Experimental application of Takagi-Sugeno observers and controllers in a nonlinear electromechanical system

[EN] In this paper, a systematic methodology to design fuzzy Takagi-Sugeno observers and controllers will be used to estimate the angular positions and speeds, as well as to stabilise an experimental mechanical system with 3 degrees of freedom (fixed quadrotor). Takagi-Sugeno observers and controllers are compared to observers and controllers based on the linearized model, both designed with the same optimization criteria and design parameters. Experimental results confirm that Takagi-Sugeno models and observers behave similarly to linear ones around the linearization point, but have a better performance over a larger operating range, as intuitively expected.The work of Zs. Lendek was supported by a grant of the Romanian National Authority for Scientific Research, CNCS UEFISCDI, project number PN-II-RU-TE-2011-3-0043, contract number 74/05.10.2011. Spanish authors are grateful to grants DPI2011-27845-C02-01 (A. Sala), DPI2011-27845-C02-02 (R. Sanchis), DPI2011-28507-C02-01 (P. Garcia) from Spanish Government, and PROMETEOII/2013/004 (A. Sala, P. Garcia) from Generalitat Valenciana.Lendek, Z.; Sala, A.; García Gil, PJ.; Sanchis Llopis, R. (2013). Experimental application of Takagi-Sugeno observers and controllers in a nonlinear electromechanical system. Control Engineering and Applied Informatics. 15(4):3-14. http://hdl.handle.net/10251/150453S31415

Multicriteria fuzzy-polynomial observer design for a 3DoF nonlinear electromechanical platform

This paper proposes local fuzzy-polynomial observer discrete-time designs for state estimation of a nonlinear 3DoF electromechanical platform (fixed quadrotor). A trade-off between H∞ norm bounds and speed of convergence performance is taken into account in the design process. Actual experimental data are used to compare performance of the fuzzy polynomial design with classical ones based on the Takagi–Sugeno and linearized models, both using the same optimization criteria and design parameters.The authors are grateful to the financial support of the Spanish government under research project DPI2011-27845-C02-01 and FPI Grant BES-2009-013882, as well as to Generalitat Valenciana grant PROMETEOII/2013/004. The authors are also grateful to Ph.D. students A. Berna, J. Guzman and associate professor P.J. Garcia for their laboratory data acquisition work.Pitarch Pérez, JL.; Sala Piqueras, A. (2014). Multicriteria fuzzy-polynomial observer design for a 3DoF nonlinear electromechanical platform. Engineering Applications of Artificial Intelligence. 30:96-106. https://doi.org/10.1016/j.engappai.2013.11.006S961063

Asymptotically exact stabilisation for constrained discrete Takagi-Sugeno systems via set-invariance

[EN] Given a Takagi-Sugeno (TS) system, this paper proposes a novel methodology to obtain the state feedback controller guaranteeing, asymptotically as a Polya-related complexity parameter grows, the largest (membership-shape independent) possible domain-of-attraction with contraction-rate performance lambda, based on polyhedral lambda-contractive sets from constrained linear systems literature. The resulting controller is valid for any realisation of the memberships, as usual in most TS literature. For a finite complexity parameter, an inner estimate of such largest set is obtained; the frontier of such approximation can be understood as the level set of a polyhedral control-Lyapunov function. Convergence of a proposed iterative algorithm is asymptotically necessary and sufficient for TS system stabilisation: for a high-enough value of the complexity parameter, any conceivable shape-independent Lyapunov controller design procedure will yield a proven domain of attraction smaller or equal to the algorithm's output. (C) 2016 Elsevier B.V. All rights reserved.This work has been supported by grants DPI2015-70433- P and DPI2016-81002-R, from Spanish Government (MINECO) and grant PROMETEOII/2013/004 from Generalitat Valenciana.Ariño-Latorre, CV.; Sala, A.; Pérez Soler, E.; Bedate Boluda, F.; Querol-Ferrer, A. (2017). Asymptotically exact stabilisation for constrained discrete Takagi-Sugeno systems via set-invariance. Fuzzy Sets and Systems. 316:117-138. https://doi.org/10.1016/j.fss.2016.10.004S11713831

Fuzzy control turns 50: 10 years later

In 2015, we celebrate the 50th anniversary of Fuzzy Sets, ten years after the main milestones regarding its applications in fuzzy control in their 40th birthday were reviewed in FSS, see [1]. Ten years is at the same time a long period and short time thinking to the inner dynamics of research. This paper, presented for these 50 years of Fuzzy Sets is taking into account both thoughts. A first part presents a quick recap of the history of fuzzy control: from model-free design, based on human reasoning to quasi-LPV (Linear Parameter Varying) model-based control design via some milestones, and key applications. The second part shows where we arrived and what the improvements are since the milestone of the first 40 years. A last part is devoted to discussion and possible future research topics.Guerra, T.; Sala, A.; Tanaka, K. (2015). Fuzzy control turns 50: 10 years later. Fuzzy Sets and Systems. 281:162-182. doi:10.1016/j.fss.2015.05.005S16218228

