Fuzzy decoupling predictive functional control for nonlinear hydro-turbine governing systems with mechanical time delay of the hydraulic servo system

This study presents fuzzy decoupling predictive functional control for nonlinear hydro-turbine governing systems with time delay and strong coupling. Here, the Takagi–Sugeno fuzzy approach and fuzzy neural network decoupling algorithm are implemented in the pretreatment of a four-dimensional time delay hydro-turbine governing system model, aiming to solve the nonlinearity and separate coupling variables of the hydro-turbine governing system effectively. Then, a new fuzzy decoupling predictive functional control strategy proposed by combining the simplified hydro-turbine governing system model and predictive function control as well as the robustness and stability of the designed controller are verified by theoretical derivation. Numerical experiment demonstrates effectiveness and superiority of the proposed approach in comparison with fuzzy control under different operation conditions.

Implicit Co-Simulation and Solver-Coupling: Efficient Calculation of Interface-Jacobian and Coupling Sensitivities/Gradients

We consider implicit co-simulation and solver-coupling methods, where different subsystems are coupled in time domain in a weak sense. Within such weak coupling approaches, a macro-time grid is introduced. Between the macro-time points, the subsystems are integrated independently. The subsystems only exchange information at the macro-time points. To describe the connection between the subsystems, coupling variables have to be defined. For many implicit co-simulation and solver-coupling approaches an Interface-Jacobian is required. The Interface-Jacobian describes, how certain subsystem state variables at the interface depend on the coupling variables. Concretely, the Interface-Jacobian contains partial derivatives of the state variables of the coupling bodies with respect to the coupling variables. Usually, these partial derivatives are calculated numerically by means of a finite difference approach. A calculation of the coupling gradients based on finite differences may entail problems with respect to the proper choice of the perturbation parameters and may therefore cause problems due to ill-conditioning. A second drawback is that additional subsystem integrations with perturbed coupling variables have to be carried out. In this manuscript, analytical approximation formulas for the Interface-Jacobian are derived, which may be used alternatively to numerically calculated gradients based on finite differences. Applying these approximation formulas, numerical problems with ill-conditioning can be circumvented. Moreover, efficiency of the implementation may be increased, since parallel simulations with perturbed coupling variables can be omitted. The derived approximation formulas converge to the exact gradients for small macro-step sizes.

Singularity Analysis and Representation of 6DOF Parallel Robot Using Natural Coordinates

Singularity research is carried out. The problem, which is about six-dimensional parameters of position and orientation can not realize three-dimensional visualization for 6DOF parallel robot, has been solved. Firstly, according to the structural characteristics of the 6DOF parallel robot with the planar platform, the position and orientation of the mobile platform are described, respectively, and the six equations of forward kinematics are established by choosing the natural coordinates of three representative points as parameters. Then, the singularities of the 6DOF parallel robot with a planar platform are divided into input singularity and output singularity. Aiming at the output singularity, in combination with six constraint equations among the position vectors of three representative points, an analytical algorithm is proposed to express the coupling singularity of position and orientation and the analytical expression is derived. In further research, three kinds of output singularities are found, the spatial distribution of the output singular trajectory is determined, and a unified three-dimensional fully visualized description of six-dimensional coupling variables is realized for the first time. The problems of finding the singular orientation at a given position or the singular position at a given orientation are solved. The analysis of the singularity lays a solid foundation for the description of the three-dimensional complete visualization of a six-dimensional singularity-free workspace based on forward kinematics. What is more, it has great significance for both trajectory planning and control design of the parallel robot.

Explicit parallel co-simulation approach: analysis and improved coupling method based on H-infinity synthesis

Co-simulation is widely used in the industry for the simulation of multidomain systems. Because the coupling variables cannot be communicated continuously, the co-simulation results can be unstable and inaccurate, especially when an explicit parallel approach is applied. To address this issue, new coupling methods to improve the stability and accuracy have been developed in recent years. However, the assessment of their performance is sometimes not straightforward or is even impossible owing to the case-dependent effect. The selection of the coupling method and its tuning cannot be performed before running the co-simulation, especially with a time-varying system.In this work, the co-simulation system is analyzed in the frequency domain as a sampled-data interconnection. Then a new coupling method based on the H-infinity synthesis is developed. The method intends to reconstruct the coupling variable by adding a compensator and smoother at the interface and to minimize the error from the sample-hold process. A convergence analysis in the frequency domain shows that the coupling error can be reduced in a wide frequency range, which implies good robustness. The new method is verified using two co-simulation cases. The first case is a dual mass–spring–damper system with random parameters and the second case is a co-simulation of a multibody dynamic (MBD) vehicle model and an electric power-assisted steering (EPAS) system model. Experimental results show that the method can improve the stability and accuracy, which enables a larger communication step to speed up the explicit parallel co-simulation.

Enhanced Secure SWIPT in Heterogeneous Network via Intelligent Reflecting Surface

In this paper, secure transmission in a simultaneous wireless information and power transfer technology-enabled heterogeneous network with the aid of multiple IRSs is investigated. As a potential technology for 6G, intelligent reflecting surface (IRS) brings more spatial degrees of freedom to enhance physical layer security. Our goal is to maximize the secrecy rate by carefully designing the transmit beamforming vector, artificial noise vector, and reflecting coefficients under the constraint of quality-of-service. The formulated problem is hard to solve due to the nonconcave objective function as well as the coupling variables and unit-modulus constraints. Fortunately, by using alternating optimization, successive convex approximation, and sequential Rank-1 constraint relaxation approach, the original problem is transformed into convex form and a suboptimal solution is achieved. Numerical results show that the proposed scheme outperforms other existing benchmark schemes without IRS and can maintain promising security performance as the number of terminals increases with lower energy consumption.

