Geometric Algebra (GA) provides a unified, compact mathematical framework for geometric computing, simplifying relations typically handled with more complex tools like matrix multiplication. In fields like robotics, GA replaces conventional coordinate-based approaches with the multiplication of special elements called rotors, offering greater efficiency. Despite its advantages, GA’s complexity and the lack of symbolic tools hinder its broader adoption among applied mathematicians and engineers. To address this, this article introduces Symbolic and User-friendly Geometric Algebra Routines (SUGAR), an open source Matlab toolbox. SUGAR streamlines GA usage in Matlab through a collection of user-friendly functions that support both numeric and symbolic computations, even in high-dimensional algebras. Designed for applied mathematics and engineering, it enables intuitive manipulation of geometric elements and transformations in two- and three-dimensional projective and conformal GAs, consistent with established computational methods. Moreover, SUGAR manages multivector functions such as exponential, logarithmic, sinusoidal, and cosine operations, enhancing its applicability in domains like robotics, control systems, and power electronics. Finally, this article also presents three validation examples across these fields, showcasing SUGAR’s practical utility in solving real-world engineering and applied mathematics problems.

In industrial microgrids with medium power rating photovoltaic systems, the low-voltage ride-through capability should be incorporated to help keep power system stability. The goal of this paper is to present a control strategy that allows taking advantage of the maximum capability of the inverters to support the most dropped phase in a photovoltaic-based industrial microgrid during voltage sags. Depending on the grid code requirements, the rated current value could be injected by the local inverters during these disturbances. The currents can be injected through the positive and negative sequences depending on the sag characteristics and the power rating of the local inverters. Also, to prevent overcurrent, the controller can apply active power curtailment. Lastly, selected simulation results are presented to validate the performance of the control scheme.

A key objective to be fulfilled by distributed voltage source inverters working in parallel in islanded MicroGrids (MGs) is to ensure active power sharing while keeping the frequency at a desired setpoint. Recently, consensus-based control techniques have been applied at the secondary control level for active power sharing while correcting the frequency deviation that the droop control implemented at the primary control level introduces. To this end, inverters work in a cooperative way by sharing their own corrective action with their neighbors over a digital communication network. The contribution of this paper is to analyze how changes in the network topology affect the consensus-based active power sharing control goal. In particular, the analysis focuses on the network structure in terms of adjacency, that is, in terms of the number of connections that each node has. The theoretical analysis based on graph theory provides results that indicate the pattern that steady-state active power values will follow according to the network structure. Numerical examples are used to illustrate the theoretical results, and select simulations on a low-scale MG complete the analysis. The paper results provide insight into the existing design tradeoff between power sharing accuracy and number of network connections.

Grid codes are continuously evolving to improve the ride-through services during voltage sags. The main reason for this evolution is the increasing flexible capabilities of distribution generation inveters. The problem of selecting an appropriate strategy during grid faults is an open research topic that depends on many aspects. Among the possible solutions, this paper solves an optimization problem based on the maximization of the voltage support during grid faults. The control strategy is based on raising as much as possible the positive sequence voltage. This strategy allows to reduce the risk of disconnection by under-voltage that can led to a blackout. The problem is related to two main issues: the amount of injected current and the grid impedance. Regarding the injected current, it should be desirable to develop the references so as to inject the rated current of the inverter. Therefore the voltage support could be improved while keeping the inverter within a safety operation mode. Regarding the impedance, the strategy for inductive or resistive grids should be different. For a combination of both impedances, an optimal solution should exist in order to maximize the voltage increment. This solution is related to the amount of active and reactive current injected by the inverter. The work proposes a voltage support control strategy intended to increase as much as possible the positive sequence voltage and to inject the maximum rated current of the grid-connected distributed generation inverter. The problem is mathematically solved for any type of grid impedance, even resistive, inductive or a combination of both. Simulation results are presented to corroborate the theoretical solution.

In islanded microgrids, parallel operation of voltage source inverters is commonly enabled by primary droop control to achieve power sharing and secondary control that removes the frequency deviation by mimicking at some extend the operation of an integral controller. Often the main task of the distinct secondary control approaches is to compute a corrective term considering the frequency error that is then used by the droop mechanism for frequency compensation. This paper considers the secondary control approach where local integral controllers that compute the frequency corrective term are implemented at each inverter. And considering that integrals are performed in different nodes, the paper shows that global time between nodes achieved through clock synchronization is mandatory for accurate power sharing and frequency restoration.