Parallelized particle filtering for freeway traffic state tracking

We consider parallelized particle filters for state tracking (estimation) of freeway traffic networks. Particle filters can accurately solve the state estimation problem for general nonlinear systems with non-Gaussian noises. However, this high accuracy may come at the cost of high computational demand. We present two parallelized particle filtering algorithms where the calculations are divided over several processing units (PUs) which reduces the computational demand per processing unit. Existing parallelization approaches typically assign sets of particles to PUs such that each full particle resides at one PU. In contrast, we partition each particle according to a partitioning of the network into subnetworks based on the topology of the network. The centralized case and the two proposed approaches are evaluated with a benchmark problem by comparing the estimation accuracy, computational complexity and communication needs. This approach is in general applicable to systems where it is possible to partition the overall state into subsets of states, such that most of the interaction takes place within the subsets. Keywords: Parallel particle filters, freeway traffic state tracking

Time-Varying Fractional-Order PID Control for Mitigation of Derivative Kick

In this thesis work, a novel approach for the design of a fractional order proportional integral derivative (FOPID) controller is proposed. This design introduces a new time-varying FOPID controller to mitigate a voltage spike at the controller output whenever a sudden change to the setpoint occurs. The voltage spike exists at the output of the proportional integral derivative (PID) and FOPID controllers when a derivative control element is involved. Such a voltage spike may cause a serious damage to the plant if it is left uncontrolled. The proposed new FOPID controller applies a time function to force the derivative gain to take effect gradually, leading to a time-varying derivative FOPID (TVD-FOPID) controller, which maintains a fast system response and significantly reduces the voltage spike at the controller output. The time-varying FOPID controller is optimally designed using the particle swarm optimization (PSO) or genetic algorithm (GA) to find the optimum constants and time-varying parameters. The improved control performance is validated through controlling the closed-loop DC motor speed via comparisons between the TVD-FOPID controller, traditional FOPID controller, and time-varying FOPID (TV-FOPID) controller which is created for comparison, with all three PID gain constants replaced by the optimized time functions. The simulation results demonstrate that the proposed TVD-FOPID controller not only can achieve 80% reduction of voltage spike at the controller output but also is also able to keep approximately the same characteristics of the system response in comparison with the regular FOPID controller. The TVD-FOPID controller using a saturation block between the controller output and the plant still performs best according to system overshoot, rise time, and settling time

