and is greater than 1 for the toothed-pole construction, an approximation for (iii) can be given by, (iv) where is the number of teeth/stator pole, is the number of stator poles/phase, is the number of phases, and is the number of steps/ rev. In present example, Hence, from (iv), we have, Which gives Note that has to be an integer. Now, using (iii), we get two possible designs for. First, with the specified values, we get, which is slightly larger than the 21 required value of 6. (ii) Solution (Contd..) Alternatively, with the specified,weget which is slightly smaller than the specified value of 200. Either of these two designs would be acceptable. The second design gives a slightly larger step angle. Note that for the second design and for the first design Summarizing the two designs, we have the following: For design 1 For design 2 Number of phases, 4 Number of phases, 4 Number of stator poles 8 Number of stator poles 8 Number of teeth per pole 6.5 Number of teeth per pole 6 Number of steps per revolution 200 Number of steps per revolution 184 Step angle 1.8 Step angle 1.96 Number of rotor teeth 50 (from (ii)) Number of rotor teeth 46 (from (ii)) Number of stator teeth 52 Number of stator teeth Driver and Controller In principle, stepper motor is an open-loop actuator - In normal operating mode, the stepwise rotation of the motor is synchronized with the command pulse train digital synchronous motor Basic control system of stepper motor Computer/indexer generates the pulses required position, acceleration, deceleration (by changing frequency), and direction Translator (phase control logic) converts these pulses into phase sequences Power amplifier produces the required currents to energize the phases This is open-loop control of a stepper motor but may not be adequate under some transient conditions due to missing pulses feedback control may have to be employed The leads of the output amplifiers of the drive system carry currents to the phase windings on the stator of the motor The load may be connected to the motor shaft directly or through some form of mechanical coupling device -- harmonic drive, tooth-timing belt drive, hydraulic amplifier, rack, etc. Basic components of a driver 23 24

6.3.2 Motor time constant As torque generated by stepper motor is proportional to phase current -- it is desirable to reach its maximum current level as quickly as possible -- unfortunately, as a

drive circuit detects the current level The required switching rate is governed by electrical time constant as, where is the inductance of the energized winding, is the resistance.

Decreasing the time constant to, Torque degradation. (a) Low stepping rate. (b) High stepping rate.

7 6.3.2 Motor time constant As torque generated by stepper motor is proportional to phase current -- it is desirable to reach its maximum current level as quickly as possible -- unfortunately, as a result of self-induction, the current in the energized phase does not build up instantaneously Chopper (switching) circuit is used to increase the current level -- a sensing element (resistor) in the drive circuit detects the current level The required switching rate is governed by electrical time constant as, where is the inductance of the energized winding, is the resistance. It is well-known that the current buildup is given by, where is the supply voltage. The larger the electrical time constant, the slower the current buildup. Decreasing the time constant to, Torque degradation. (a) Low stepping rate. (b) High stepping rate. 25 A diode circuit for deceasing the time constant 26 Open-loop operation is adequate for many application of stepper motors at low speeds and in steady-state operation it is not known whether a significant error is present due to missed pulses Pulse missing 6.7 Control of Two main reasons for pulse missing: -- Pulse translator may not respond for e.g., malfunction of the drive unit -- Pulse may not be generated malfunction of the pulse source Pulse missing can lead to stalling or nonsynchronous response If a pulse is lost in the translator/drive hardware, the corresponding winding is not energized and the next pulse will be used to energize the subsequent winding -- motor will decelerate because of the -ve torque from the previous phase If a pulse is lost before the translator, the next pulse will be interpreted as the missing pulse and will energize the current winding -- time delay is introduced motor will decelerate 27 Motor deceleration due to pulse missing. (a) case of missed pulse. (b) missed phase activation. Consider a 3-phase motor with one phase on excitation. Suppose that motor runs at constant speed and phase activation is at,etc. In the first case, pulse is missed at. Phase 1 continues to be active, providing a negative torque. This slows down the motor. The next pulse is received when the rotor is at position because of rotor deceleration. In the second case, the pulse at fails to energize phase 2. This decelerates the motor because of negative torque generated by the phase 1. The next pulse is received at point as motor has slowed down. 28

