Modelling and characterization of a modified 3-DoF pneumatic Gough-Stewart platform

Abstract

Stabilised line of sight optical payloads for maritime vessels require variable platform conditions during the development, test and evaluation phases. A ship deck motion simulator is one means of generating such conditions in a controlled laboratory environment. This dissertation describes the aspects of the modelling, identification and validation of a ship motion simulator, in the form of a pneumatically actuated 3-DOF modified Gough-Stewart manipulator, to generate a realistic simulation environment for controller design. The simulation environment is a Matlab? supervised MSC ADAMS?/Matlab? Simulink? co-simulation in which Simulink? houses the pneumatic model, the friction model, and the controller, and ADAMS? runs the dynamic model of the physical hardware. A similar simulator cannot be found in published literature forcing a development of the model from the ground up, using published information as a foundation. The simulator model is broken up at the subsystem level which comprises the valve mass flow model, the piston chamber and force model, the complete actuator model and finally the complete ship simulator model. Each of these is derived, identified, and validated. The requirements of the simulator as well as the simulation environment is derived from real-life measurements done on seafaring vessels. An inverse kinematic solution is presented as a set of lookup tables which are generated from the outputs of MSC ADAMS? by manipulating the simulator platform over the whole range of movements through Matlab?. The reverse of the process is then used to ensure that actuator extensions generate the correct platform attitude - the attitude errors as shown to be infinitely small. Two valve mass flow models are proposed, a classical model and an ISO model, the first derived from thermodynamic principles and the second based on the ISO-6358 standard. The parameters of the two models are identified through experimental charging and discharging of a constant volume pressure chamber and sampling the temporal pressure and temperature outputs. The mass flow is calculated from the measured data through parameter estimation. Validation is done by comparing the temporal pressure outputs of the models with the actual measured pressure signals. The mean absolute error for the best fit ISO model is less than half of the Classic model at 0.4 MPa (MAE < 2 kPa) and the temporal pressure relationships in the closed-loop and open-loop tests shows a 93% correlation against measured pressure signals. The combination of the derived actuator chamber model and the valve mass flow model produces a realistic actuator model. The force equation of each of the actuators makes provision for a nonlinear friction component. The actuator friction model is based on a simple stick-slip relation with an acceleration dependent Stribeck function and an exponential viscous friction component. This model is also identified with data from the actual hardware. The complete ship motion simulator model is validated through openloop as well as closed-loop tests. The open-loop tests are performed with chirp or sinusoidal signal excitation from a stable elevated offset starting condition. The ratio of the measured and simulated extension amplitudes in the open-loop is larger than 0:95 while the ratio of the rise times (tm=ts) is approximately 0.85. The closed-loop validation tests are conducted with both heave and roll inputs and compared well with the real system. A 14% difference in the actuator position amplitude (between the simulated and measured systems), and a 20% slower extension rate at 0.05 Hz that increases at 1 Hz to match the measured rate are observed. The maximum large signal bandwidth is 0:617 Hz, and is only limited by the mass flow. A simplified plant model is derived and compared with the high performance model and is subsequently used for a state feedback controller design and evaluation. The final controller gains deliver a stable system with the same 0:617Hz bandwidth limitation and a controller that is insensitive to loop gain changes from 0.5 to 15.

