| 1. |
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| 2. |
- Aminifar, Amir, et al.
(författare)
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Control-Quality Driven Design of Embedded Control Systems with Stability Guarantees
- 2018
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Ingår i: IEEE Design and Test. - : IEEE. - 2168-2356 .- 2168-2364. ; 35:4, s. 38-46
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Tidskriftsartikel (refereegranskat)abstract
- Today, the majority of control applications in embedded systems, e.g., in the automotive domain, are implemented as software tasks on shared platforms. Ignoring implementation impacts during the design of embedded control systems results in complex timing behaviors that may lead to poor performance and, in the worst case, instability of control applications. This article presents a methodology for implementation-aware design of high-quality and stable embedded control systems on shared platforms with complex timing behaviors.
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| 3. |
- Barzegaran, Mohammadreza, et al.
(författare)
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Towards quality-of-control-aware scheduling of industrial applications on fog computing platforms
- 2019
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Ingår i: IoT-Fog 2019 - Proceedings of the 2019 Workshop on Fog Computing and the IoT. - New York, NY, USA : ACM. - 9781450366984 ; , s. 1-5
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Konferensbidrag (refereegranskat)abstract
- In this paper we address Industrial IoT control applications which are safety-critical and real-time, and which have very low latency and jitter requirements. These control applications are virtualized as software tasks running on a Fog Computing Platform that brings computing and deterministic communication closer to the edge of the network, where the industrial "things" are located. Due to the demanding dependability and timing requirements, we consider that the tasks are scheduled with a static-cyclic scheduling policy. We are interested to determine the mapping of the tasks and a schedule table of their activation, such that we maximize the quality-of-control for the control tasks and meet the timing requirements for all tasks, including non-critical real-time tasks. We have proposed a Simulated Annealing-based metaheuristic to solve this problem, and we have evaluated the solution on several test cases.
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| 4. |
- Cederqvist, L, et al.
(författare)
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Improved Temperature and Depth Control During FSW of Copper Canisters Using Feedforward Compensation
- 2016
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Ingår i: Friction Stir Welding and Processing VIII. - Hoboken, NJ, USA : John Wiley & Sons, Inc.. - 9781119082491 ; , s. 69-76
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Konferensbidrag (refereegranskat)abstract
- The welding procedure to seal copper canisters requires variable power input throughout the 45 minute long weld cycle to keep the probe temperature within the process window. By using a cascaded loop that determines the power input requirement, the controller will not be dependent on repeatability in the necessary power input between weld cycles, and the lag time in the probe temperature measurement will not be critical. Due to fast-changing thermal boundary conditions during the downward sequence, a feedforward to the power input was designed to further improve controller performance. In addition to the cascade controller adjusting the tool rotation rate, a depth controller is adjusting the axial force to control the shoulder depth. The purpose is to eliminate flash due to excessive shoulder depth and to control the position of the probe tip, which influeces the size and shape of the hook defect produced. Controlling depth is challenging for several reasons, including deflection in the welding machine and thermal expansion of the weld material, and also results in cross-coupling between axial force and spindle torque. The cross-coupling was handled by another feedforward compensator that adjusts the tool rotation rate based on the commanded axial force. The implemented controllers and feedforward compensators have been evaluated over several welds with good results, where the depth is kept within ±0.1mm when the tool reaches the joint line sequence and the probe temperature is held within ±5°C during full circumferential welds compared to a process window of ±60°C.
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| 5. |
- Cervin, Anton
(författare)
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Event-Based Control and Estimation of Server Systems
- 2018
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Ingår i: Proceedings of the 4th International Conference on Event-Based Control, Communication, and Signal Processing, EBCCSP 2018.
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Konferensbidrag (refereegranskat)abstract
- Feedback control is increasingly being applied in server systems to make them more robust and efficient. This includes managing quality of service, minimizing power consumption, and adapting to varying workloads. Successful adaptation and control in turn relies on accurate tracking of workload variations and timely detection of changes in the computing infrastructure. Given that server systems are inherently event based, it is natural to consider event-based control and estimation schemes for them. As a prototypical problem, we study a single server system with time-varying arrival rate and derive optimal switching rules for the service rate. The goal is to keep the response time within bounds while minimizing the energy consumption of the server. We also design an event-based estimator of the server states using a particle filter approach. Finally, we outline some research challenges related to event-based control and information fusion in server systems.
