Sensor Fusion of Proprioception, Force and Vision in Estimation and Robot

Sensor-based robot control allows manipulation in dynamic environments with uncertainties. Vision is a versatile low-cost sensory modality, but low sample rate, high sensor delay and uncertain measurements limit its usability, especially in strongly dynamic environments. Force is a complementary sensory modality allowing accurate measurements of local object shape when a tooltip is in contact with the object. In multimodal sensor fusion, several sensors measuring different modalities are combined to give a more accurate estimate of the environment. As force and vision are fundamentally different sensory modalities not sharing a common representation, combining the information from these sensors is not straightforward. In this thesis, methods for fusing proprioception, force and vision together are proposed. Making assumptions of object shape and modeling the uncertainties of the sensors, the measurements can be fused together in an extended Kalman filter. The fusion of force and visual measurements makes it possible to estimate the pose of a moving target with an end-effector mounted moving camera at high rate and accuracy. The proposed approach takes the latency of the vision system into account explicitly, to provide high sample rate estimates. The estimates also allow a smooth transition from vision-based motion control to force control. The velocity of the end-effector can be controlled by estimating the distance to the target by vision and determining the velocity profile giving rapid approach and minimal force overshoot. Experiments with a 5-degree-of-freedom parallel hydraulic manipulator and a 6-degree-of-freedom serial manipulator show that integration of several sensor modalities can increase the accuracy of the measurements significantly.

Novel Methods for Error Modeling and Parameter Identification of a Redundant Serial-Parallel Hybrid Robot

To obtain the desirable accuracy of a robot, there are two techniques available. The first option would be to make the robot match the nominal mathematic model. In other words, the manufacturing and assembling tolerances of every part would be extremely tight so that all of the various parameters would match the “design” or “nominal” values as closely as possible. This method can satisfy most of the accuracy requirements， but the cost would increase dramatically as the accuracy requirement increases. Alternatively, a more cost-effective solution is to build a manipulator with relaxed manufacturing and assembling tolerances. By modifying the mathematical model in the controller, the actual errors of the robot can be compensated. This is the essence of robot calibration. Simply put, robot calibration is the process of defining an appropriate error model and then identifying the various parameter errors that make the error model match the robot as closely as possible. This work focuses on kinematic calibration of a 10 degree-of-freedom (DOF) redundant serial-parallel hybrid robot. The robot consists of a 4-DOF serial mechanism and a 6-DOF hexapod parallel manipulator. The redundant 4-DOF serial structure is used to enlarge workspace and the 6-DOF hexapod manipulator is used to provide high load capabilities and stiffness for the whole structure. The main objective of the study is to develop a suitable calibration method to improve the accuracy of the redundant serial-parallel hybrid robot. To this end, a Denavit–Hartenberg (DH) hybrid error model and a Product-of-Exponential (POE) error model are developed for error modeling of the proposed robot. Furthermore, two kinds of global optimization methods, i.e. the differential-evolution (DE) algorithm and the Markov Chain Monte Carlo (MCMC) algorithm, are employed to identify the parameter errors of the derived error model. A measurement method based on a 3-2-1 wire-based pose estimation system is proposed and implemented in a Solidworks environment to simulate the real experimental validations. Numerical simulations and Solidworks prototype-model validations are carried out on the hybrid robot to verify the effectiveness, accuracy and robustness of the calibration algorithms.

Stiffness based trajectory planning and feedforward based vibration suppression control of parallel robot machines

