## 2 Materials and Methods  
### Flexible Arm Benchmark Problem  
A flexible arm motion setup from Figure 1 is used to demonstrate the applicability of the presented methods in various stages of mechatronic system design. The motion system consists of an electrical drive (590 W permanent magnets synchronous motor driven by a servo amplifier), flexible coupling, bearing housing, inertia flywheel, and removable flexible arm with adjustable load mass. One degree of freedom allows the arm to rotate freely around the vertical axis. Details of the drive and arm assembly are shown in Figure 2.  
Albeit simple, its mechanical structure allows emulating various practical motion control problems encountered in industrial applications. Some essential features are given below:  
* Distributed parameter system exhibiting oscillatory dynamics with a possible introduction of multiple resonance modes, nonlinear friction effects and parametric uncertainty (e.g., load mass and/or position)
* A diverse range of dynamic response achievable by adjusting/interchanging the attached load  
Figure 1: Flexible arm motion stage used in the experiments: (**left**) Considered flexible load configuration; (**right**) Schematics of the motion control setup, C-velocity/position compensator to be designed using the motor-side feedback, \(\varphi_{m}\),\(\varphi_{l}\)-motor and load angle. Figure 2: Flexible arm motion stage details: drive to arm transmission assembly consisting of electrical drive, flexible coupling, bearing housing, inertial load, and adjustable compliant arm. Both actuator and load-side feedback possible through the optical encoder at the motor shaft and MEMS accelerometers attached to the load
* Industrial grade drive system with servo amplifier implementing field-oriented control loop
* EtherCAT communication with 5 kHz update rate to the B&R Automation PC master controller
* Hard real-time Linux-based software environment with REXYGEN control system [10]  
A wide range of dynamic behaviour can be achieved in order to emphasise specific desired characteristics of a represented motion system. Typical scenarios include, for example, a rigid body system, flexible load with one or several dominant bending modes, friction-dominant system, unbalanced rotor system etc. The setup proved to be a valuable benchmark problem for the evaluation of various methods from the field of mechatronics, including modelling, identification, and feedback control design [11; 12; 13; 14]. Table 1 summarises the important specifications of the employed actuator, sensors, and control instrumentation. Table 2 provides mechanical parameters of the flexible arm motion system under study. The purpose of the installed sensory system is twofold. The high-fidelity motor side optical sensor is used for precise control of the actuator serving for its electronic commutation using field-oriented control algorithm as well as for supervisory velocity and position loops. Removable accelerometers can be installed at different positions of the flexible arm in order to evaluate the load-side dynamic responses. They were used to validate both open- and closed-loop predictions provided by developed mathematical models in our actual application. This additional load-side feedback may also serve for employing advanced control schemes allowing to improve overall performance of the motion system, see, e.g., [14]. However, this topic is out of scope of this study, which focuses on the modelling, identification, and control aspects using conventional control topologies available in current industrial-grade automation equipment. For the case study presented in this paper, we focused on the load configuration producing a dynamics with three dominant bending modes. This situation is often encountered in robotic applications, where the oscillatory dynamics results from the mechanical compliance of either gearing, the robot arm itself, or due to combination of flexibility of both components [15; 16].