Hardware in the Loop Simulation of Production Systems Dynamics

Hardware in the Loop Simulation of Production Systems Dynamics Sascha Röck 1 1 Institute for Control Engineering of Machine Tools and Manufacturing Units (ISW), University of Stuttgart Abstract Constantly growing competitive pressure forces machine and plant manufacturers to find new innovative ways to reduce the development costs as well as to increase the quality. In order to achieve these goals, simulation tools are used in many phases of the development process. An integrated simulation of the system production plant requires not only the dynamic behavior of the production system but also the consideration of the applied control technology. For this purpose, especially the coupled simulation between real control system and virtual machine became widely accepted in recent years. This paper will give an overview of the current state of the art of hardware-in-the-loop simulation (HiLS) of production systems dynamics at the ISW. Keywords Control, Simulation, Machine Tool 1. Introduction Hardware-in-the-loop simulation in the context of production engineering means that the real control system is connected with a virtual machine or plant via the real field or drive bus (hardware). Thus, the simulation system calculates the machine behavior and provides the machine data (actual values) relevant for the control and, in addition, protocols internal state variables for diagnosis which can then be displayed to the engineer (Fig. 1). This allows a highly realistic test of the control programs on the real hardware with all runtime effects without having to use the real machine or plant. The additional benefit lies in the possibility to generate the control programs at an early stage in the development process and, at the same time, be able to test them very close to reality. The hardware-in-the-loop simulation is suitable for the virtual set-up of control software and hardware, testing control functions and the human machine interface, training the machine operators to eliminate irregularities efficiently, 1

the optimization of control programs and machine cycle times. Figure 1: Hardware in the loop simulation of a machine control At the Institute for Control Engineering of Machine Tools and Manufacturing Units (ISW) hardware-in-the-loop simulation has been a research topic for many years. In particular, the focus is put on real-time simulation of the dynamics of production systems. In this context, scientists of the ISW developed the real-timecapable simulation environment VIRTUOS in close cooperation with the industry partner Industrielle Steuerungssoftware GmbH, Stuttgart (ISG). This software is successfully applied today in the industry. The design of VIRTUOS is shown in Figure 2. Essentially VIRTUOS consists of three components: The real-time solver VIRTUOS.S, the graphical user interface VIRTUOS.M for modeling and monitoring and the graphical user interface VIRTUOS.V for online 3D visualization of the machine motions. The real-time solver VIRTUOS.S computes all state variables and communicates with the control systems via bus interfaces to a number of popular bus systems. It is operated on a real-time operating system absolutely synchronously to the control cycle. Modeling is done in VIRTUOS.M with block diagrams. A MATLAB/SIMULINK import interface allows the inclusion of SIMULINK models. 2

Figure 2: Design of the hardware in the loop simulator VIRTUOS The hard real-time monitoring (synchronous to the control cycle without loss of data) of all computed state variables is done by VIRTUOS.M while the machine motions are displayed in VIRTUOS.V during the simulation in soft real-time (as fast as possible). This allows for a realistic observation of the virtual production system. In the following chapters various dynamic models are presented that have been designed at the ISW for a hardware-in-the-loop simulation and implemented in VIRTUOS. 2. Mass dynamics Mainly in case of highly dynamic motion sequences as, for example, pick and place operations or high-speed cutting, inertia forces affect the control system. High inertia forces limit the process speed, which often can only be taken into consideration during the set-up of the control programs on the real machine. In this context, virtual set-up allows for an early optimization of the machine dynamics respectively the dynamics of the machine-control interaction. Since the used path planning algorithms in modern machine control systems (NC, RC) for 3

high-speed applications are - for reasons of competition - insufficiently published, the use of a hardware-in-the-loop simulation is often the only way to test the entire control system without the need of the real machine or plant. Additionally, the hardware-in-the-loop simulation allows for the transient analysis over the entire control program. All time-dependent system variables like accelerations, speeds, forces and moments etc. can be analyzed over the entire control program and all data can be used for further optimizations. By displaying the variables, e.g. versus the path of the tool center point (TCP), critical process points and its location in the control program can easily be found. The example in Figure 3 shows the hardware-in-the-loop simulation of the mass dynamics of a machine tool with parallel kinematics in VIRTUOS. The model was validated by means of the motor currents. The representation of the feed rate over the work piece surface was used for analyzing the control system. Figure 3: Hardware-in-the -loop simulation of a machine tool with parallel kinematics in VIRTUOS 4

