Benchmark Control Problem Research Articles

An Efficient Chicken Search Optimization Algorithm for the Optimal Design of Fuzzy Controllers

A proposed architecture to design the optimal parameters of Membership Functions (MFs) of Type-1 Fuzzy Logic Systems (T1FLSs) using the Chicken Search Optimization (CSO) is applied to three Fuzzy Logic Controllers (FLCs) in this paper. Two types of MFs are considered in the study: triangular and trapezoidal ones. The performance and efficiency of the CSO algorithm are particularly good when perturbations are added during the execution in each control problem. Two benchmark control problems: Water Tank Controller and Inverted Pendulum Controller are considered for testing the proposed approach. Also, the optimal design of a fuzzy controller for trajectory tracking of an Autonomous Mobile Robot (AMR) is considered to test the CSO. The main goal is to highlight the efficiency of CSO algorithm in finding optimal fuzzy controllers of non-linear plants. Two types of perturbations are considered in each control problem. Results show that the CSO algorithm presents excellent results in the field of Fuzzy Logic Controllers. Two types of Fuzzy Inference Systems: Takagi-Sugeno and Mamdani FLSs, are implemented in this paper. The most important metrics usually applied in control are used in this paper, such as: Integral Time Absolute Error (ITAE), Integral Time Squared Error (ITSE), Integral Absolute Error (IAE), Integral Square Error (ISE), Mean Square Error (MSE), and Root Mean Square Error (RMSE).

Load balancing and neural dynamic model to optimize replicator dynamics controllers for vibration reduction of highway bridge structures

Earthquakes cause irreparable damages to the built environment, which has led bridge engineers to develop structural control systems to mitigate damage and improve vibration reduction in real-time. Among control systems, base isolation is one of the most commonly used passive control strategies for seismic protection of civil structures. Yet, it lacks real-time adaptability, has lower energy dissipation, and poor performance during near-fault earthquakes. To overcome these limitations, a hybrid control system comprised of semi-active magneto-rheological (MR) dampers and passive base isolation bearings is installed at the deck and piers for vibration reduction of highway bridge structures. This paper, inspired by evolutionary game theory and artificial intelligence, proposes data-driven replicator dynamic control algorithms to distribute the command voltage to the current driver of the semi-active MR dampers. It incorporates a load balancing strategy to reallocate additional resources. To achieve a high-performance design of the game-theory-inspired controllers, a patented neural dynamic model is used to optimize the control parameters. The evaluation of the proposed methodology uses a benchmark control problem based on the 91/5 highway bridge in Southern California subjected to near-field earthquake accelerograms. The performance of five different proposed controllers is compared with conventional Lyapunov and fuzzy logic control algorithms using 21 performance criteria. Results show the load balancing capability of the proposed control algorithms to mitigate the vibrations experienced by the bridge structure and further increase the durability of semi-active devices. The novelty of the methodology impacts how game-theory controllers make control decisions among multiple devices in engineering problems.

Late‐lumping fuzzy boundary geometric control of nonlinear partial differential systems

SummaryIn this article, a fuzzy boundary geometric controller that stabilizes a class of nonlinear distributed parameter systems (DPSs) is proposed. The design procedure relies on the use of Takagi‐Sugeno (T‐S) type fuzzy partial differential equation (PDE) model, which approximates the dynamical behavior of the nonlinear DPS. The T‐S fuzzy PDE model is constructed through “fuzzy blending” of local linear PDE models of infinite characteristic indexes. This is a challenging task in the design procedure of fuzzy PDE model‐based boundary controller in the framework of the well‐established geometric control theory. To overcome this constraint, it is proposed in this article to resort to the concept of extended operator in order to transform the T‐S fuzzy PDE model with boundary control to an equivalent fuzzy PDE model with punctual control and finite characteristic index. Based on the developed fuzzy model, a fuzzy boundary geometric controller is derived and sufficient conditions of exponential stability of the resulting closed‐loop system are established by employing the Lyapunov direct method. The stabilizing performance of the proposed fuzzy PDE model‐based boundary geometric controller is evaluated on benchmark control problems and compared with other existing control methods via numerical simulations.