Optiese loonvragte vir maritieme vaartuie, waarvan die siglyn gestabiliseer word, benodig veranderlike platform toestande tydens ontwikkeling, toets en evaluasie. Een manier om veranderlike dektoestande in ?n laboratorium te emuleer, is deur ?n skeepsdeksimulator te gebruik. Hierdie verhandeling beskryf aspekte van die modelering, stelsel identifikasie en validasie van ?n drie grade van vryheid skeepsdeksimulator wat gebruik word om ?n realistiese simulasieomgewing te skep. Die simulator is in die vorm van ?n gemodifiseerde pneumatiese Gough-Stewart manipulator. ?n Gesamentlike MSC ADAMS?/Matlab? Simulink? simulasie, wat deur Matlab? bedryf word, vorm ?n simulasieomgewing waarin ADAMS? die dinamiese model van die fisiese hardeware huisves, en Simulink? die pneumatiese model, die wrywingsmodel en die beheerder hanteer. Daar kan geen soortgelyke simulator gevind word in gepubliseerde literatuur nie, wat tot gevolg het dat ?n model van eerste beginsels opgestel is deur die gepubliseerde inligting as fondasie te gebruik. Die simulasiemodel is opgebreek op substelselvlak wat die massavloei model van die klep, die silinderkamermodel, sowel as die kragmodel van die suier, die volledige aktuatormodel en ook, laastens, die volledige skeepsdeksimulatormodel insluit. Al hierdie modelle is afgelei, die parameters ge?dentifiseer and gevalideer. Die behoeftestellings van die simulator, sowel as die simulasieomgewing, is afgelei uit werklike metings van soortgelyke seevarende vaartuie. Opsoektabelle, wat bereken is deur met Matlab? die simulatorplatform binne MSC ADAMS? deur sy volledige bewegingsberyk te manipuleer, stel die inverse kinematika voor. Infinietdesimale klein foute is verkry deur die proses in tru aan te wend en die platform ori?ntasie tydens verskeie aktuatortposisies te toets. Daar is twee klep massavloeimodelle beskryf, ?n klassieke model wat van basiese termodinamiese geginsels afgelei is, en ?n ISO model wat gebaseer is op die ISO-6358 standaard. Beide hierdie modelle se parameters is deur eksperimentele stelselidentifikasieprosedures bepaal tydens opblaas- en afblaastoetse. Hiervoor is ?n konstante volume druktenk gebruik en beide die tydafhanklike interne druk en lugtemperature is gemeet. Die massavloei is bepaal deur parameterestimasietegnieke toe te pas op die voorgestelde modelle, en validering deur die tydafhanklike druk te vergelyk met die uitsette van die modelle. By ?n werksdruk van 0.4 MPa is die gemiddelde absolute fout van die ISO model minder as die helfte van die fout van die klassieke model (MAE < 2 kPa), en die tydafhanklike drukverwantskap in beide die geslotelus-, sowel as die ooplustoetse toon ?n 93% korrelasie teen die gemete drukwaardes. Die kombinasie van die afgeleide silindermodel en die klep massavloeimodel lewer ?n geloofwaardige wrywingslose aktuatormodel, en deur die dinamiese kragvergelyking te gebruik, word dit aangevul deur ?n nie-linie?re wrywingskomponent. ?n Steek-glip wrywingsmodel met ?n versnellingsafhanklike Stribeckfunksie en ?n eksponeti?le viskeuse wrywingskomponent stel die aktuatorwrywing voor. Die wrywingsmodel is ook ge?dentifiseer deur werklike gemete data. Die valideringsoefening van die volledige skeepsdeksimulator is voltooi deur beide ooplustoetse, sowel as gelotelustoetse uit te voer. Die ooplustoetse is vanaf halfuitgestrekte aktuatorposisies gedoen deur sinuso?dale en tjirp opwekkingsseine te gebruik. Die amplitudeverhouding tussen die gemete posisies en die gesimuleerde posisies is groter as 95%, terwyl die stygtydverhouding (tm=ts) ongeveer 0.85 is. Vir geslotelusvaliderinstoetse is beide deining and rol stelpunte as insette gebruik en die simulasie resultate is met die werklike gemete waardes vergeleik. Die gemete amplitude van die aktuatorposisie is ongeveer 14% kleiner as die gesimuleerde amplitude, die gemete aktuatorspoed is ongeveer 20% stadiger by 0.06 Hz en terwyl dit ongeveer dieselfde is by 1 Hz. Die maksimum grootseinbandwydte is 0.617 Hz en word beperk deur die massvloeivermo? van die klep. ?n Vereenvoudigde stelselmodel is afgelei, ?n toestandsterugvoerbeheerder is ontwerp en die beheerder ge-evalueer met beide die ho? akkuraatheid model, sowel as die vereenvoudigde model. Die finale beheerder lewer ?n stabiele stelsel met dieselfde 0.617Hz bandwydte wat onsensitief is vir luswinsveranderinge vanaf 0.5 tot 15.