The increasing deployment of distributed generation (DG) such as photovoltaic panels (PV) connected to low-voltage (LV) grids is becoming a common trend in urban areas. The advances of information and communication technology (ICT) facilitates the collaborative operation of DG systems to achieve collective benefits. The fusion of these two trends creates a new scenario where reactive power control methods can offer additional features and benefits beyond the conventional voltage regulation provided by the droop method. Taking advantage of this new scenario, this paper formulates the application of reactive power control as an optimization problem where simple and ideal settings are imposed by design in order to facilitate the exploration search as well as to avoid over-constraining the optimization space. By appropriately using the reactive power capacity of inverters, the desired collective benefit is to minimize power losses while individual voltages at each inverter should be kept within the statutory limits. The simulated solution of the optimization problem is applied to a real-inspired PV-LV grid subject to an over-voltage situation, which may typically occur during periods of high production but low consumption. Simulation results reveal unexpected optimal settings for reactive power control set-points at each inverter, which calls for a final discussion to review the applicability of the optimization approach.

A topic of interest within the microgrid (MG) community is to achieve accurate sharing of active and reactive power among voltage source inverters (VSI) working in parallel while keeping the voltage frequency and amplitude stable, and close to a given reference. This problem has been mainly solved by the so-called frequency and voltage droop controllers that are local control loops implemented in each VSI. However, since they introduce a frequency and amplitude deviation, a secondary integral-like control loop using a communication system is usually deployed to enable each VSI to cancel the deviations. This paper evaluates two secondary control implementations of the frequency restoration with respect to properties of the communication system. Networked control applications are subject to known problems that are inherent to the use of a communication system such as message losses or varying sampling/transmission intervals, to name a few. The performance analysis reveals that control policies should be designed accounting also for the properties of the communication system. Otherwise, unexpected results violating the control specifications may appear.

The evolution of technology and application needs leads to design complex systems both at hardware and software levels. Modeling approaches and automatic code generation are mature techniques in several application areas to shorten development times even in complex applications. This paper introduces the application of these techniques to critical embedded systems such as networked control systems (NCS). In particular, the case of an Internet-based control of a ball&plate system is presented. The first part of the paper is devoted to the plant modeling and control design strategy taking into account the distributed layout. The second part covers the automatic code generation process: from ScicosLab diagrams, C code is automatically generated onto multiple and physically distributed threads, with the automatic synthesis of thread scheduling, communication and access to the I/O primitives for sampling and actuation. The case study corroborates that model-based design tools mastering NCS complexity can contribute to the success of future industrial projects.

One of the main concerns in the design of networked control systems (NCS's) is the inherent delays induced by the networking infrastructure. Rather than considering delays as a threat, delays may be considered as an opportunity for novel controller design procedures, where delays become a design parameter. The benefits may range from easier and cheaper implementations to improved performance. To enable procedures where the explicit specification of a delay may be profitable, alternative models for a discrete-time LTI system with an arbitrary delay used for controller design must be investigated. This paper presents a modeling effort different than the common approach of extending the state-space model with new state variables. The new model is also capable of representing the same system with a delay but using a state-space modeling structure that keeps the original system order. The focus of the paper is to show that both models are equivalent. A direct consequence is that it will be possible to design a controller for a system without delay in such a way that the closed loop system behaves like having a delay. In other words, a relation between desired control performance (via e.g. closed-loop system poles), controller, and delay is established, which provides a new design criterion for NCS.

The majority of existing Networked Control Systems (NCS) models are discrete-time formulations based on the exact discretization of the continuous-time linear plant over a sample interval. In the state-space formalism, standard control textbooks suggest that a simple approach to model discrete-time LTI systems with time delay shorter or equal than the sampling period is to extend the state vector with a new state variable representing the last control signal, which implies increasing the order of the model by one. In this paper an alternative state-space model for discrete-time LTI systems with time delay is introduced that does not require increasing the order of the model. The relation between both the standard model and the new model is established, and the potential benefits of the new model with respect to the standard one are discussed. Numerical examples illustrate the concepts discussed throughout the paper.

Penetration of distributed power generation poses new problems in energy distribution. For example, photovoltaic generation systems may difficult the voltage management in distribution lines and voltage rise may occur. To overcome this problem, several voltage control strategies are available and they can be classified as autonomous or distributed regarding whether communication is available between dispersed generators. Through a preliminary case study, this paper investigates the impact that the communication infrastructure has for a given distributed voltage control strategy. Communication issues like transmission rate, delays, and losses are analyzed with respect to the voltage control application performance.

In Networked Control Systems (NCS), the amount of control data exchanged between sensors, controllers and actuators nodes highly depends on the control performance specifications given to each networked control loop. The periodic execution of each loop helps meeting the control specifications while imposing a static network traffic. This paper presents an alternative execution mechanism for each networked control loop that permits to dynamically lower the traffic while ensuring the same or better control performance than the achieved by the periodic case. Simulation results illustrate the theoretical analysis.

