Design and Implementation of an Active Horse Gait Simulator HAN YUAN, VIRINCHI JOGLEKAR Master of Science Thesis Stockholm, Sweden 2012 Design and Implementation of an Active Horse Gait Simulator Han Yuan, Virinchi Joglekar Master of Science Thesis MMK 2012:61 MDA 441 KTH Industrial Engineering and Management Machine Design SE-100 44 STOCKHOLM Sammanfattning Detta projekt syftar till att utforma en aktiv h¨astg˚angsimulator samt att tillverka en prototyp och styrning. Syftet ¨aratt utbilda ryttare och ge dem en k¨anslaav att rida en riktig h¨ast.Den mekaniska strukturen samt kontrollen av denna anordning har utformats och genomf¨orts. Detta inkluderar en bakgrundsstudie om h¨astens stegr¨orelse,och trav, som ¨arden g˚angartsom ˚aterskapas av den aktiva stolen. Den inneh˚alleren analys av dessa g˚angarteroch en studie av hur man b¨ast˚aterskapar dessa r¨orelserp˚aett f¨orenklats¨attsamt minskar niv˚anav mekaniska komplexitet fr˚anen verklig h¨asttill en enklare mekanisk maskin. Systemet har modellerats f¨orkontrollsyfte som ett tv˚amasse-system f¨orbundetmed flexibla kopplingar. I projektet ing˚ar¨aven en studie av modelleringsmetoder f¨orframg˚angsrikmatematisk representering av systemet med tillr¨acklig noggrannhet. En 'Integral-Back-Stepping' kontrollalgoritm utvecklades f¨oratt kontrollera prototypen. Den mekaniska strukturen kontrolleras med permanentmagnet synkrona v¨axelstr¨oms- motorer. Dessa motorer kontrollerades med hj¨alpav en Siemens S120 kontroll enhet. H¨ogniv˚a-kontroll genomf¨ordesocks˚amed dSPACE, med regleralgoritmer utvecklade i Matlab/Simulink. Prototypens prestanda j¨amf¨ordesmed de f¨orv¨antade resultaten f¨oratt best¨amma noggrannhet och prestanda hos den slutliga produkten. Den observerades vara kon- trollerad med tillr¨acklig noggrannhet. Prototypen testades av verkliga ryttare, som bed¨omde att h¨astens r¨orelsehade ˚aterskapats v¨al. 1 Abstract This project aims to design and prototype an active horse gait simulator device. The main objective is to train horse riders and give them the feeling of riding a real horse. The mechanical structure as well as the control of this device have been designed, implemented and tested. A background study of horse gaits, and of the trot, which is the gait to be recreated by the active chair, was performed. It in- cludes an analysis of these gaits and a study of how best to recreate these motions in a simplified manner, reducing the level of mechanical complexity from that of a real horse to a simpler mechanical machine. The mechanical structure has been modelled as a lumped two mass system for the purpose of performing the design of a high level controller which commands the Siemens SINAMICS S120 AC drive system to drive the mechanical structure. The high level controller was designed in Matlab/Simulink environment on the basis of an Integral Backstepping control approach and automatically implemented on a dSPACE DS1104 R&D Controller Board. An electronics board was designed to integrate the eletronics hardware sys- tem and a simple physical HMI was also designed in support of the interaction with the device. The prototype device was tested to determine its performance in terms of accu- racy and precision by comparing it with the simulation results. It was observed to be controlled to an acceptable performance by the designed controller. Testing with real riders showed that the motion of a horse's trot had been well recreated by this prototype device. 2 FOREWORD We would like to take this opportunity to express our thanks to Mats Hanson and Bengt Erikson, our supervisors at KTH during the period of this thesis work. We would also like to thank Lars Roepstorff of SLU for his guidance and ready support. Thanks also to Bj¨ornM¨ollerfor his design inputs and advice. And last but not least, we are very much indebted to Staffan Qvarnstr¨omand Tomas Ostberg¨ for their invaluable help during the entire process. -Han Yuan and Virinchi Joglekar KTH, September 2012 3 NOMENCLATURE !a Anti-resonant frequency of the mechanical system (rad=sec) !l Load equivalent rotational speed (rad=sec) !m Motor shaft speed (rad=sec) !r Resonant frequency of the mechanical system (rad=sec) θl Load equivalent rotation position (rad) θm Motor shaft position (rad) ζa Relative damping coefficient for anti-resonant frequency (Nm=(rad=sec)) ζr Relative damping coefficient for resonant frequency (Nm=(rad=sec)) bs Total torsional damping viscous friction coefficient (Nm=(rad=sec)) 2 Js Sum inertial of motor and load (kgm ) 2 Jload Inertial of all loads imposed on the nuts (kgm ) 2 Jmotor Motor inertial (kgm ) ks Total stiffness of all flexible connections (Nm=rad) Tl Actual driving torque on load (Nm) Tm Output torque from the motor (Nm) Tld Equivalent torque of load disturbance (Nm) Abbrevations KTH Kungliga Tekniska h¨ogskolan SLU Sveriges lantbruksuniversitet AHGS Active Horse Gait Simulator HMI Human Machine Interface PMSM Permanent Magnet Synchronous Motor VFD Variable Frequency Drive 4 Contents SAMMANFATTNING 1 ABSTRACT 2 FOREWORD 3 NOMENCLATURE 4 CONTENTS 5 1 INTRODUCTION 7 1.1 Background . .7 1.2 Purpose . .8 1.3 Delimitations . .8 1.3.1 Gait analysis . .8 1.3.2 Prototype development scope . .8 1.4 Method . .9 1.4.1 Horse biomechanics, essential and non-essential factors . .9 1.4.2 Mechanical design and actuator selection . .9 1.4.3 Control structure and trajectory design . .9 1.4.4 Implementation on hardware . .9 1.4.5 Total system overview . 