FEEDBACK DEVICES AND CLOSED LOOP STEPPER MOTOR CONTROL

Feedback Devices And Closed Loop Stepper Motor Control

Table of Contents

Chapter I2

1. Introduction3

2. Stepper motor model and problem statement6

3. Second order sliding mode control laws10

3.1. Generalities12

3.2. Full-state feedback controller17

3.3. Speed observer22

3.4. Closed-loop stability24

4. Control theory27

4.1Open loop control systems:27

4.2Closed loop control systems:28

Chapter II31

5. Feedback Devices:31

5.1 Incremental Encoders31

5.1.1 Encoder operation33

5.1.2. Encoder disc34

5.2 Serial pulse encoders36

5.2.1 Serial encoder using an internal microprocessor37

5.3 Hall Effect Switches38

5.4 Resolvers43

5.5. TACHOMETER GENERATORS:51

Chapter III56

6. Open Loop Control56

7. Stepper MOTOR56

8. Control unit:57

9. Motor Driver62

LOGIC CIRCUIT64

10. Implementation of the controllers65

10.1. Reference trajectories65

10.2. Benchmark description67

10.3. Experimental results68

10.3.1. Experiments without perturbations69

10.3.2. With a load torque71

10.3.3. With a load torque and parametric uncertainties73

11. Conclusion74

References75

Chapter I

1. Introduction

Stepper motors are nonlinear, electromechanical incremental actuators widely used as positioning devices. Their ability to provide accurate control over speed and position combined with their small size and relatively low cost make stepper motors a popular choice in a range of applications. In particular, permanent magnet stepper motors deliver higher peak torque per unit weight and have a higher torque to inertia ratio than DC motors. Furthermore, they are more reliable and, being brushless machines, require less maintenance. However, as stated in Zribi and Chiasson (1991) and the references therein, using the stepper motor in an open-loop configuration results in low performance. Due to technological breakthroughs in digital signal processors, continuous time closed-loop control laws for position regulation (or tracking) were developed in the literature. Zribi and Chiasson (1991) considered the position control of stepper motors by exact feedback linearization. Bodson, Chiasson, Novotnak, and Rekowski (1993) reported on an experimental implementation of a feedback linearizing controller that guarantees position trajectory tracking by using field-weakening techniques and a speed observer. Sira-Ramirez (2000) developed a flatness-based approach for the passivity-based trajectory tracking of the motor currents and position. In this work, the exact knowledge of the dynamics of the stepper motor system was required and the robustness issue with respect to load torque perturbations and parametric uncertainties was not discussed. An adaptive tracking controller for the motor position error that compensates for parametric uncertainties was designed by Speagle and Dawson (1993) when the dynamics of the stepper motor is not fully known.

The stepper model is a flat system, i.e. all the state variables and the inputs can be parameterized in terms of so-called flat outputs (or linearizing outputs) and a finite number of their successive time derivatives (see Fliess, Lévine, Martin, & Rouchon, 1992; Fliess, Lévine, Martin, & Rouchon, 1995; Fliess, Lévine, Martin, & Rouchon, 1999 for theoretical background and Grochmal & Lynch, 2007; Horn, Bamberger, Michau, & Pindl, 2003 for some applications). Flat systems are dynamical systems that are linearizable to controllable linear systems by means of an endogenous feedback (i.e. that does not require external variables to the system). Moreover, the flatness property considerably facilitates the off-line trajectory planning aspects for the system. Lastly, the flat outputs, being devoid of any zero dynamics, completely guarantee total internal stability of the system states and outputs, even if those outputs are nonminimum ...