The development of database applications in most CASE tools has been insufficient because most of these tools do not provide the software necessary to validate these applications. Validation means ensuring whether a given application fulfils the user requirements. We suggest validation of database applications by using the functional testing technique, which is a fundamental black-box testing technique for checking the software without being concerned about its implementation and structure. Our main contribution to this work is in providing a MDA approach for deriving testing software from the OCL specification of the integrity constraints. This testing software is used to validate the database applications, which are used to enforce these constraints. The generated testing software includes three components: validation queries, test cases and initial data inserted before the testing process. Our approach is implemented as an add-in tool in Rational Rose called OCL2TestSW.

The successful operation of Networked Control Systems (NCS) requires employing appropriate approaches for dealing with network induced time delays, i.e. time intervals elapsed from consecutive sampling and actuation operations. Effective approaches often require to impose periodic execution for the sampling and/or actuation operations, enforcing synchronized constant time delays. And considering that sampling and actuation is performed in different nodes, global time between nodes achieved by clock synchronization is the standard assumption or strategy that enables such synchronized operations. This paper presents a technique that permits to implement these synchronized operations in NCS in the absence of global time. Experimental results corroborate the effectiveness of the presented approach.

The Controller Area Network (CAN) provides the basis for many cost-effective distributed embedded systems. In this paper, we present a novel approach to networked control systems (NCS) analysis and design that provides increased control performance for a set of control loops that share a single CAN network. This is achieved by enabling the following functionality for each control loop: first, standard periodic messaging is guaranteed to ensure stability, and second, non-periodic additional messaging is added whenever bandwidth is available in such a way that the aggregated control performance for all control loops is improved. To validate the presented approach, a proof-of-concept implementation is presented, and the extensive experimental results show the type of benefits that can be achieved as well as the resulting behavior depending on several key parameters. Moreover, it demonstrates that the approach can be implemented in practice.

This paper presents the schedulability analysis for control messages when networked control loops, built on top of the controller area network (CAN), are dynamically allocating bandwidth in terms of their controlled plants' dynamics. The bandwidth allocation policy is theoretically described by an optimization problem and practically solved by the distributed bitwise arbitration of CAN messages when message identifiers, i.e., priorities, reflect control applications demands. This poses the problem of assessing whether the set of real-time messages will meet their deadlines regardless of run-time priority changes. This is solved by a schedulability analysis based on recent results on worst-case response time techniques for real-time CAN applications. The analysis ends up with the schedulability test for this type of applications.

In many application areas, including control systems, careful management of system resources is key to providing the best application performance. Traditional control systems with multiple control loops statically allocate a fixed portion of the system resources to each controller based on their average or worst-case resource requirements. However, controllers' resource needs vary depending on the jobs they perform and the state of the systems they control. A controller of a plant operating close to its equilibrium requires fewer resources than a controller of a plant operating far from its equilibrium point. The Draco dynamic rate control system exploits this fact by dynamically allocating resources to control systems based on system state. Our research demonstrates that Draco provides significantly better overall control performance with much less resources than static controllers. Our experimental evaluation shows that in the control scenarios we examined Draco provides up to 25% better control performance with 30% less resources.

The standard design of control systems is based on theperiodic sampling. Every period the data is read from theinput, the control law is computed, and the output is writtento the actuators. However the periodicity of the samplinginstants is a constraint that arises from the ease of implementationand it is not strictly necessary in the control system.In this paper we present an execution model that samplesthe input "when needed". This model saves a considerableamount of computational resources. We show the schedulabilityanalysis for a set of control-driven tasks using bothFixed Priority (FP) and Earliest Deadline First (EDF).

Embedded control systems are often implemented in small microprocessors enabled with real-time technology. In this context, control laws are often designed according to discrete-time control systems theory and implemented as hard real-time periodic tasks. Standard discrete-time control theory mandates to periodically sample (input) and actuate (output). Depending on how input/output (I/O) operations are performed within the hard real-time periodic task, different control task models can be distinguished. However, existing task models present important drawbacks. They generate task executions prone to violate the periodic control demands, a problem known as sampling and latency jitter, or they impose synchronized I/O operations at each task job execution that produce a constant but artificially long I/O latency. In this paper, the one-shot task model for implementing control systems in embedded multitasking hard real-time platforms is presented. The novel control task model is built upon control theoretical results that indicate that standard control laws can be implemented considering only periodic actuation. Taking advantage of this property, the one-shot task model is shown to remove endemic problems for real-time control systems such as sampling and latency jitters. In addition, it can minimize the harmful effects that long I/O latencies have on control performance. Extensive simulations and real experiments show the feasibility and effectiveness of the novel task model, compared to previous real-time and/or control-based solutions.