The dissertation proposes two control strategies, which include the trajectory planning and vibration suppression, for a kinematic redundant serial-parallel robot machine, with the aim of attaining the satisfactory machining performance. For a given prescribed trajectory of the robot's end-effector in the Cartesian space, a set of trajectories in the robot's joint space are generated based on the best stiffness performance of the robot along the prescribed trajectory. To construct the required system-wide analytical stiffness model for the serial-parallel robot machine, a variant of the virtual joint method (VJM) is proposed in the dissertation. The modified method is an evolution of Gosselin's lumped model that can account for the deformations of a flexible link in more directions. The effectiveness of this VJM variant is validated by comparing the computed stiffness results of a flexible link with the those of a matrix structural analysis (MSA) method. The comparison shows that the numerical results from both methods on an individual flexible beam are almost identical, which, in some sense, provides mutual validation. The most prominent advantage of the presented VJM variant compared with the MSA method is that it can be applied in a flexible structure system with complicated kinematics formed in terms of flexible serial links and joints. Moreover, by combining the VJM variant and the virtual work principle, a systemwide analytical stiffness model can be easily obtained for mechanisms with both serial kinematics and parallel kinematics. In the dissertation, a system-wide stiffness model of a kinematic redundant serial-parallel robot machine is constructed based on integration of the VJM variant and the virtual work principle. Numerical results of its stiffness performance are reported. For a kinematic redundant robot, to generate a set of feasible joints' trajectories for a prescribed trajectory of its end-effector, its system-wide stiffness performance is taken as the constraint in the joints trajectory planning in the dissertation. For a prescribed location of the end-effector, the robot permits an infinite number of inverse solutions, which consequently yields infinite kinds of stiffness performance. Therefore, a differential evolution (DE) algorithm in which the positions of redundant joints in the kinematics are taken as input variables was employed to search for the best stiffness performance of the robot. Numerical results of the generated joint trajectories are given for a kinematic redundant serial-parallel robot machine, IWR (Intersector Welding/Cutting Robot), when a particular trajectory of its end-effector has been prescribed. The numerical results show that the joint trajectories generated based on the stiffness optimization are feasible for realization in the control system since they are acceptably smooth. The results imply that the stiffness performance of the robot machine deviates smoothly with respect to the kinematic configuration in the adjacent domain of its best stiffness performance. To suppress the vibration of the robot machine due to varying cutting force during the machining process, this dissertation proposed a feedforward control strategy, which is constructed based on the derived inverse dynamics model of target system. The effectiveness of applying such a feedforward control in the vibration suppression has been validated in a parallel manipulator in the software environment. The experimental study of such a feedforward control has also been included in the dissertation. The difficulties of modelling the actual system due to the unknown components in its dynamics is noticed. As a solution, a back propagation (BP) neural network is proposed for identification of the unknown components of the dynamics model of the target system. To train such a BP neural network, a modified Levenberg-Marquardt algorithm that can utilize an experimental input-output data set of the entire dynamic system is introduced in the dissertation. Validation of the BP neural network and the modified Levenberg- Marquardt algorithm is done, respectively, by a sinusoidal output approximation, a second order system parameters estimation, and a friction model estimation of a parallel manipulator, which represent three different application aspects of this method.

Novel Robot Solutions for Carrying out Field Joint Welding and Machining in the Assembly of the Vacuum Vessel of ITER

It is necessary to use highly specialized robots in ITER (International Thermonuclear Experimental Reactor) both in the manufacturing and maintenance of the reactor due to a demanding environment. The sectors of the ITER vacuum vessel (VV) require more stringent tolerances than normally expected for the size of the structure involved. VV consists of nine sectors that are to be welded together. The vacuum vessel has a toroidal chamber structure. The task of the designed robot is to carry the welding apparatus along a path with a stringent tolerance during the assembly operation. In addition to the initial vacuum vessel assembly, after a limited running period, sectors need to be replaced for repair. Mechanisms with closed-loop kinematic chains are used in the design of robots in this work. One version is a purely parallel manipulator and another is a hybrid manipulator where the parallel and serial structures are combined. Traditional industrial robots that generally have the links actuated in series are inherently not very rigid and have poor dynamic performance in high speed and high dynamic loading conditions. Compared with open chain manipulators, parallel manipulators have high stiffness, high accuracy and a high force/torque capacity in a reduced workspace. Parallel manipulators have a mechanical architecture where all of the links are connected to the base and to the end-effector of the robot. The purpose of this thesis is to develop special parallel robots for the assembly, machining and repairing of the VV of the ITER. The process of the assembly and machining of the vacuum vessel needs a special robot. By studying the structure of the vacuum vessel, two novel parallel robots were designed and built; they have six and ten degrees of freedom driven by hydraulic cylinders and electrical servo motors. Kinematic models for the proposed robots were defined and two prototypes built. Experiments for machine cutting and laser welding with the 6-DOF robot were carried out. It was demonstrated that the parallel robots are capable of holding all necessary machining tools and welding end-effectors in all positions accurately and stably inside the vacuum vessel sector. The kinematic models appeared to be complex especially in the case of the 10-DOF robot because of its redundant structure. Multibody dynamics simulations were carried out, ensuring sufficient stiffness during the robot motion. The entire design and testing processes of the robots appeared to be complex tasks due to the high specialization of the manufacturing technology needed in the ITER reactor, while the results demonstrate the applicability of the proposed solutions quite well. The results offer not only devices but also a methodology for the assembly and repair of ITER by means of parallel robots.