On the Linear Convergence of Random Search for Discrete-Time LQR

Model-free reinforcement learning techniques directly search over the parameter space of controllers. Although this often amounts to solving a nonconvex optimization problem, for benchmark control problems simple local search methods exhibit competitive performance. To understand this phenomenon, we study the discretetime Linear Quadratic Regulator (LQR) problem with unknown state-space parameters. In spite of the lack of convexity, we establish that the random search method with two-point gradient estimates and a fixed number of roll-outs achieves E-accuracy in O(log (1/ϵ)) iterations. This significantly improves existing results on the model-free LQR problem which require O(1/ϵ) total roll-outs.

Invariant extended Kalman filter on matrix Lie groups

We derive symmetry preserving invariant extended Kalman filters (IEKF) on matrix Lie groups. These Kalman filters have an advantage over conventional extended Kalman filters as the error dynamics for such filters are independent of the group configuration which, in turn, provides a uniform estimate of the region of convergence. The proposed IEKF differs from existing techniques in literature on the account that it is derived using minimal tools from differential geometry that simplifies its representation and derivation to a large extent. The filter error dynamics is defined on the Lie algebra directly instead of identifying the Lie algebra with an Euclidean space or defining the error dynamics in local coordinates using exponential map, and the associated differential Riccati equations are described on the corresponding space of linear operators using tensor algebra. The proposed filter is implemented for the attitude dynamics of the rigid body, which is a benchmark problem in control, and its performance is compared against a conventional extended Kalman filter (EKF). Numerical experiments support that the IEKF is computationally less intensive and gives better performance than the EKF.

A Reflective Framework for Performance Management (REFORM) of Real-Time Hybrid Simulation.

Currently, the lack of (1) a sufficiently integrated, adaptive, and reflective framework to ensure the safety, integrity, and coordinated evolution of a real-time hybrid simulation (RTHS) as it runs, and (2) the ability to articulate and gauge suitable measures of the performance and integrity of an experiment, both as it runs and post-hoc, have prevented researchers from tackling a wide range of complex research problems of vital national interest. To address these limitations of the current state-of-the-art, we propose a framework named Reflective Framework for Performance Management (REFORM) of real-time hybrid simulation. REFORM will support the execution of more complex RTHS experiments than can be conducted today, and will allow them to be configured rapidly, performed safely, and analyzed thoroughly. This study provides a description of the building blocks associated with the first phase of this development (REFORM-I). REFORM-I is verified and demonstrated through application to an expanded version of the benchmark control problem for real-time hybrid simulation.

Use of memristive chaotic signal as a desired trajectory for a two-link flexible manipulator using contraction theory based on a composite control technique

Flexible manipulators are being considered as bench mark control problem in the field of nonlinear dynamics. Many of their inherent advantages create challenges while dealing with the dynamics. Tracking control and vibration suppression are two main control problems considered. In this paper a composite controller is designed for the memristive chaotic system signal as trajectory tracking control of a two-link flexible robot manipulator. The dynamics of the flexible manipulator is modelled by using assumed modes method and divided into two subsystems using the singular perturbation technique. The subsystems are called as the slow subsystem involving rigid dynamics of the manipulator and the fast sub-system which incorporates flexible dynamics of the manipulator. Separate control techniques are designed for each subsystem. Contraction theory based controllers are designed for the slow sub-system and fast subsystem for fast trajectory tracking of signal of a memristive chaotic system and quick suppression of the link deflections. The simulation results confirm the better performances of the proposed composite technique.