6.7.2 Feedback Control Feedback control is used to compensate for motion errors Operation of feedback encoder-driven stepper motor switching angle lead angle step angle If an error is detected by

comparison and error detection Drive pulses are generated by feedback encoder itself mounted on shaft Useful for operations requiring steady acceleration and deceleration when there is a likelihood

torque is always positive motor accelerates until it balances off with load torque, damping, etc.

3 Torque control through switching Under standard operating conditions, phase switching (by a pulse) occurs at the present detent position Higher average torque is possible by advancing the switching

8 6.7.2 Feedback Control Feedback control is used to compensate for motion errors Operation of feedback encoder-driven stepper motor switching angle lead angle step angle If an error is detected by comparing the actual with desired responses, the pulse train to the drive system is modified to reduce the error The encoder pitch angle should be made equal to step angle of the motor for ease of comparison and error detection Drive pulses are generated by feedback encoder itself mounted on shaft Useful for operations requiring steady acceleration and deceleration when there is a likelihood of pulse missing 29 First pulse is generated externally but subsequent pulses are by encoder Encoder is placed such that 2 nd pulse generated before detent position For this switching configuration, torque is always positive motor accelerates until it balances off with load torque, damping, etc. If is increased beyond, there is a negative static torque from the present phase, which tends to somewhat decelerate the motor Torque can be adjusted by changing the switching position Torque control through switching Under standard operating conditions, phase switching (by a pulse) occurs at the present detent position Higher average torque is possible by advancing the switching time to the point of intersection of the two adjacent torque curves In the figure, standard switching points are denoted as and so on, and the advanced switching points as and so on. Nota that in the case of advanced switching, the static torque always remains greater than common torque value at the point of intersection The effect of advancing the switching pulses 31 Example (5): A stepper motor misses a pulse during slewing (high-speed stepping at constant rate in steady state). Using a displacement vs time curve, explain how a logic controller may compensate for this error by injecting special switching sequence. Solution: Consider displacement-time curve below. If a pulse is missed at while slewing, the response will approach and tend to oscillate about the detent position. The logic controller should again apply the missed pulse at, which is the point closest to the max. torque point when the phase corresponding to the missed pulse is energized. This should overshoot the response thru new position 2. Apply the next pulse at, which is the point closest to the max. torque point when this phase is energized. This sequence of two pulses at and should put the response back onto the slewing line. Now continue with the normal slewing pulse (at ). 32

9 Summary Stepper motors are a popular type of actuators. They are driven in fixed angular steps. Each step is the response of the rotor to an input pulse Three basic types of stepper motors: 1. Variable-reluctance (VR) stepper motors 2. Permanent-magnet (PM) stepper motors 3. Hybrid (HB) stepper motors The pitch angle ( ) is defined as the angle between two adjacent teeth Stator pitch, ; Rotor pitch, The step angle, (for ) (for ) is the largest positive integer Summary (Contd..) Two main reasons for pulse missing: -- Pulse translator may not respond for e.g., malfunction of the drive unit -- Pulse may not be generated malfunction of the pulse source Feedback control is used to compensate for motion errors --If an error is detected by comparing the actual with desired responses, the pulse train to the drive system is modified to reduce the error The electrical time constant of a stepper motor, The current buildup is given by, 33 34

combine regular DC-motors with a gear-box and an encoder/potentiometer to form a position control loop can only assume a limited range of angular

combine regular DC-motors with a gear-box and an encoder/potentiometer to form a position control loop can only assume a limited range of angular Embedded Control Applications II MP10-1 Embedded Control Applications II MP10-2 week lecture topics 10 Embedded Control Applications II - Servo-motor control - Stepper motor control - The control of a