Abstract
The paper deals with development of a methodology for mechatronic system design using state-of-the-art model-based system engineering methods. A simple flexible robotic arm is considered as a benchmark problem for the evaluation of various techniques used in the phases of modelling, analysis, control system design, validation, and implementation. The flexible nature of the mechanical structure introduces inherently oscillatory dynamics in the target bandwidth range, which complicates all the above-mentioned design steps. This paper demonstrates the process of deriving a complex nonlinear model of the flexible arm setup. An initial idea about the plant dynamics is acquired from analytical modelling using the Euler–Bernoulli beam theory. A more thorough understanding is subsequently acquired from finite element analysis. Linearisation and order reduction are the next steps necessary for the derivation of a simplified control-relevant model. A time-dependent variable parameter of load mass position is considered and a robust controller is subsequently designed in order to fulfil certain performance criteria for all the admissible plant configurations. This is performed using a recent H-infinity loop shaping method for fixed structure controller design. The results are validated by means of a physical plant, comparing the experimental data with the model predictions.
Highlights
Published: 19 April 2021Mathematical modelling has become the cornerstone of many technical disciplines.Models generally allow us to gain insight, answers, and guidance when analysing and predicting the behaviour of complex systems
For the case study presented in this paper, we focused on the load configuration producing a dynamics with three dominant bending modes
The first part deals with the development of physics-based models using analytical and finite element method (FEM) approaches
Summary
Published: 19 April 2021Mathematical modelling has become the cornerstone of many technical disciplines.Models generally allow us to gain insight, answers, and guidance when analysing and predicting the behaviour of complex systems. Model-based engineering methods provide essential tools in the field of mechatronics. Derivation of relevant models enables the optimisation of machine design before physical prototype assembly. This may help to avoid costly build-and-test cycles, speeding up the whole development process considerably. A high-fidelity model is a necessary prerequisite for employing modern control engineering methods and algorithms. An excessively complex model, albeit well suited for numerical simulations and predictions, may turn out to be useless for the process of control algorithms design. A general rule of thumb is to use a control-relevant model that is as simple as possible while capturing the significant features of the physical plant’s dynamics essential for achieving formulated design requirements
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