In recent years, approaches to control performance and resource optimization for embedded control systems have been receiving increased attention. Most of them focus on theory, whereas practical aspects are omitted. Theoretical advances demand flexible real-time kernel support for multitasking and preemption, thus requiring more sophisticated and expensive software/hardware solutions. On the other hand, embedded control systems often have cost constraints related with mass production and strong industrial competition, thus demanding low-cost solutions. In this paper, it is shown that these conflicting demands can be softened and that a compromise solution can be reached. We advocate that recent research results on optimal resource management for control tasks can be implemented on simple multitasking preemptive real-time kernels targeting low-cost microprocessors, which can be easily built in-house and tailored to actual application needs. The experimental evaluation shows that significant control performance improvement can be achieved without increasing hardware costs.

Transient overload conditions may cause unpredictable performance degradations in computer controlled systems if not properly handled. To prevent such problems, a common technique adopted in periodic task systems is to reduce the workload by enlarging activation periods. In a digital controller, however, the variation applied on the task period also affects the control law, which needs to be recomputed for the new activation rate. If computing a new control law requires too much time to be performed at runtime, a set of controllers has to be designed offline for different rates and the system has to switch to the proper controller in the presence of an overload condition. In this paper, we present a method for reducing the number of controllers to be designed offline, while still guaranteeing a given control performance. The proposed approach has been integrated with the elastic scheduling theory to promptly react to overload conditions. The effectiveness of the proposed approach has been verified through extensive simulation experiments performed on an inverted pendulum. In addition, the method has been implemented on a real inverted pendulum. Experimental results and implementation issues are reported and discussed

This paper presents a resource management strategy for control tasks that maximizes control performance within the available resources by readjusting the task periods at runtime. A feedback scheduler is used to determine on-line the optimal task periods considering the response over a finite time horizon of the plants controlled by arbitrary linear control laws. We show how this problem can be expressed as an optimization problem, where the objective function relates the sampling periods to the transient responses of the controlled plants, and where restrictions are based on EDF schedulability constraints. For the general case, the solution of the optimization problem is computationally expensive, and thus, an approximate procedure to be executed on-line has been developed. We present simulation results that validate the presented approach

An optimal bandwidth allocation policy for axis distributed control using networked control systems (NCS) is presented. First, the benefits of structuring highly articulated robots using networked control systems are discussed. Afterwards, an optimal bandwidth allocation policy for axes distributed control that allows to enhance robot tracking within the available bandwidth is introduced. It will be shown that axes control performance and thus tracking can be significantly improved by using feedback to dynamically allocate bandwidth to axis controllers as a function of the current state of each axis. Simulation results on a multiple axes robot corroborate our approach.

In many application areas, including control systems, careful management of system resources is key to providing the best application performance. Most traditional resource management techniques for real-time systems with multiple control loops are based on open-loop strategies that statically allocate a constant CPU share to each controller, independent of their current resource needs. This provides average control performance with minimal overhead but in general fails to provide the best performance possible within the available resources. We show that by using feedback to dynamically allocate resources to controllers as a function of the current state of their controlled systems, control performance can be significantly improved. We present an optimal resource allocation policy that maximizes control performance within the available resources and provide experimental results showing that the optimal policy 1) significantly increases control performance compared to traditional control system implementations (by more than 20% in our experiments), 2) maximizes control performance over other feedback-based policies, 3) saves resources when perturbations occur infrequently, and 4) incurs negligible overhead.

Abstract Domain analysis was first used 15 years ago as one of the most important techniques for software reuse. Even today, new techniques appear every year, and different authors propose different domain representation structures to represent and store all the different software components and the relationships among them. These relationships among components are the kernel of the domain semantics. In this report, a set of techniques and tools is presented regarding mathematical, statistical, and neural fields that, when linked together, enable semi‐automatically building domain representations and storing them in a thesaurus structure of software components. Thesaurus structures, widely used in information science, are presented as the domain‐modeling key concept, due to their higher automation possibilities compared with previous structures. New metrics to evaluate the quality, consistency, and completeness of the domain model obtained through this technique are also presented.

The increasing use of internet in the automation field has brought new challenges in the remote control, supervision and management of industrial processes. Specifically, process data information has to be available anywhere/anytime on the internet. This brings together two main problems: process data abstraction and process data accessibility. In this paper, we present a specification for an environment aimed to virtually model industrial plants, for their remote control, supervision and management. In this environment, we model real industrial plants by means of communication objects called virtual industrial devices (VID). A VID is a software component, which may contain other VIDs and represents, with different degrees of abstraction, an entity of an industrial plant. These objects communicate and are accessible through a peer-to-peer industrial communication protocol that allo15 messaging interchange between virtual industrial devices (and graphic user interfaces) regardless the communication technology that supports the actual messaging.