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| 6. |
- Cervin, Anton
(författare)
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JitterTime 1.0—Reference Manual
- 2019
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- This technical report describes JitterTime, a Matlab toolbox for calculating the time-varying state covariance of a mixed continuous/discrete linear system driven by white noise. It also integrates a quadratic cost function for the system. The passing of time and the updating of the discrete-time systems are explicitly managed by the user in a simulation run. Since the timing is completely handled by the user, any complex timing scenario can be analyzed, including scheduling algorithms, timing jitter and drift, and asynchronous execution in distributed systems. Some examples of how the toolbox can be used to evaluate the control performance of time-varying systems are given.
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| 7. |
- Cervin, Anton
(författare)
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LQG-optimal PI and PID control as benchmarks for event-based control
- 2016
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Ingår i: 2016 2nd International Conference on Event-Based Control, Communication, and Signal Processing, EBCCSP 2016 - Proceedings. - 9781509041961
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Konferensbidrag (refereegranskat)abstract
- We formulate two simple benchmark problems for event-based control, where the optimal solutions in the continuous-time setting turn out to be ordinary PI and PID controllers. The benchmarks can be used to compare the performance of continuous-time, discrete-time, and various event-based controllers with regard to for instance disturbance attenuation, control effort, and average sampling or actuation rates. They can also be used to evaluate heuristic event-based PI(D) controllers and see how their performance compare to each other and to regular sampled-data control. We give two benchmark examples, where we study the trade-off between event frequency and regulator performance for a number of previously proposed approaches to event-based control.
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| 8. |
- Cervin, Anton, et al.
(författare)
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TrueTime : Simulation Tool for Performance Analysis of Real-Time Embedded Systems
- 2018
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Ingår i: Model-Based Design for Embedded Systems. - : CRC Press. - 9781420067842 - 9781420067859 ; , s. 145-176
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Bokkapitel (refereegranskat)abstract
- Embedded systems and networked embedded systems play an increasingly important role in today’s society. They are often found in consumer products (e.g., in automotive systems and cellular phones), and are therefore subject to hard economic constraints. The pervasive nature of these systems generates further constraints on physical size and power consumption. These product-level constraints give rise to resource constraints on the implementation platform, for example, limitations on the computing speed, memory size, and communication bandwidth. Because of economic considerations, this is true in spite of the rapid hardware development. In many applications, using a processor with a larger capacity than strictly necessary cannot be justified.
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| 9. |
- Cervin, Anton, et al.
(författare)
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Using JitterTime to Analyze Transient Performance in Adaptive and Reconfigurable Control Systems
- 2019
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Ingår i: 2019 24th IEEE International Conference on Emerging Technologies and Factory Automation (ETFA). - 9781728103037 - 9781728103020 - 9781728103044
-
Konferensbidrag (refereegranskat)abstract
- This paper presents JitterTime, a small Matlab toolbox for calculating the transient performance of a control system in non-ideal timing scenarios. Such scenarios arise in networked and embedded systems, where several applications share a set of limited and varying resources. Technically, the toolbox evaluates the time-varying state covariance of a mixed continuous/discrete linear system driven by white noise. It also integrates a quadratic cost function for the system. The passing of time and the updating of the discrete-time systems are explicitly managed by the user in a simulation run. Since the timing is completely handled by the user, any complex timing scenario can be analyzed, including adaptive scheduling and reconfiguration between different system modes. Three examples of how the toolbox can be used to evaluate the control performance of such time-varying systems are given.
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| 10. |
- Khalilzad, Nima
(författare)
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Adaptive and Flexible Scheduling Frameworks for Component-Based Real-Time Systems
- 2015
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Modern computer systems are often designed to play a multipurpose role. Therefore, they are capable of running a number of software components (software programs) simultaneously in parallel. These software components should share the system resources (e.g. processor and network) such that all of them run and finish their computations as expected. On the other hand, a number of software components have timing requirements meaning that they should not only access the resources, but this access should also be in a timely manner. Thus, there is a need to timely share the resources among different software components. The time-sharing is often realized by reserving a time-portion of resources for each component. Such a reservation should be adequate and resource-efficient. It should be sufficient to preserve the timing properties of the components. Also, the reservations should be resource-efficient to reduce the components' footprint on the resources which in turn allows integration of more software components on a given hardware resource. In this thesis, we mainly focus on the resource-efficiency of the reservations. We consider two cases. (I) Components which can tolerate occasional timing violations (soft real-time components): in this case we adjust the reservations during run-time to match the reservation sizes based on the instantaneous requirements of the components. (II) Components which cannot tolerate any timing violations (hard real-time components): in this case we use flexible approaches which allow us to improve the resource-efficiency at the design time.