A more detailed description of the simulation of mass dynamics in real-time can be found in [1]. 3. Contact dynamics A significant part of the control software for handling systems has to be developed and tested on the real machine during their set-up. The reason for this is that the exact process sequences and, in particular, their interaction with the control system are mostly unknown before the plant is assembled. Especially in case of large plants with many interlinked machining stations, the set-up of the mostly very heterogeneous control technology is very time-consuming and expensive. In cooperation with industrial partners, a real-time-capable library for handling operations was designed and integrated into the real-time simulation platform VIRTUOS. Some exemplary simulation scenarios are illustrated in Figure 4. Bottle transfer unit Part selection Roller conveyor Gripper operations Figure 4: Real-time-capable simulation of handling systems with VIRTUOS The examples shown in fig. 4 require the modeling of contact dynamics. In order to be able to simulate contact-driven movements, collision detection and contact 5

force computation between the moving bodies and their environment has to be processed. A real-time-capable collision detection could be achieved with the Closest Feature method of Lin and Canny [2]. This method allows for the efficient computation of minimal distances between two geometric primitives (point, edge, surface) by their localization in a space divided into Voronoi regions. The resulting geometric primitives that are closest to each other are called Closest Features. The existence of Closest Features is only clearly indicated with convex geometries, because two convex geometries can only collide in one point at a time. In case of non-convex geometries, these have to be decomposed into convex geometries, which could result in several Closest Features and thus in several simultaneous collisions between two geometries. The real-time computation of contact forces of multiple contacts on one collision object is processed by inserting a discrete spring-damper element at each contact point. Thereby, static and dynamic friction can also be taken into consideration in the contact points. The used methods have been verified by means of the bottle transfer unit illustrated in fig. 4 (top left). The contour of the star wheel has more than 200 polygon points. Here, the number of simultaneous collisions between the bottles and the star wheel varies from 6 to 11 while the bottles pass through the transfer unit (Fig. 5). Figure 5: Real-time capable computation of a bottle transfer unit in VIRTUOS Essential phenomena like the bouncing of the bottles and the jamming due to the high bottle back pressure at the star wheel entrance could be simulated accurately 6

enough for the use in a virtual set-up application. The real-time capability could also be verified, as can be seen in Figure 5. The diagram represents the percentaged response time of the model triggered by the real-time tick of the realtime OS. In this example, the CPU load of the real-time process was almost constantly 28 %. 4. Structural and process dynamics The simulative prediction of the machine behavior in consideration of the cutting process has been a research topic of different research groups for decades. The use of simulation technology for analyzing the interaction of the machine and the cutting process is a big challenge. The reason is that a large variety of phenomena exist and they have to be modeled very much in detail for the specific problems. An overview is given by Altintas and Brecher in [3]. Especially the process simulation imposes very high demands on the simulation tools. For predicting the process forces and the process stability, a high degree of expertise about the process and its numerical simulation is necessary. Brecher presents an overview of this in [4]. A good description of predicting the stability of cutting processes can be found in [5, 6]. The application of simulation models in interaction with the real control technology in a hardware-in-the-loop simulation requires a time-deterministic and highly efficient computation of the models. Contributions to the real-time simulation of the dynamics of machine tools have been presented in [1] and [7]. A numerical analysis for describing the process stability for a time domain simulation of the process-machine interaction in milling has been discussed in detail in [8]. The virtual set-up of cutting machine tools is one of the biggest challenges in the field of dynamic simulation of production systems. Beyond doubt it would make sense to check the machining process virtually, especially if small lot sizes and high work piece costs make the set-up process extremely time-consuming and expensive. The challenging factor is basically the complexity of the required model, since the machine dynamics as well as the process dynamics and their interactions have to 7