Co-Simulation of Multibody Systems With Contact Using Reduced Interface Models

Co-simulation techniques enable the coupling of physically diverse subsystems in an efficient and modular way. Communication between subsystems takes place at discrete-time instants and is limited to a given set of coupling variables, while the internals of each subsystem remain undisclosed and are generally not accessible to the rest of the simulation environment. In noniterative co-simulation schemes, commonly used in real-time applications, this may lead to the instability of the numerical integration. The stability of the integration in these cases can be enhanced using interface models, i.e., reduced representations of one or more subsystems that provide physically meaningful input values to the other subsystems between communication points. This work describes such an interface model that can be used to represent nonsmooth mechanical systems subjected to unilateral contact and friction. The dynamics of the system is initially formulated as a mixed linear complementarity problem (MLCP), from which the effective mass and force terms of the interface model are derived. These terms account for contact detachment and stick–slip transitions, and can also include constraint regularization in case of redundancy in the system. The performance of the proposed model is shown in several challenging examples of noniterative multirate co-simulation schemes of a mechanical system with hydraulic components, which feature faster dynamics than the multibody subsystem. Using an interface model improves simulation stability and allows for larger integration step-sizes, thus resulting in a more efficient simulation.

On the cosimulation of multibody systems and hydraulic dynamics

The simulation of mechanical devices using multibody system dynamics (MBS) algorithms frequently requires the consideration of their interaction with components of a different physical nature, such as electronics, hydraulics, or thermodynamics. An increasingly popular way to perform this task is through co-simulation, that is, assigning a tailored formulation and solver to each subsystem in the application under study and then coupling their integration processes via the discrete-time exchange of coupling variables during runtime. Co-simulation makes it possible to deal with complex engineering applications in a modular and effective way. On the other hand, subsystem coupling can be carried out in a wide variety of ways, which brings about the need to select appropriate coupling schemes and simulation options to ensure that the numerical integration remains stable and accurate. In this work, the co-simulation of hydraulically actuated mechanical systems via noniterative, Jacobi-scheme co-simulation is addressed. The effect of selecting different co-simulation configuration options and parameters on the accuracy and stability of the numerical integration was assessed by means of representative numerical examples.

An automated methodology to select functional co-simulation configurations

The development of machinery often requires system-level analysis, in which non-mechanical subsystems, such as hydraulics, need to be considered. Co-simulation allows analysts to divide a problem into subsystems and use tailored software solutions to deal individually with their respective dynamics. On the other hand, these subsystems must be coupled at particular instants in time, called communication points, through the exchange of coupling variables. Between communication points, each subsystem solver carries out the integration of its states without interacting with its environment. This may cause the integration to become unstable, especially when non-iterative co-simulation is used. The co-simulation configuration, i.e., the parameters and simulation options selected by the analyst, such as the way to handle the coupling variables or the choice of subsystem solvers, is often a critical factor regarding co-simulation stability. In practice it is difficult to anticipate which selection is the most appropriate for a particular problem, especially if some inputs come from external sources, such as human operators, and cannot be determined beforehand. We put forward a methodology to automatically determine a stable and computationally efficient configuration for Jacobi-scheme co-simulation. The method uses energy residuals to gain insight into co-simulation stability. The relation between energy residual and communication step-size is exploited to monitor co-simulation accuracy during a series of tests in which the external inputs are replaced with predetermined input functions. The method was tested with hydraulically actuated mechanical examples. Results indicate that the proposed method can be used to find stable and accurate configurations for co-simulation applications.

Interface Models for Multirate Co-Simulation of Nonsmooth Multibody Systems

Co-simulation techniques enable the coupling of physically diverse subsystems in an efficient and modular way. Complex engineering applications can be simulated in co-simulation setups, in which each subsystem is solved and integrated using numerical methods tailored to its physical behaviour. Co-simulation implies that the communication between subsystems takes place at discrete-time instants and is limited to a given set of coupling variables, while the internals of each subsystem are generally not accessible to the rest of the simulation environment. In non-iterative co-simulation schemes, this may lead to the instability of the integration. Increasingly demanding requirements in the simulation of machinery have led to the coupling, in real-time co-simulation setups, of multibody models of mechanical systems to computational representations of non-mechanical subsystems, such as hydraulics and electronics. Often, these feature faster dynamics than their mechanical counterparts, which leads to the use of multirate integration in non-iterative co-simulation environments. The stability of the integration in these cases can be enhanced using interface models, i.e., reduced representations of the multibody system, to provide meaningful input values to faster subsystems between communication points. This work describes such interface models that can be used to represent nonsmooth mechanical systems subjected to unilateral contact and friction.

Parallel Co-Simulation Approach With Macro-Step Size and Order Control Algorithm

This contribution deals with the parallelization of multibody systems by making use of co-simulation techniques. The overall model is split into a user-defined number of subsystems, which are coupled and computed by means of a co-simulation approach. The co-simulation methods considered here are weak coupling approaches, which implies that each subsystem is solved independently from the other subsystems within a macro-time step. Information (i.e. coupling variables) is only exchanged between the subsystems at certain communication-time points (macro-time points). Within each macro-time step, the unknown coupling variables are approximated by extrapolation polynomials. The separate integration of the subsystems is the crucial point for a parallelized computation. A main drawback of many co-simulation implementations is that they are based on a constant macro-step size. Using an equidistant communication-time grid may in many practical applications be not very efficient with respect to computation time, especially in connection with highly nonlinear models or in context with models with strongly varying quantities. Here, a co-simulation approach is presented which incorporates a macro-step size and order control algorithm. Numerical examples show the benefit of this implementation and the significant reduction in computation time compared to an implementation with an equidistant communication-time grid.