Micro Data Repositories: Increasing the Value of Research on the Web

Presentation at Open Repositories 2014, Helsinki, Finland, June 9-13, 2014

Data-parallel computation in parallel and distributed environments

The past few decades have seen a considerable increase in the number of parallel and distributed systems. With the development of more complex applications, the need for more powerful systems has emerged and various parallel and distributed environments have been designed and implemented. Each of the environments, including hardware and software, has unique strengths and weaknesses. There is no single parallel environment that can be identified as the best environment for all applications with respect to hardware and software properties. The main goal of this thesis is to provide a novel way of performing data-parallel computation in parallel and distributed environments by utilizing the best characteristics of difference aspects of parallel computing. For the purpose of this thesis, three aspects of parallel computing were identified and studied. First, three parallel environments (shared memory, distributed memory, and a network of workstations) are evaluated to quantify theirsuitability for different parallel applications. Due to the parallel and distributed nature of the environments, networks connecting the processors in these environments were investigated with respect to their performance characteristics. Second, scheduling algorithms are studied in order to make them more efficient and effective. A concept of application-specific information scheduling is introduced. The application- specific information is data about the workload extractedfrom an application, which is provided to a scheduling algorithm. Three scheduling algorithms are enhanced to utilize the application-specific information to further refine their scheduling properties. A more accurate description of the workload is especially important in cases where the workunits are heterogeneous and the parallel environment is heterogeneous and/or non-dedicated. The results obtained show that the additional information regarding the workload has a positive impact on the performance of applications. Third, a programming paradigm for networks of symmetric multiprocessor (SMP) workstations is introduced. The MPIT programming paradigm incorporates the Message Passing Interface (MPI) with threads to provide a methodology to write parallel applications that efficiently utilize the available resources and minimize the overhead. The MPIT allows for communication and computation to overlap by deploying a dedicated thread for communication. Furthermore, the programming paradigm implements an application-specific scheduling algorithm. The scheduling algorithm is executed by the communication thread. Thus, the scheduling does not affect the execution of the parallel application. Performance results achieved from the MPIT show that considerable improvements over conventional MPI applications are achieved.

Introducing massively parallel computers into operational weather forecasting

Numerical weather prediction and climate simulation have been among the computationally most demanding applications of high performance computing eversince they were started in the 1950's. Since the 1980's, the most powerful computers have featured an ever larger number of processors. By the early 2000's, this number is often several thousand. An operational weather model must use all these processors in a highly coordinated fashion. The critical resource in running such models is not computation, but the amount of necessary communication between the processors. The communication capacity of parallel computers often fallsfar short of their computational power. The articles in this thesis cover fourteen years of research into how to harness thousands of processors on a single weather forecast or climate simulation, so that the application can benefit as much as possible from the power of parallel high performance computers. The resultsattained in these articles have already been widely applied, so that currently most of the organizations that carry out global weather forecasting or climate simulation anywhere in the world use methods introduced in them. Some further studies extend parallelization opportunities into other parts of the weather forecasting environment, in particular to data assimilation of satellite observations.

Studies on integrating kinematic design method with mechanical systems simulation techniques