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| 11. |
- Mohaqeqi, Morteza, et al.
(författare)
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On the problem of finding optimal harmonic periods
- 2016
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Ingår i: Proc. 24th International Conference on Real-Time Networks and Systems. - New York : ACM Press. - 9781450347877 ; , s. 171-180
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Konferensbidrag (refereegranskat)
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| 12. |
- Mohaqeqi, Morteza, et al.
(författare)
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Optimal harmonic period assignment: complexity results and approximation algorithms
- 2018
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Ingår i: Real-time systems. - : Springer. - 0922-6443 .- 1573-1383. ; 54:4, s. 830-860
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Tidskriftsartikel (refereegranskat)abstract
- Harmonic periods have wide applicability in industrial real-time systems. Rate monotonic (RM) is able to schedule task sets with harmonic periods up to 100% utilization. Also, if there is no release jitter and execution time variation, RM and EDF generate the same schedule for each instance of a task. As a result, all instances of a task are interfered by the same amount of workload. This property decreases the jitters that happen during sampling and actuation of the tasks, and hence, it increases the quality of service in control systems. In this paper, we consider the problem of optimal period assignment where the periods are constrained to be harmonic and the task set is required to be feasible. We study two variants of this problem. In the first one, the objective is to maximize the system utilization, while in the second one, the goal is to minimize the total weighted sum of the periods. First, we assume that an interval is determined a priori for each task from which its period can be selected. We show that both variants of the problem are (at least) weakly NP-hard. This is shown by reducing the NP-complete number partitioning problem to the mentioned harmonic period assignment problems. Afterwards, we consider a variant of the second problem in which the periods are not restricted to a special interval. We present two approximation algorithms with polynomial-time complexity for this problem and show that the maximum relative error of these algorithms is bounded by a factor of 1.125. Our evaluations show that, on the average, results of the approximation algorithms are very close to an optimal solution.
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| 13. |
- Nylén, Anders, et al.
(författare)
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Control Design Based on FMI: A Diesel Engine Control Case Study
- 2016
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Ingår i: 8th IFAC Symposium on Advances in Automotive Control AAC 2016. - : Elsevier BV. ; 49:11, s. 231-238
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Konferensbidrag (refereegranskat)abstract
- Modelica allows systems to be described with reuseable components and with a high precision. To be able to use such complex models efficiently, high demands are set on tools that allow the user to extract the information needed from the models in a straight-forward manner. For this purpose, design-of-experiments techniques can be used to systematically analyze the complex models.In this paper, it is demonstrated how a Modelica model of a diesel engine can be used for control design. The engine model has multiple inputs and outputs, it is nonlinear, has many parameters, and has a higher order than most control design algorithms are able to handle in a numerically robust way.It is shown how the features for dynamic design-of-experiments analysis in the FMI Toolbox for MATLAB can be used to analyze the variation in system dynamics across the engine operating range. A gain scheduling of nine multivariable linear-quadratic-gaussian (LQG) controllers, is designed based on linearization and model reduction of the original nonlinear FMU model.
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| 14. |
- Pazzaglia, Paolo, et al.
(författare)
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DMAC: Deadline-Miss-Aware Control
- 2019
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Ingår i: 31st Euromicro Conference on Real-Time Systems : ECRTS 2019 - ECRTS 2019. - 1868-8969. - 9783959771108 ; 133, s. 1-24
-
Konferensbidrag (refereegranskat)abstract
- The real-time implementation of periodic controllers requires solving a co-design problem, in which the choice of the controller sampling period is a crucial element. Classic design techniques limit the period exploration to safe values, that guarantee the correct execution of the controller alongside the remaining real-time load, i.e., ensuring that the controller worst-case response time does not exceed its deadline. This paper presents DMAC: the first formally-grounded controller design strategy that explores shorter periods, thus explicitly taking into account the possibility of missing deadlines. The design leverages information about the probability that specific sub-sequences of deadline misses are experienced. The result is a fixed controller, that on average works as the ideal clairvoyant time-varying controller that possesses knowledge of deadline hits and misses. We obtain a safe estimate of the hit and miss events using the scenario theory, that allows us to provide probabilistic guarantees. The paper analyzes controllers implemented using the Logical Execution Time paradigm and three different strategies to handle deadline miss events: killing the job, letting the job continue but skipping the next activation, and letting the job continue using a limited queue of jobs. Our experimental results show that our design proposal – i.e., that exploring the space where deadline can be missed and handled with different strategies – greatly outperforms classical control design techniques.