Distributed Fuzzy and Stochastic Observers for Nonlinear Systems

Many problems in decision making, control, and monitoring require that all variables of interest, usually states and parameters of the system, are known at all times. However, in practical situations, not all variables are measurable or they are not measured due to technical or economical reasons. Therefore, these variables need to be estimated using an observer, based on a model of the system and measured data. For such a purpose, dynamic systems are often modeled in the state space framework, using a state transition model, which describes the evolution of the states over time; and a measurement model, which relates the measurements to the states. In some cases, these models also consider random external disturbances influencing the process. While for linear systems several solutions to estimate the unknown variables exist, state estimation for general nonlinear systems still represents a challenge. This thesis develops efficient observer design methods for nonlinear systems. Two types of systems are considered: deterministic nonlinear systems, represented by Takagi-Sugeno (TS) fuzzy models, and stochastic systems. For a large-scale or time-varying system, the design and tuning of an observer may be complicated and may involve large computational costs. By taking into account the specific properties of the system (such as cascaded, distributed, or time-varying), the observer design becomes easier and the computational costs are reduced. In the first part of the thesis, we consider nonlinear systems represented by TS fuzzy models, and investigate three system structures: cascaded systems, distributed systems, and systems affected by unknown disturbances. The motivation for investigating the cascaded and distributed structures comes from large scale systems. Many large-scale systems, such as power networks, material processing systems, communication and transportation networks are composed of interconnected lower dimensional subsystems. An important class of these systems can be represented as a cascade of subsystems. We study the cascade of nonlinear systems represented by TS fuzzy models. For cascaded TS systems with normalized membership functions we prove that the stability of the subsystems implies the stability of the cascade. Therefore, the stability analysis of a cascaded TS system may be performed by analyzing the individual subsystems. This approach is also extended to observer design. In order to design observers for the cascaded TS system it is sufficient to design observers for the subsystems. We also show that a cascaded design does not lead to the loss of performance in the terms of the estimation error decay rate. Therefore, the cascaded approach reduces the computational costs, while preserving the performance of the observer. In order to determine whether a nonlinear system is a cascade of subsystems, we give an algorithm that partitions a nonlinear system into cascaded subsystems. However, large-scale systems are in general not cascaded, but distributed, i.e., the influence among the subsystems is not unidirectional. In addition, the structure is often not fixed, i.e., subsystems may be added or removed on-line. For such systems, decentralized analysis and design present several advantages, such as flexibility and easier analysis. Therefore, we consider the stability analysis and observer design for distributed systems where each subsystem is represented by a TS fuzzy model. The conditions previously obtained for cascaded TS systems are extended to distributed TS systems. We analyze the stability of the overall TS system based on the stability of the subsystems, allowing that new subsystems may be added on-line. When the structure of the system is not fixed, the influence of the interconnection terms due to the addition of a new subsystem is not known before the subsystem is actually added. Moreover, even though the new subsystem is stable, the interconnection terms may have a destabilizing effect. Therefore, we derive conditions on the strength of the interconnection terms so that the stability of the overall system is maintained. Next, the approach is extended to observer design. We assume that a fuzzy observer is already designed for an existing subsystem or a collection of subsystems. When a new subsystem, together with the interconnection terms is added, a new observer is designed only for this subsystem. Since the already analyzed parts of the system or designed observers do not need to be analyzed or designed again, the computational costs are reduced. We also study TS systems that are influenced by unknown inputs (disturbances) or that change over time. The design of observers in the presence of unknown inputs is an important problem, since in many cases not all the inputs are known. The unknown inputs may also represent effects of actuator or plant component failures. Two types of inputs are considered in this thesis: model-plant mismatch and time-varying disturbances that can be represented as or approximated by polynomial functions of time. Based on the known part of the fuzzy model, we design observers that simultaneously estimate both the states and the unknown inputs. In case of a polynomial input, the observer guarantees an exponential convergence of the error to zero. When the input is only approximated by a polynomial function of time, a bound on the estimation error is derived. If the disturbance is due to a model mismatch, the true model is estimated, with an asymptotic convergence of the error to zero. In the second part of the thesis, we consider stochastic systems, and investigate the combination of different observers for cascaded stochastic systems. In many applications, in order to efficiently analyze the process or to efficiently design observers, one also has to consider the noise that is affecting the states or the measurements. In such cases, probabilistic estimation methods have to be used. The most well-known of these are the Kalman filter (KF), its nonlinear variants, the extended and unscented KF, and particle filters (PFs). We consider combinations of KFs for stochastic systems that are cascades of subsystems. We compare cascaded and centralized KFs both from a theoretical point of view and on simulation examples. If the KFs are designed independently for the subsystems, the individual KFs are optimal for the subsystems. Our theoretical results show that the cascaded KFs are jointly optimal and therefore have the same performance as a centralized KF for all possible inputs and outputs if and only if the subsystems are decoupled. However, simulation results indicate that for practical purposes, the performance of the centralized and cascaded KFs is comparable. We also compare cascaded and centralized stochastic observers on two real-world applications, namely the estimation of the overflow losses in a hopper dredger and the estimation of the model parameters in a water treatment plant. In both cases, the models are nonlinear and non-Gaussian, and the states of interest are not measurable. By employing the cascaded approach, an unscented KF and a PF are combined to obtain a better estimate of the overflow losses in a hopper dredger. In the second application, PFs are used in cascade to estimate the model parameters in a water treatment plant. In both cases, the cascaded filters are easier to tune and yield better estimation results than a centralized filter, with reduced computational costs. The thesis closes with some concluding remarks and a discussion on important open issues regarding the approaches studied. Additionally, some fundamental unsolved issues in state estimation are discussed, and promising research directions to address these issues are suggested.Delft Center for Systems and ControlMechanical, Maritime and Materials Engineerin

Stability of Cascaded Fuzzy Systems and Observers

A large class of nonlinear systems can be well approximated by Takagi-Sugeno (TS) fuzzy models with linear or affine consequents. It is well known that the stability of these consequent models does not ensure the stability of the overall fuzzy system. Therefore, several stability conditions have been developed for TS fuzzy systems. We study a special class of nonlinear dynamic systems that can be decomposed into cascaded subsystems, which are represented as TS fuzzy models. We analyze the stability of the overall TS system based on the stability of the subsystems and prove that the stability of the subsystems implies the stability of the overall system. The main benefit of this approach is that it relaxes the conditions imposed when the system is globally analyzed, thereby solving some of the feasibility problems. Another benefit is that by using this approach, the dimension of the associated linear matrix inequality (LMI) problem can be reduced. For naturally distributed applications, such as multiagent systems, the construction and tuning of a centralized observer may not be feasible. Therefore, we also extend the cascaded approach to the observer design and use fuzzy observers to individually estimate the states of these subsystems. A theoretical proof of stability and simulation examples are presented. The results show that the distributed observer achieves the same performance as the centralized one, while leading to increased modularity, reduced complexity, lower computational costs, and easier tuning. Applications of such cascaded systems include multiagent systems, distributed process control, and hierarchical large-scale systems.Delft Center for Systems and ControlMechanical, Maritime and Materials Engineerin