Benchmark control problem for real-time hybrid simulation

Abstract This paper presents the problem definition and guidelines for a benchmark control problem in real-time hybrid simulation for a seismically excited building, to appear in a Special Issue of Mechanical Systems and Signal Processing. Benchmark problems have been especially useful in enabling a community of researchers to leap forward on a given topic, distill the lessons learned, and identify the capabilities and limitations of various approaches. The focus here is on the design of an effective transfer system displacement tracking controller which is a commonly used approach for ensuring that interface conditions between numerical and experimental substructures are satisfied. In this study, a laboratory model of a three-story steel frame is considered as the reference structure. Realistic numerical models are developed and provided to represent the numerical and experimental substructures and the transfer system, which is comprised of hydraulic actuation, sensing instrumentation, and control implementation hardware. Experimental components are identified and provided as Simulink models, which are executed in real-time using Simulink Desktop Real-Time capability to enable realistic virtual real-time hybrid simulation. The task of each participant of the Special Issue is to design, evaluate, and report on their proposed controller approaches using the numerical models and computational codes provided. Such approaches will be assessed for robustness and performance using the provided tools. This benchmark problem is expected to further the understanding of the relative merits, as well as provide a clear basis for evaluating the performance of various control approaches and algorithms for RTHS. To illustrate some of the design challenges, a sample control strategy employing a proportional-integral (PI) controller is included, in addition to the built-in control loop of the transfer system.

Lower order controller design using weighted singular perturbation approximation

Most of the analytical design procedures yield controllers of almost the same order as that of the plant. Resultantly, if the plant is of a high order, the controller obtained from these design procedures is also of a high order. The order of the controller should be practically acceptable for easy implementation. There are two indirect methods for designing a low order controller for high order plants: plant reduction and compensator reduction. In compensator reduction, the order of the controller designed for the original higher order plant is reduced. In plant reduction, the order of the plant is reduced for designing a lower order controller. The order of the controller or plant is reduced using model order reduction techniques. In this paper, we propose a hybrid algorithm (plant-compensator reduction) based on frequency-weighted singular perturbation approximation, which gives an improved performance as compared to existing algorithms. The proposed hybrid technique can be used with $H_{\infty}$, LQG, or any other loop shaping procedures to obtain a lower order controller. The proposed technique is validated on benchmark control problems.

Impedance matching control design for the benchmark problem in real-time hybrid simulation

Abstract This paper presents an application of impedance matching to the benchmark control problem in real-time hybrid simulation (RTHS). Impedance matching is conceptually different from conventional approaches to designing controllers for RTHS. Rather than view the transfer system merely as a device to realize prescribed boundary conditions between the virtual and physical substructures, the controller is designed to match the impedance of transfer system as closely as possible to that of the virtual substructure. Some of the key features of impedance matching are—(i) it does not explicitly require a tracking controller, greatly simplifying the control design process, (ii) control design is decoupled from the physical substructure (demonstrated in this paper by introducing nonlinearity in the physical substructure), (iii) the controller is easy to evaluate and implement, (iv) performance is less sensitive to the choice of partitioning configuration compared to provided sample controller, and (v) exhibits robust stability. Overall, controllers designed based on impedance matching are found to result in stable and accurate RTHS.

A study on a benchmark control problem for real-time hybrid simulation with a tracking error-based adaptive compensator combined with a supplementary proportional-integral-derivative controller

Abstract Real-time hybrid simulation (RTHS) is a reliable and cost-effective testing technique to evaluate the dynamic response of a structural system, especially when the system includes rate-dependent components. Numerous studies suggest that the stability and accuracy of a RTHS are governed by the tracking errors between the calculated displacements and measured displacements during the test. In this study, frequency domain-based error indicators were designed to quantify the tracking errors in real-time. Consequently, an adaptive two degree-of-freedom phase-lead compensator was introduced to cancel out the identified tracking errors. Additionally, a proportional-integral -derivative controller was included as a supplement to further improve the tracking performance. The details of how to design the combined outer-loop controller were provided. A benchmark control problem in RTHS was used to assess the performance and robustness of the designed controller by carrying out a series of virtual RTHS (vRTHS), where different force excitations, partitioning configurations, and plant uncertainties were considered in MATLAB Simulink. Nine evaluation criteria were used to quantify the results of the vRTHS in this study. As a result, the proposed combined outer-loop controller was shown to be effective and robust to provide good stability and accuracy in RTHS.