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| 15. |
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Projects in Automatic Control 2017
- 2018
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- This report contains the student papers describing the projects in the 2017 course Projects in Automatic Control (FRTN40). The course is given annually by the Department of Automatic Control, Lund University, during the second half of the fall semester, with the possibility of projects starting at other times upon agreement. It is an advanced level course, giving 7.5 ECTS credits. The main purpose of the course is to consolidate and develop the students’ knowledge through a practical project. Each project contains several of the elements typical for an automatic control project, such as modelling, identification, analysis, synthesis and computer implementation. For further information, see the course home page https://www.control.lth.se/FRTN40/ or the course syllabus (Swedish) https://kurser.lth.se/kursplaner/17_18/FRTN40.html. The course receives an annual participant evaluation, which can be found at https://www.ceq.lth.se.
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| 16. |
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| 17. |
- Ruuskanen, Johan, et al.
(författare)
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Event-Based State Estimation Using the Auxiliary Particle Filter
- 2019
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Ingår i: 2019 European Control Conference (ECC). - 9783907144008
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Konferensbidrag (refereegranskat)abstract
- Event-based sampling provides a way of lowering the resource utilization in sensing and communication applications. By sending a sample only when some triggering condition is fulfilled, we can ensure that the transmitted samples actually carry innovation. However, in an event-based system, the state estimation problem becomes complicated, as the information of not receiving a measurement must be taken into consideration. Recent research has examined the feasibility of using particle filters for solving the event-based state estimation problem. To the best of our knowledge, only the simple bootstrap particle filter has so far been considered in this setting. We argue that, as this filter does not fully utilize the current measurement, it is not well suited for state estimation in event-based systems.We propose an extension to the auxiliary particle filter for systems with event-based measurements, in which certain existing techniques for finding an approximation of the fully adapted filter can easily be utilized. In a simulation study, we demonstrate that at new measurement events, the benefits of using the auxiliary particle filter increases when fewer measurements are being sent.
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| 18. |
- Ruuskanen, Johan, et al.
(författare)
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Internal Server State Estimation Using Event-based Particle Filtering
- 2018
-
Ingår i: Proceedings of the 4th International Conference on Event-Based Control, Communication, and Signal Processing.
-
Konferensbidrag (refereegranskat)abstract
- Closed-loop control of cloud resources requires there to be measurements readily available from the process in order to use the feedback mechanism to form a control law. If utilizing state-feedback control, sought states might be unfeasible or impossible to measure in real applications; instead they must be estimated. However, running the estimators in real time for all measurements will require a lot of computational overhead. Further, if the observer and process are disjoint, sending all measurements will put extra strain on the network.In this work-in-progress paper, we propose an event-based particle filter approach to capture the internal dynamics of a server with CPU-intensive workload whilst minimizing the required computation or inter-system network strain. Preliminary results show some promise as it outperforms estimators derived from analytic expression for stationary systems in service rate estimation over number of samples used for a simulation experiment. Further we show that for the same simulation, an event-based sampling strategy outperforms periodic sampling.
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| 19. |
- Soltesz, Kristian, et al.
(författare)
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When is PID a good choice?
- 2018
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Ingår i: IFAC-PapersOnLine. - : Elsevier BV. - 2405-8963. ; 51:4, s. 250-255
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Tidskriftsartikel (refereegranskat)abstract
- A new and freely available model-based PID design tool for Matlab is introduced. It can be used to solve Maximal Integral Gain Optimization (MIGO) and (load) Integral Absolute Error (IAE) problems. Robustness is ensured through H-inf constraints on the closed-loop transfer functions. A Youla parameter (Q design) method for comparison with the optimal linear time-invariant (LTI) controller for the considered IAE optimization problem is presented. Several realistic design examples are provided, in which the tool is used to compare achievable PID and optimal LTI controller performance, to illustrate whether PID is a good choice for a given combination of process dynamics and closed-loop robustness requirements.