be considered. Only then reliable statements in regard to process stability, process results and the work piece quality can be made. Figure 6 shows the occurring interactions of the machine control up to the material removal during cutting. Figure 6: Interactions of control and material removal In the case of a high-speed cutting machine process dynamics play an important role during the set-up, because process instabilities like regenerative chatter lead to worse process results and can damage the work piece as well as the tool. To avoid this, extensive measurements and system analyses on the real machine are necessary. The use of a reliable simulation for predicting the process stability in connection with the real control system would reduce the measurement efforts during the set-up and the risk of instabilities. But this requires valid and accurate models of the process-machine interaction in a hardware-in-the-loop simulation. In the following chapters the modeling and its numerical problems for a hardwarein-the-loop simulation of the process-machine interaction will be presented in consideration of the process stability during cutting. 4.1 Structural dynamics The structural dynamics of machine components can be described by means of linear finite element models. For the application in a hardware-in-the-loop simulation the generally high number of degrees of freedom of such systems must 8

be reduced. For this purpose, efficient reduction methods are available today [9]. Furthermore, linear systems can be decoupled in their modes, which allows for an efficient and robust computation of the model. Figure 7 illustrates the inclusion of a finite element model in a hardware-in-the-loop simulation. Figure 7: Import interface for FE structures in a hardware-in-the-loop simulation The model matrices (e.g. mass matrix, damping matrix and stiffness matrix) are imported from the commercial FEM tool ANSYS into MATLAB and supplemented in SIMULINK by control structures. In an interface developed by ISW between MATLAB/SIMULINK and the hardware-in-the-loop simulator VIRTUOS, a state space model of the controller-coupled structure is generated. Thereby the system matrix is decomposed in its modes by a modal transformation and becomes block-diagonal form, which can be solved very efficiently in VIRTUOS by means of implicit solution methods. A more detailed description of the interface can be found in [7]. 4.2 Process-Machine Interaction (PMI) As mentioned above, the simulation of the process-machine interaction is very important for the prediction of the entire machine behavior during a simulation- 9

based set-up. This requires a time domain simulation that takes into account the process instability due to the regenerative chatter. The process stability can be illustrated in stability diagrams, where the critical depth of cut is shown via the spindle speed. The critical depth of cut represents here the stability limit of the real process (Figure 8). Figure 8: Stability diagrams and the critical depth of cut In order to be able to solve the equations of motion on a digital computer system in the time domain, a time domain discretization is required. The discretization is basically only an approximation of the exact solution and leads to numerical errors. The numerical errors affect the solution of the equations and respectively the process stability, as shown in Figure 8. The critical depth of cut which results from the numerical solution cannot match the real stability limit of the process, because of the numerical error resulting from the time domain discretization. The stability limit which results from the numerical solution does not match the real stability limit. Thus regenerative chatter already occurs for smaller respectively major cutting depths in the simulation and the simulation model is either less or more stable as the real cutting process. Figure 9 shows an example of the result of two basic discretizations via numerical integration by means of the Adams-Moulton method of 1 st and 2 nd order [10]. It also should be noted that the Adams-Moulton method of 1 st order complies with the implicit Euler method, and the Adams-Moulton method of 2 nd order complies with the implicit trapezoidal rule. The method to calculate the diagrams in figure 9 is presented in [8]. 10

5 4.5 4 3.5 Adams-Moulton 1 Adams-Moulton 2 5 4.5 4 3.5 Analytic h=0.002 h=0.001 h=0.0005 h=0.0002 3 3 2.5 2.5 2 2 1.5 1 0.5 Analytic h=0.002 h=0.001 h=0.0005 h=0.0002 0 100 200 300 400 500 600 700 Spindle Speed [rev/min] Figure 9: Results of critical depths of cut after discretization in the time domain with Adams- 1.5 0.5 Moulton integration 1 0 100 200 300 400 500 600 700 Spindle Speed [rev/min] The Adams-Moulton method of 1 st order (AM1) produces a stabilizing effect and, therefore, provides solutions of a stable process even though instability would actually occur. The Adams-Moulton method of 2 nd order (AM2), however, works destabilizing and indicates the instability too early. By minimizing the discretization step size h (time step size) the numerical error decreases in both methods, as expected. But a reduction of the time step size induces more calculation steps per time interval and respectively more computational effort, which should be avoided in a real-time simulation. At a usual NC control cycle of about 1-5 milliseconds a time step size should not be significantly smaller and in the ideal case it should be conform to it. The example shows that both methods are insufficient with step sizes in this range. However, these methods can be used for simulating the process stability. By a linear combination of both methods with AAM= AM1+ 1 AM2 we receive an adaptive integration method (AAM) with the adaption variable. If is varied between 0 and 1, the methods are weighted differently and the stabilizing or destabilizing effect can be manipulated according to the weighting. The stability limits are shown in the left diagram in Figure 10 with different adaption variables. Figure 10 on the right shows the numerical stability limit of the adaptive Adams-Moulton method at a time step size of 1 millisecond and the 11