Theultimate goal of any research in the mechanism/kinematic/design area may be called predictive design, ie the optimisation of mechanism proportions in the design stage without requiring extensive life and wear testing. This is an ambitious goal and can be realised through development and refinement of numerical (computational) technology in order to facilitate the design analysis and optimisation of complex mechanisms, mechanical components and systems. As a part of the systematic design methodology this thesis concentrates on kinematic synthesis (kinematic design and analysis) methods in the mechanism synthesis process. The main task of kinematic design is to find all possible solutions in the form of structural parameters to accomplish the desired requirements of motion. Main formulations of kinematic design can be broadly divided to exact synthesis and approximate synthesis formulations. The exact synthesis formulation is based in solving n linear or nonlinear equations in n variables and the solutions for the problem areget by adopting closed form classical or modern algebraic solution methods or using numerical solution methods based on the polynomial continuation or homotopy. The approximate synthesis formulations is based on minimising the approximation error by direct optimisation The main drawbacks of exact synthesis formulationare: (ia) limitations of number of design specifications and (iia) failure in handling design constraints- especially inequality constraints. The main drawbacks of approximate synthesis formulations are: (ib) it is difficult to choose a proper initial linkage and (iib) it is hard to find more than one solution. Recentformulations in solving the approximate synthesis problem adopts polynomial continuation providing several solutions, but it can not handle inequality const-raints. Based on the practical design needs the mixed exact-approximate position synthesis with two exact and an unlimited number of approximate positions has also been developed. The solutions space is presented as a ground pivot map but thepole between the exact positions cannot be selected as a ground pivot. In this thesis the exact synthesis problem of planar mechanism is solved by generating all possible solutions for the optimisation process ¿ including solutions in positive dimensional solution sets - within inequality constraints of structural parameters. Through the literature research it is first shown that the algebraic and numerical solution methods ¿ used in the research area of computational kinematics ¿ are capable of solving non-parametric algebraic systems of n equations inn variables and cannot handle the singularities associated with positive-dimensional solution sets. In this thesis the problem of positive-dimensional solutionsets is solved adopting the main principles from mathematical research area of algebraic geometry in solving parametric ( in the mathematical sense that all parameter values are considered ¿ including the degenerate cases ¿ for which the system is solvable ) algebraic systems of n equations and at least n+1 variables.Adopting the developed solution method in solving the dyadic equations in direct polynomial form in two- to three-precision-points it has been algebraically proved and numerically demonstrated that the map of the ground pivots is ambiguousand that the singularities associated with positive-dimensional solution sets can be solved. The positive-dimensional solution sets associated with the poles might contain physically meaningful solutions in the form of optimal defectfree mechanisms. Traditionally the mechanism optimisation of hydraulically driven boommechanisms is done at early state of the design process. This will result in optimal component design rather than optimal system level design. Modern mechanismoptimisation at system level demands integration of kinematic design methods with mechanical system simulation techniques. In this thesis a new kinematic design method for hydraulically driven boom mechanism is developed and integrated in mechanical system simulation techniques. The developed kinematic design method is based on the combinations of two-precision-point formulation and on optimisation ( with mathematical programming techniques or adopting optimisation methods based on probability and statistics ) of substructures using calculated criteria from the system level response of multidegree-of-freedom mechanisms. Eg. by adopting the mixed exact-approximate position synthesis in direct optimisation (using mathematical programming techniques) with two exact positions and an unlimitednumber of approximate positions the drawbacks of (ia)-(iib) has been cancelled.The design principles of the developed method are based on the design-tree -approach of the mechanical systems and the design method ¿ in principle ¿ is capable of capturing the interrelationship between kinematic and dynamic synthesis simultaneously when the developed kinematic design method is integrated with the mechanical system simulation techniques.

On sliding mode control ofhydraulic servo systems and a manipulator

The aim of the study is to developa novel robust controller based on sliding mode control technique for the hydraulic servo system with flexible load and for a flexible manipulator with the lift and jib hydraulic actuators. For the purpose of general control design, a dynamic model is derived describing the principle physical behavior for both the hydraulic servo system and the flexible hydraulic manipulator. The mechanism of hydraulic servo systems is described by basic mathematical equations of fluid powersystems and the dynamics of flexible manipulator is modeled by the assumed modemethod. The controller is constructed so as to track desired trajectories in the presence of model imprecision. Experimental and simulation results demonstratethat sliding mode control has benefits which can be used to guarantee stabilityin uncertain systems and improve the system performance and load tolerance.

Liikesimulaattorialustan kehittäminen virtuaaliprototyypin avulla

Työn tarkoituksena oli kehittää kuuden vapausasteen liikesimulaattorialusta virtuaaliprototyypin avulla siten, että alustan dynamiikka mallinnetaan Adams-ohjelmistolla ja ohjaus- ja säätöpiiri Matlab Simulink:llä. Tarkoituksena oli tutkia dynaamisen mallin ja säätöteknisen mallin yhdistämistä ja niiden yhteen toimimista. Tarkoituksena oli myös selvittää tulevaisuudessa rakennettavan Stewart:n alustan mekaniikan mitat ja hydraulikomponenttien koot. Työssä tutkittiin alustan käyttäytymistä halutulla liikealueella, nopeuksia joita saavutetaan ja mekaanisia rajoitteita. Työn tuloksesta on tarkoitus rakentaa fyysinen prototyyppi liittyen KONSI-projektiin, jossa kehitetään satamanosturisimulaattori nosturiohjaajan koulutuksen tueksi. Malli tullaan kytkemään Teppo Lehtisen diplomityönä tehtyyn satamanosturi kontin simulointimalliin ja koko järjestelmän on tarkoitus toimia reaaliaikaisena.