A high-speed interval type 2 fuzzy system approach for dynamic parameter adaptation in metaheuristics

Fuzzy dynamic adaptation of parameters in meta-heuristic algorithms has recently been shown to provide an improvement in efficiency with respect to meta-heuristic algorithms with static parameters. However, executing a fuzzy inference in each iteration represents an increase in the computational cost, and this is even more critical in the case of using Type-2 Fuzzy Logic systems. On the other hand, fuzzy dynamic adaptation with Type-2 Fuzzy Logic has shown better performance when compared with respect to Type-1 Fuzzy Logic in diverse areas of application; therefore, the goal of this paper is aimed at reducing the computational cost of Type-2 Fuzzy Logic processing for dynamic adaptation of parameters in meta-heuristic algorithms. To reduce the computational cost of processing the Interval Type-2 Fuzzy system for dynamic adaptation of metaheuristic parameters, the use of an approximation to the Continuous Karnik–Mendel method (CEKM) is proposed. The proposed approach provides an analytical approximation to the CEKM method, in this way reducing the computational cost of evaluating the Interval Type-2 Fuzzy System. The performance of the proposed approach was tested with five benchmark functions and with one benchmark control problem. The proposed approach was tested with two different meta-heuristic algorithms, the Differential Evolution algorithm (DE) and the Harmony Search algorithm (HS), in both cases achieving a reduction in the computational cost, while maintaining the performance with respect to the Type-2 Dynamic adaptation of parameters with the conventional type reduction methods.

Dynamic parameter adaptation in the harmony search algorithm for the optimization of interval type-2 fuzzy logic controllers

At the present time there are several types of metaheuristics which have been used to solve various types of problems in the real world. These metaheuristics contain parameters that are usually fixed throughout the iterations. However, various techniques exist to adjust the parameters of an algorithm such as probabilistic, fuzzy logic, among others. This work describes the methodology and equations for building Triangular and Gaussian interval type-2 membership functions, and this methodology was applied to the optimization of a benchmark control problem with an interval type-2 fuzzy logic controller. To validate in the best way the effect of uncertainty we perform experiments using noise (Pulse generator) and without noise. Also, a statistical z-test is presented to verify the effectiveness of the proposed method. The main contribution of this article is the proposed use of the theory of interval type-2 fuzzy logic to the dynamic adjustment of parameters for the harmony search algorithm and then its application to the optimal design of interval type-2 fuzzy logic controller.

Water Pump Control: A Hybrid Data-Driven and Model-Assisted Active Disturbance Rejection Approach

Water pump control, prevalent in various industrial plants, such as wastewater treatment and steam generator facilities, plays a significant role in maintaining economic efficiency and stable plant operation. Due to its slow dynamics, strong nonlinearity, and various disturbances, it is also widely studied as a typical benchmark problem in process control. The current control strategies can be categorized into two aspects: one branch resorts to model-based design and the other to data-driven design. To merge the merits and overcome the deficiencies of each paradigm, this paper proposes a hybrid data-driven and model-assisted control strategy, namely modified active disturbance rejection control (MADRC). The model information regarding water dynamics is incorporated into an extended state observer (ESO), which is used to estimate and mitigate the limitations of slow dynamics, strong nonlinearity, and various disturbances by analyzing the real-time data. The tuning formula is given in terms of the desired closed-loop performance. It is shown that MADRC is able to produce a satisfactory control performance while maintaining a low sensitivity to the measurement noise under general parametric setting conditions. The simulation results verify the clear superiority of MADRC over the proportional-integral (PI) controller and the conventional ADRC, and the results also evidence its noise reduction effects. The experimental results agree well with the simulation results based on a water tank setup. The proposed MADRC approach is able to improve the control performance while reducing the actuator fluctuation. The results presented in this paper offer a promising methodology for the water control loops widely used in the water industry.