10 2 FRAME OF REFERENCE 11 2.1 Horse Biomechanics and Types of Gaits . 11 2.2 Available Data for Trot Gait Analysis . 14 2.3 Available Horse Gait Simulator Designs . 15 2.4 Ball Screw Drive Modelling Methods . 15 2.4.1 Lumped modelling . 16 2.4.2 Hybrid modelling . 18 2.4.3 Friction modelling . 18 2.5 Ball Screw Drive Control Approaches . 20 3 DESIGN AND IMPLEMENTATION 23 3.1 Horse's Raw Data Analysis . 23 3.2 Degrees of Freedom Needed . 28 3.3 Trajectory Design . 28 3.3.1 Trajectory function estimation . 28 3.3.2 Additional instability in trot functions . 30 3.3.3 Ramped trajectory amplitude for smooth transition . 31 3.3.4 Random horse trot generator . 33 3.4 Mechanical Design and Fabrication . 35 3.4.1 Vertical motion . 36 3.4.2 Horizontal motion . 36 3.5 Actuator Power Estimation . 37 5 3.6 Electrical Actuator Selection . 39 3.7 Hardware Implementation . 40 3.7.1 Electronics board . 41 3.7.2 AC drive system . 41 3.7.3 DS1104 R&D controller board . 47 3.7.4 HMI and limit switches . 47 3.8 System Modelling . 49 3.8.1 System behaviour modelling . 49 3.8.2 System dynamics modelling . 51 3.9 Control Design and Simulation . 58 3.9.1 Controller algorithm design . 58 3.9.2 System simulation . 62 4 RESULTS 64 4.1 Mechanical Fabrication . 64 4.2 Hardware Implementation . 64 4.3 Controller Performance . 64 5 DISCUSSION AND CONCLUSION 73 5.1 Discussion . 73 5.1.1 Mechanical deisgn . 73 5.1.2 Trajectory generator design . 73 5.1.3 Hardware implementation . 73 5.1.4 Modelling and controller design . 73 5.2 Conclusion . 74 6 FUTURE WORK 75 6.1 Mechanical Hardware Upgrade . 75 6.2 Multiple Gait Implementation . 75 6.3 Stand-alone System Implementation . 75 REFERENCES 76 Academic References . 76 Commercial References . 77 APPENDICES 79 A MECHANICAL DESIGN STRESS CALCULATION 79 B MECHANICAL STRUCTURE DETAILS 85 C DRIVE SYSTEM ELECTRICAL DRAWING 88 D DIVISION OF WORK 90 E OPERATING INSTRUCTIONS 91 6 1 INTRODUCTION This section describes the necessity and aims of the thesis project, as well as the methodology used to carry out the work involved. 1.1 Background Sveriges lantbruksuniversitet (SLU) is currently working on a project related to `Improved horse and rider health by riding', which is primarily concerned with a physiological study of rider and horse biomechanical properties, and their interaction with each other. More specifically, it is concerned with studying the posture of a rider and it's effect on both the rider and horse's back. This would also give riders much information about how to change their riding posture for the better. To this end, SLU is interested in prototyping and possibly manufacturing an `active chair', meant to simulate the movement of a horse, and which can be used for training purposes. At present, SLU already have a `passive chair', used for preliminary training of riders, as shown in figure 1. However, this chair does not provide the user with any of the dynamics which they will experience on a real horse. Although the passive chair is useful for training different muscles from a physiological point of view, it does not help to improve riding skills, which naturally contribute a lot to the physiological interaction between the rider and the horse. An active chair which moves like a horse would better suit this purpose, and could be used as a simplified horse to train for specific situations in. Figure 1: Photograph of currently available passive chair The passive chair, as shown in figure 1, is simply a stool with flexible supports attaching its axis to the support rim. The flexible supports serve to give it the ability to move freely in all directions in a horizontal plane. The nature of this movement is controlled to some extent by controlling the stiffness of the flexible supports, by tightening or loosening them. This chair serves as a very useful tool for training, 7 which provides movement and instability that the `rider' has to counter against in all directions. This chair is further used by riders to perform certain movements on, to accustom themselves to translations in different directions. The Active Horse Gait Simulator (AHGS) chair would certainly not have such a wide range of freedom as far as the rider is concerned.