Developing of the Variable Speed Drive -control in simulated parallel pumping systems

This thesis presents briefly the basic operation and use of centrifugal pumps and parallel pumping applications. The characteristics of parallel pumping applications are compared to circuitry, in order to search analogy between these technical fields. The purpose of studying circuitry is to find out if common software tools for solving circuit performance could be used to observe parallel pumping applications. The empirical part of the thesis introduces a simulation environment for parallel pumping systems, which is based on circuit components of Matlab Simulink —software. The created simulation environment ensures the observation of variable speed controlled parallel pumping systems in case of different controlling methods. The introduced simulation environment was evaluated by building a simulation model for actual parallel pumping system at Lappeenranta University of Technology. The simulated performance of the parallel pumps was compared to measured values of the actual system. The gathered information shows, that if the initial data of the system and pump perfonnance is adequate, the circuitry based simulation environment can be exploited to observe parallel pumping systems. The introduced simulation environment can represent the actual operation of parallel pumps in reasonably accuracy. There by the circuitry based simulation can be used as a researching tool to develop new controlling ways for parallel pumps.

Error Modeling and Accuracy Analysis of a Novel Mobile Hybrid Parallel Robot

Over the last decades, calibration techniques have been widely used to improve the accuracy of robots and machine tools since they only involve software modification instead of changing the design and manufacture of the hardware. Traditionally, there are four steps are required for a calibration, i.e. error modeling, measurement, parameter identification and compensation. The objective of this thesis is to propose a method for the kinematics analysis and error modeling of a newly developed hybrid redundant robot IWR (Intersector Welding Robot), which possesses ten degrees of freedom (DOF) where 6-DOF in parallel and additional 4-DOF in serial. In this article, the problem of kinematics modeling and error modeling of the proposed IWR robot are discussed. Based on the vector arithmetic method, the kinematics model and the sensitivity model of the end-effector subject to the structure parameters is derived and analyzed. The relations between the pose (position and orientation) accuracy and manufacturing tolerances, actuation errors, and connection errors are formulated. Computer simulation is performed to examine the validity and effectiveness of the proposed method.

Alternative Energy Conversion Systems for a Micro Scale Wind Turbine

This Master's thesis deals with a Micro Scale Wind Wind Turbine application. The thesis consists of nine chapters. The first chapter is an introduction to the philosophy of a small scale wind turbine application. The second defines concepts, and lists the requirements. The third presents the whole application for an On-Grid , and for an Off-Grid arrangement, with main concentration on lighting, heating, and energy storage. The fourth deals with the Inverter's technology, which are used for the conversion of the produced power. The fifth chapter presents the available storage technology and it's possibilities. The sixth deals with the system, and the technological means used for the implementation. The seventh presents the PLC device, which was used as the controller for the management of the whole application. The eighth deals with the concept and the control application philosophy that the PLC involves. And the final chapter presents conclusions and ideas for further considerations.

A Practical Micro Mechanical Model Based Local Approach Methodology for the Analysis of Ductile Fracture of Welded T-Joints

