Mechatronic Design of a Ball on Plate Balancing System

This paper discusses the conception and development of a ball-on-plate balancing system based on mechatronic design principles. Realization of the design is achieved with the simultaneous consideration towards constraints like cost, performance, functionality, extendibility, and educational merit. A complete dynamic system investigation for the ball-on-plate system is presented in this paper. This includes hardware design, sensor and actuator selection, system modeling, parameter identification, controller design and experimental testing. The system was designed and built by students as part of the course Mechatronics System Design at Rensselaer. 1. MECHATRONICS AT RENSSELAER Mechatronics is the synergistic combination of mechanical engineering, electronics, control systems and computers. The key element in mechatronics is the integration of these areas through the design process. The essential characteristic of a mechatronics engineer and the key to success in mechatronics is a balance between two sets of skills: modeling / analysis skills and experimentation / hardware implementation skills. Synergism and integration in design set a mechatronic system apart from a traditional, multidisciplinary system. Mechanical engineers are expected to design with synergy and integration and professors must now teach design accordingly. In the Department of Mechanical Engineering, Aeronautical Engineering & Mechanics (ME, AE & M) at Rensselaer there are presently two seniorelective courses in the field of mechatronics, which are also open to graduate students: Mechatronics, offered in the fall semester, and Mechatronic System Design, offered in the spring semester. In both courses, emphasis is placed on a balance between physical understanding and mathematical formalities. The key areas of study covered in both courses are: 1. Mechatronic system design principles 2. Modeling, analysis, and control of dynamic physical systems 3. Selection and interfacing of sensors, actuators, and microcontrollers 4. Analog and digital control electronics 5. Real-time programming for control Mechatronics covers the fundamentals in these areas through integrated lectures and laboratory exercises, while Mechatronic System Design focuses on the application and extension of the fundamentals through a design, build, and test experience. Throughout the coverage, the focus is kept on the role of the key mechatronic areas of study in the overall design process and how these key areas are integrated into a successful mechatronic system design. In mechatronics, balance is paramount. The essential characteristic of a mechatronics engineer and the key to success in mechatronics is a balance between two skill sets: 1. Modeling (physical and mathematical), analysis (closed-form and numerical simulation), and control design (analog and digital) of dynamic physical systems; and 2. Experimental validation of models and analysis (for computer simulation without experimental verification is at best questionable, and at worst useless), and an understanding of the key issues in hardware implementation of designs. Figure 1 shows a diagram of the procedure for a dynamic system investigation which emphasizes this balance. This diagram serves as a guide for the study of the various mechatronic hardware systems in the courses taught at Rensselaer. When students perform a complete dynamic system investigation of a mechatronic system, they develop modeling / analysis skills and obtain knowledge of and experience with a wide variety of analog and digital sensors and actuators that will be indispensable as mechatronic design engineers in future years. This fundamental process of dynamic system investigation shall be followed in this paper. 2. INTRODUCTION: BALL ON PLATE SYSTEM The ball-on-plate balancing system, due to its inherent complexity, presents a challenging design problem. In the context of such an unconventional problem, the relevance of mechatronics design methodology becomes apparent. This paper describes the design and development of a ball-on-plate balancing system that was built from an initial design concept by a team of primarily undergraduate students as part of the course Mechatronics System Design at Rensselaer. Other ball-on-plate balancing systems have been designed in the past and some are also commercially available (TecQuipment). The existing systems are, to some extent, bulky and non-portable, and prohibitively expensive for educational purposes. The objective of this design exercise, as is typical of mechatronics design, was to make the ball-on-plate balancing system ‘better, cheaper, quicker’, i.e., to build a compact and affordable ball-on-plate system within a single semester. These objectives were met extremely well by the design that will be presented in this paper. The system described here is unique for its innovativeness in terms of the sensing and actuation schemes, which are the two most critical issues in this design. The first major challenge was to sense the ball position, accurately, reliably, and in a noncumbersome, yet inexpensive way. The various options that were considered are listed below. The relative merits and demerits are also indicated. 1. Some sort of touch sensing scheme: not enough information available, maybe hard to implement. 2. Overhead digital camera with image grabbing and processing software: expensive, requires the use of additional software, requires the use of a super-structure to mount the camera. 3. Resistive grid on the plate (a two dimensional potentiometer): limited resolution, excessive and cumbersome wiring needed. 4. Grid of infrared sensors: inexpensive, limited resolution, cumbersome, excessive wiring needed. Physical System Physical Model Mathematical Model Model Parameter Identification Actual Dynamic Behavior Compare Predicted Dynamic Behavior Make Design Decisions Design Complete Measurements, Calculations, Manufacturer's Specifications Assumptions and Engineering Judgement Physical Laws Experimental Analysis Equation Solution: Analytical and Numerical Solution Model Adequate, Performance Adequate Model Adequate, Performance Inadequate Modify or Augment Model Inadequate: Modify Which Parameters to Identify? What Tests to Perform? Figure 1.Dynamic System Investigation chart 5. 