characteristics of the adaption variable. It can be seen that stabilization and destabilization effects do not occur anymore. Critical depth of cut [mm] 5 4.5 4 3.5 3 2.5 2 1.5 Analytic α = 0.0 α = 0.2 α = 0.4 α = 0.6 α = 0.8 α = 1.0 Adaptive Adams-Moulton Scheme with h=0.001 sec. 5 4.5 4 3.5 3 2.5 2 1.5 Analytic AAM h=0.001 Adapt.Variable α 1 0.5 1 0.5 α 0 0 100 200 300 400 500 600 700 100 200 300 400 500 600 700 Spindle Speed [rev/min] Spindle Speed [rev/min] Figure 10: Results of critical depths of cut with adaptive Adams-Moulton integration The computation of the adaption variables for the respective spindle speeds can be done in the initialization phase and does not need any additional computation time during the simulation. Since the spindle speeds are usually known in advance, this is also possible without restrictions. However, the identification of the real stability limit is necessary. It can be identified in advance with already known methods [5][6]. This approach allows the consideration of the stability limits of the cutting process in a real-time simulation, respectively hardware-in-the-loop simulation. Thus a large scale simulation in time domain is possible in consideration of the complete NC program and the process forces at any point of the work piece. The process instability based on the regenerative chatter is taken into account. Figure 11 illustrates the simulation of the process forces in a basic plane cutting process. For this purpose, various cutting depths were selected at a spindle speed of 400 revolutions per minute. The time plots of the process forces show the predicted stability limits and the occurrence of process instability respectively regenerative chatter. 12

Figure 11: Simulated process forces Figure 11 shows the results of the time domain simulations of the process forces with the methods described above. Only the adaptive method (AAM) supplies accurate results at a time step size of 1 millisecond. The research of the ISW focuses presently on the changes of the work piece by material removal and the related modifications of the cut geometry. Beyond that, questions about the numerical effects in cutting processes with high spindle speeds and the modeling of friction and thermal effects in cutting processes for the hardware-in-the-loop simulation are still unanswered. At the moment, public research grants are being applied for in regard to this topic. 13

5. Summary The examples in this paper demonstrate the presently possible applications of hardware-in-the-loop simulation of the dynamics of production systems at the ISW. It could be shown that the mass dynamics in high-speed applications as well as the contact dynamics in handling operations and the structural dynamics in cutting processes can be simulated in a hardware-in-the-loop simulation. But also the limits have been presented. Because of the high requirements of a real-time simulation in regard to computing power and time determinism, model simplifications are necessary and many common computation methods that are normally used for the simulation of dynamics cannot be applied. Nevertheless, the so far achieved solutions indicate that hardware-in-the-loop simulation has potential to be used more frequently in the industry in the years to come. The ISW will also contribute in the future to this specific research. 6. Acknowledgement I would like to thank the German Research Foundation (DFG) for financial support of the project within the Cluster of Excellence in Simulation Technology (EXC 310/1) at the University of Stuttgart. I also appreciate very much that Prof. Alexander Verl, director of the Institute for Control Engineering of Machine Tools and Manufacturing Systems (ISW), strongly supported my work. My special thanks go to Prof. Günter Pritschow who always supported my scientific work and finally, I want to thank the members of staff of the company Industrielle Steuerungstechnik GmbH (ISG) for the excellent cooperation with the ISW. 14

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