This thesis concentrates on developing a practical local approach methodology based on micro mechanical models for the analysis of ductile fracture of welded joints. Two major problems involved in the local approach, namely the dilational constitutive relation reflecting the softening behaviour of material, and the failure criterion associated with the constitutive equation, have been studied in detail. Firstly, considerable efforts were made on the numerical integration and computer implementation for the non trivial dilational Gurson Tvergaard model. Considering the weaknesses of the widely used Euler forward integration algorithms, a family of generalized mid point algorithms is proposed for the Gurson Tvergaard model. Correspondingly, based on the decomposition of stresses into hydrostatic and deviatoric parts, an explicit seven parameter expression for the consistent tangent moduli of the algorithms is presented. This explicit formula avoids any matrix inversion during numerical iteration and thus greatly facilitates the computer implementation of the algorithms and increase the efficiency of the code. The accuracy of the proposed algorithms and other conventional algorithms has been assessed in a systematic manner in order to highlight the best algorithm for this study. The accurate and efficient performance of present finite element implementation of the proposed algorithms has been demonstrated by various numerical examples. It has been found that the true mid point algorithm (a = 0.5) is the most accurate one when the deviatoric strain increment is radial to the yield surface and it is very important to use the consistent tangent moduli in the Newton iteration procedure. Secondly, an assessment of the consistency of current local failure criteria for ductile fracture, the critical void growth criterion, the constant critical void volume fraction criterion and Thomason's plastic limit load failure criterion, has been made. Significant differences in the predictions of ductility by the three criteria were found. By assuming the void grows spherically and using the void volume fraction from the Gurson Tvergaard model to calculate the current void matrix geometry, Thomason's failure criterion has been modified and a new failure criterion for the Gurson Tvergaard model is presented. Comparison with Koplik and Needleman's finite element results shows that the new failure criterion is fairly accurate indeed. A novel feature of the new failure criterion is that a mechanism for void coalescence is incorporated into the constitutive model. Hence the material failure is a natural result of the development of macroscopic plastic flow and the microscopic internal necking mechanism. By the new failure criterion, the critical void volume fraction is not a material constant and the initial void volume fraction and/or void nucleation parameters essentially control the material failure. This feature is very desirable and makes the numerical calibration of void nucleation parameters(s) possible and physically sound. Thirdly, a local approach methodology based on the above two major contributions has been built up in ABAQUS via the user material subroutine UMAT and applied to welded T joints. By using the void nucleation parameters calibrated from simple smooth and notched specimens, it was found that the fracture behaviour of the welded T joints can be well predicted using present methodology. This application has shown how the damage parameters of both base material and heat affected zone (HAZ) material can be obtained in a step by step manner and how useful and capable the local approach methodology is in the analysis of fracture behaviour and crack development as well as structural integrity assessment of practical problems where non homogeneous materials are involved. Finally, a procedure for the possible engineering application of the present methodology is suggested and discussed.

Parallel-Operating Three-Phase Voltage Source Inverters – Circulating CurrentModeling, Analysis and Mitigation

The maximum realizable power throughput of power electronic converters may be limited or constrained by technical or economical considerations. One solution to this problemis to connect several power converter units in parallel. The parallel connection can be used to increase the current carrying capacity of the overall system beyond the ratings of individual power converter units. Thus, it is possible to use several lower-power converter units, produced in large quantities, as building blocks to construct high-power converters in a modular manner. High-power converters realized by using parallel connection are needed for example in multimegawatt wind power generation systems. Parallel connection of power converter units is also required in emerging applications such as photovoltaic and fuel cell power conversion. The parallel operation of power converter units is not, however, problem free. This is because parallel-operating units are subject to overcurrent stresses, which are caused by unequal load current sharing or currents that flow between the units. Commonly, the term ’circulatingcurrent’ is used to describe both the unequal load current sharing and the currents flowing between the units. Circulating currents, again, are caused by component tolerances and asynchronous operation of the parallel units. Parallel-operating units are also subject to stresses caused by unequal thermal stress distribution. Both of these problemscan, nevertheless, be handled with a proper circulating current control. To design an effective circulating current control system, we need information about circulating current dynamics. The dynamics of the circulating currents can be investigated by developing appropriate mathematical models. In this dissertation, circulating current models aredeveloped for two different types of parallel two-level three-phase inverter configurations. Themodels, which are developed for an arbitrary number of parallel units, provide a framework for analyzing circulating current generation mechanisms and developing circulating current control systems. In addition to developing circulating current models, modulation of parallel inverters is considered. It is illustrated that depending on the parallel inverter configuration and the modulation method applied, common-mode circulating currents may be excited as a consequence of the differential-mode circulating current control. To prevent the common-mode circulating currents that are caused by the modulation, a dual modulator method is introduced. The dual modulator basically consists of two independently operating modulators, the outputs of which eventually constitute the switching commands of the inverter. The two independently operating modulators are referred to as primary and secondary modulators. In its intended usage, the same voltage vector is fed to the primary modulators of each parallel unit, and the inputs of the secondary modulators are obtained from the circulating current controllers. To ensure that voltage commands obtained from the circulating current controllers are realizable, it must be guaranteed that the inverter is not driven into saturation by the primary modulator. The inverter saturation can be prevented by limiting the inputs of the primary and secondary modulators. Because of this, also a limitation algorithm is proposed. The operation of both the proposed dual modulator and the limitation algorithm is verified experimentally.