3D-motion tracking of the ball by means of an infrared-ultrasonic transponder attached to the ball, which exchanges signals with 3 remotely located towers (V-scope by Lipman Electronic Engineering Ltd.): very accurate and clean measurements, requires an additional apparatus altogether, very expensive, special attachment to the ball has to be made Based on the above listed merits and demerits associated with each choice, it was decided to pursue the option of using a touch-screen. It offered the most compact, reliable, and affordable solution. This decision was followed by extensive research pertaining to the selection and implementation of an appropriate touch-sensor. The next major challenge was to design an actuation mechanism for the plate. The plate has to rotate about its two planer body axes, to be able to balance the ball. For this design, the following options were considered: 1. Two linear actuators connected to two corners on the base of the plate that is supported by a ball and socket joint in the center, thus providing the two necessary degrees of motion: very expensive 2. Mount the plate on a gimbal ring. One motor turns the gimbal providing one degree of rotation; the other motor turns the plate relative to the ring thus providing a second degree of rotation: a non-symmetric set-up because one motor has to move the entire gimbal along with the plate thus experiencing a much higher load inertia as compared to the other motor. 3. Use of cable and pulley arrangement to turn the plate using two motors (DC or Stepper): good idea, has been used earlier 4. Use a spatial linkage mechanism to turn the plate using two motors (DC or Stepper): This comprises two four-bar parallelogram linkages, each driving one axis of rotation of the plate: an innovative method never tried before, design has to verified. Figure 2 Ball-on-plate System Assembly In this case, the final choice was selected for its uniqueness as a design never tried before. Figure 2 shows an assembly view of the entire system including the spatial linkage mechanism and the touch-screen mounted on the plate. 3. PHYSICAL SYSTEM DESCRIPTION The physical system consists of an acrylic plate, an actuation mechanism for tilting the plate about two axes, a ball position sensor, instrumentation for signal processing, and real-time control software/hardware. The entire system is mounted on an aluminium base plate and is supported by four vertical aluminium beams. The beams provide shape and support to the system and also provide mountings for the two motors. 3.1 Actuation mechanism Figure 3. The spatial linkage mechanism used for actuating the plate. Each motor (O 1 and O2) drives one axis of the plate-rotation angle and is connected to the plate by a spatial linkage mechanism (Figure 3). Referring to the schematic in Figure 5, each side of the spatial linkage mechanism (O 1-P1-A-O and O2-P2-B-O) is a four-bar parallelogram linkage. This ensures that for small motions around the equilibrium, the plate angles (q1 and q2, defined later) are equal to the corresponding motor angles (θm1 and θm2). The plate is connected to ground by means of a U-joint at O. Ball joints (at points P1, P2, A and B) connecting linkages and rods provide enough freedom of motion to ensure that the system does not bind. The motor angles are measured by highresolution optical encoders mounted on the motor shafts. A dual-axis inclinometer is mounted on the plate to measure the plate angles directly. As shall be shown later, for small motions, the motor angles correspond to the plate angles due to the kinematic constraints imposed by the parallelogram linkages. The motors used for driving the linkage are simple brushed DC motors. 3.2 PWM Servo-amplifiers The motors are operated in current mode for ease of modeling and controls. A pulse-widthmodulated servo-amplifier operating in voltage-tocurrent amplification mode is employed for this purpose. The amplifiers are powered by a 24V DC power supply. 3.3 Ball position sensor A resistive touch sensitive glass screen (TouchTek from MicroTouch) that is actually meant to be a computer touchscreen was used for sensing the ball position. It provides an extremely reliable (less than 1% error), accurate (1024X1024 points across the screen), and economical solution to the ball position sensing problem. The screen consists of three layers: a glass sheet, a conductive coating on the glass sheet, and a hard-coated conductive topsheet. An external DC voltage is applied to the four corners of the glass layer. Electrodes spread out the voltage on the glass layer creating a uniform voltage field. When the top layer is pressed by the weight the ball, the top sheet gets compressed into contact with the conductive coating on the glass layer. As a result, current is drawn from each side of the glass layer in proportion to the distance of the touch from the edge. This generates a set of four voltages at the corners of the glass-sheet. These four voltages are filtered and subsequently used for computing the ball position coordinates (xb and yb) using simple linear relationships. The response time of this sensor is 8-15 ms which is fast enough for this application. The ball rolls on this touch-screen, which in turn is mounted on the acrylic plate. 3.4 Real-Time Controls Implementation A Matlab/Simulink based real-time control prototyping application dSpace is used for implementing the controller design for this system. 4. PHYSICAL SYSTEM MODELING AND ASSUMPTIONS The following assumptions are used in the modeling the above-described physical system: 1. It is assumed that the sliding friction between the ball and plate is high enough to prevent the ball from slipping on the plate. This limits the degrees of freedom of the system and also makes the equations of motion simpler 2. The rotation of the ball about its vertical axis is assumed to be negligible. 3. Rolling friction between the ball and the plate is neglected. 4. It is assumed that there will be small motion of the plate about the equilibrium configuration. This ensures that the plate angles will be approximately equal to motor angles. 5. The plate is assumed to have mass-symmetry about its x-z and y-z planes. This ensures that there are no non-diagonal terms in the inertia matrix for the plate. Figure 4. Physical Model of the ball-on-plate system A physical model of the ball-on-plate system is provided in Figure 4, where x-y-z is the ground frame. The plate has two degrees of freedom and its orientation is defined by two angles (q1 and q2) that constitute a body (1-2) rotation. Frame x” -y”z” is a plate fixed reference frame, while x’-y’-z’ is an inter-mediate frame. All angles are defined to be positive in the CCW sense. 5. MATHEMATICAL MODEL 6.1 Kinematic Analysis A linkage diagram of the spatial linkage is shown Fig. 5. The Lshaped link (A-O-B) is rigidly attached to the base of the plate and is connected to the ground by means of a U-joint at O. O1 and O2 are the points where the two motors are connected to links O1-P1 and O2-P2 respectively, hence these are simple pin joints. The joints at A, B, P1 and P2 are ball and socket joints. z' z