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| 20. |
- Thelander Andrén, Marcus, et al.
(författare)
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An Improved Stochastic Send-on-Delta Scheme for Event-Based State Estimation
- 2016
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- Event-based sensing and communication holds the promise of lower resource utilization and/or better performance for remote state estimation applicationsin e.g networked control systems (NCS). However, the problem of designing an optimal event-based state estimator often becomes untractable due to nonlinear measurements. This complexity is avoided with stochastic event-triggering. In this work, we extend the previous work on stochastic triggering by proposing a simple predictor in the sensor to further improve the estimation performance.
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| 21. |
- Thelander Andrén, Marcus, et al.
(författare)
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Event-Based State Estimation Using an Improved Stochastic Send-on-Delta Sampling Scheme
- 2016
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Ingår i: 2016 Second International Conference on Event-based Control, Communication, and Signal Processing (EBCCSP). - 9781509041961
-
Konferensbidrag (refereegranskat)abstract
- Event-based sensing and communication holds the promise of lower resource utilization and/or better performance for remote state estimation applications found in e.g. networked control systems. Recently, stochastic event-triggering rules have been proposed as a means to avoid the complexity of the problem that normally arises in event-based estimator design. By using a scaled Gaussian function in the stochastic triggering scheme, the optimal remote state estimator becomes a linear Kalman filter with a case dependent measurement update. In this paper we propose a modified version of the stochastic send-on-delta triggering rule. The idea is to use a very simple predictor in the sensor, which allows the communication rate to be reduced while preserving estimation performance compared to regular stochastic send-on-delta sampling. We derive the optimal mean-square error estimator for the new scheme and present upper and lower bounds on the error covariance. The proposed scheme is evaluated in numerical examples, where it compares favorably to previous stochastic sampling approaches, and is shown to preserve estimation performance well even at large reductions in communication rate.
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| 22. |
- Thelander Andrén, Marcus, et al.
(författare)
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On Event-Based Sampling for LQG-Optimal Control
- 2018
-
Ingår i: 56th IEEE Conference on Decision and Control, CDC, 2017. ; , s. 5438-5444
-
Konferensbidrag (refereegranskat)abstract
- We consider the problem of finding an event-based sampling scheme that optimizes the trade-off between average sampling rate and control performance in a linear-quadratic-Gaussian (LQG) control problem setting with output feedback. Our analysis is based on a recently presented sampled-data controller structure, which remains LQG-optimal for any choice of sampling scheme. We show that optimization of the sampling scheme is related to an elliptic convection–diffusion type partial differential equation over a domain with free boundary, a so called Stefan problem. A numerical method is presented to solve this problem for second order systems, and thus obtain an optimal sampling scheme. The method also directly generalizes to higher order systems, although with a higher computational cost. For the special case of multidimensional integrator systems, we present the optimal sampling scheme on closed form, and prove that it will always outperform its periodic counterpart. Tight bounds on the improvement are presented. The improved performance is also demonstrated in numerical examples, both for an integrator system and a more general case.
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| 23. |
- Xu, Yang, et al.
(författare)
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Exploiting Job Response-Time Information in the Co-Design of Real-Time Control Systems
- 2015
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Ingår i: 2015 IEEE 21ST INTERNATIONAL CONFERENCE ON EMBEDDED AND REAL-TIME COMPUTING SYSTEMS AND APPLICATIONS. - : Institute of Electrical and Electronics Engineers (IEEE). - 9781467378550 - 9781467378567 ; , s. 247-256
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Konferensbidrag (refereegranskat)abstract
- We consider a real-time system of multiple tasks, each task having a plant to control. The overall quadratic control cost is to be optimized. We exploit the periodicity of the task response time, which corresponds to a periodic delay pattern in the feedback control loop. Perturbed periods are used as a tool to find a finite hyper period. We present an analytical procedure to design a periodic linear-quadratic-Gaussian (LQG) controller for tasks with fixed execution times as well as a numerical solution to the periodic -- stochastic LQG problem for tasks with variable execution times. The controllers are evaluated using simulations in real-time scheduling and control co-design examples.
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| 24. |
- Xu, Yang, et al.
(författare)
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Harmonic Scheduling and Control Co-Design
- 2016
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Ingår i: 2016 IEEE 22nd International Conference on Embedded and Real-Time Computing Systems and Applications (RTCSA). - 9781509024797
-
Konferensbidrag (refereegranskat)abstract
- Harmonic task scheduling has many attractive properties, including a utilization bound of 100% under rate-monotonic scheduling and reduced jitter. At the same time, it places a severe constraint on the task period assignment for any application. In this paper, we explore the use of harmonic task scheduling for applications with multiple feedback control tasks. We present an algorithm for finding harmonic task periods that minimizes the distance from an initial set of non-harmonic periods. We apply the algorithm in a scheduling and control co-design procedure, where the goal is to optimize the total performance of a number of control tasks that share a common computing platform. The procedure is evaluated in simulated randomized examples, where it is shown that, in general, harmonic scheduling combined with release offsets gives better control performance than standard, non-harmonic scheduling.
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| 25. |
- Xu, Yang, et al.
(författare)
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Jitter-Robust LQG Control and Real-Time Scheduling Co-Design
- 2018
-
Ingår i: Proceedings of the American Control Conference. - 9781538654286 ; 2018-June, s. 3189-3196
-
Konferensbidrag (refereegranskat)abstract
- In real-time control systems, varying task response times may lead to delays and jitter in the delays in the feedback control loops, which adversely affects both performance and robustness. Standard LQG control design does not give any guarantees on robustness, while robust control design methods often do not handle controller timing uncertainty. We propose a sampled-data controller synthesis method that minimizes an LQG cost function subject to a jitter margin constraint. By robustifying the LQG controller we are able to retain good stability margins under delay and jitter, while typically paying a small price in terms of nominal performance. We also present a co-design procedure that assigns optimal priorities and sampling periods to a set of controllers based on their performance characteristics and jitter sensitivity. The procedure is evaluated on randomized plant sets, showing an improvement over state-of-the-art methods.
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| 26. |
- Xu, Yang, et al.
(författare)
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LQG-Based Control and Scheduling Co-Design
- 2017
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Ingår i: IFAC-PapersOnLine. - : Elsevier BV. - 2405-8963. ; 50:1, s. 5895-5900
-
Tidskriftsartikel (refereegranskat)abstract
- Control and scheduling co-design becomes an issue when several controller tasks share the same execution platform and disrupt the ideal sampling and actuation patterns. In co-design the objective is to optimize the combined performance of all the controllers on the platform, subject to schedulability constraints. In the paper four LQG-based co-design methods are reviewed and evaluated: delay-aware, stochastic, periodic, and harmonic LQG co-design.
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| 27. |
- Xu, Yang, et al.
(författare)
-
LQG-Based Scheduling and Control Co-Design Using Harmonic Task Periods
- 2016
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Harmonic task scheduling has many attractive properties, including a utilization bound of 100% under rate-monotonic scheduling and reduced jitter. At the same time, it places a severe constraint on the task period assignment for any application. In this paper, we explore the use of harmonic task scheduling for applications with multiple feedback control tasks. We investigate the properties of harmonic scheduling and give an efficient algorithm to calculate response times for harmonic tasks. We present two algorithms for finding harmonic task periods: one that minimizes the distance from an initial set of non-harmonic periods and one that finds all feasible harmonic periods within a given set of ranges. We apply the algorithms in a control and scheduling co-design procedure, where the goal is to optimize the total performance of a number of control tasks that share a common computing platform. The procedure is evaluated in simulated randomized examples, where it is shown that, in general, harmonic scheduling combined with release offsets gives better control performance than standard, non-harmonic scheduling.
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| 28. |
- Årzén, Karl-Erik, et al.
(författare)
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Software and Platform Issues in Feedback Control Systems
- 2017
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Ingår i: Cyber-Physical Systems. - 9780321926968 ; , s. 165-195
-
Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- Control theory is one of the key intellectual underpinnings that allows us to analyze the interaction of software with the physical world. However, control theory abstracts software actions as actions that take no time to execute. In reality, software execution takes time – and this execution time can be affected by a number of platform issues, including the speed of the processor, the scheduler used to share the processor between multiple tasks, and network delays that occur when computations go across networks, among others. In this chapter we discuss such software and platform effects, as well as techniques used to design control systems that take these effects into account.
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