JSAE-SICE benchmark problem for vehicle dynamics control

Recently many new types of small vehicles for future urban societies have been proposed and developed. Such small vehicles tends to have reduced stability and handling ability than conventional vehicles because of their lighter weight and reduced tire performance. To cope with this problem by active collaboration of Japanese academia and industries, a benchmark problem of designing vehicle control logic for an articulated In-Wheel-Motor vehicle was settled by Japanese society of automotive industries and academia. For this purpose, simulation models of the new vehicle using multi-physics acausal modeling language Modelica were provided from the industry side. Challengers were requested to design controllers of tire steering angle, tire camber angle and tire driving force to satisfy requested vehicle dynamic characteristics. There also were some restrictions about the range of actuators. Four test scenarios were given to evaluate the control performance. Many challengers from Japanese Universities have tackled with this benchmark problem. Some results of their researches are also introduced in this paper.

A model-based approach for design and verification of Industrial Internet of Things

This investigation presents an Industrial Internet of Things (IIoT) architecture and a Model-Based Engineering (MBE) approach for design, verification, and auto-code generation of control applications in process industries. The IIoT architecture describes the hardware components, communication modules, and software. It emerges as a major enabler for providing open connectivity to process industry which provides greater data-aggregation, visibility, availability, flexible control, and cloud-connectivity. The MBE approach is based on multiple views of the systems with each domain model describing a particular view. The multi-view modelling approach is used to perform design and verification of the IIoT enabled control in process industries. We show that such an integration of MBE, cloud-computing, and IIoT provides certain desirable features such as plug-and-play control and on-the fly verification which are lacking in the process industry. The proposed MBE approach and IIoT architecture are illustrated on the quadruple tank process, a benchmark problem in control. Our deployment results verify the benefits envisaged by IIoT, cloud, and MBE integration.

Comparative Study in Fuzzy Controller Optimization Using Bee Colony, Differential Evolution, and Harmony Search Algorithms

This paper presents a comparison among the bee colony optimization (BCO), differential evolution (DE), and harmony search (HS) algorithms. In addition, for each algorithm, a type-1 fuzzy logic system (T1FLS) for the dynamic modification of the main parameters is presented. The dynamic adjustment in the main parameters for each algorithm with the implementation of fuzzy systems aims at enhancing the performance of the corresponding algorithms. Each algorithm (modified and original versions) is analyzed and compared based on the optimal design of fuzzy systems for benchmark control problems, especially in fuzzy controller design. Simulation results provide evidence that the FDE algorithm outperforms the results of the FBCO and FHS algorithms in the optimization of fuzzy controllers. Statistically is demonstrated that the better errors are found with the implementation of the fuzzy systems to enhance each proposed algorithm.

Fuzzy Dynamic Parameter Adaptation in the Harmony Search Algorithm for the Optimization of the Ball and Beam Controller

This paper presents a method for dynamic parameter adaptation in the harmony search algorithm (HS) based on fuzzy logic. The adaptation is performed using Type 1 (FHS), interval Type 2 (IT2FHS), and generalized Type 2 (GT2FHS) fuzzy systems as the number of improvisations or iterations advances, achieving a better intensification and diversification. The main contribution of this work is the dynamic parameter adaptation using different types of fuzzy systems in the harmony search algorithm applied to optimization of the membership functions for a benchmark control problem; in this case it is focused on the ball and beam controller. Experiments are presented with the HS, FHS, IT2FHS, and GT2FHS with noise (uniform random number) and without noise for the controller, and the following error metrics are obtained: ITAE, ITSE, IAE, ISE, and RMSE, to validate the efficacy of the proposed methods.

Fuzzy Dynamic Parameter Adaptation in ACO and PSO for Designing Fuzzy Controllers: The Cases of Water Level and Temperature Control

A novel approach applied to Particle Swarm Optimization (PSO) and Ant Colony Optimization is presented. The main contribution of this work is the use of fuzzy systems to dynamically update the parameters for the ACO and PSO algorithms. In the case of ACO, two fuzzy systems are designed for the Ant Colony System (ACS) algorithm variant. The first system adjusts the value for the pheromone evaporation parameter from the global pheromone trail update equation and the second system adjusts the values for the pheromone evaporation parameter from the local pheromone trail update equation. In the case of PSO, a fuzzy system is designed to find the values for the inertia weight parameter from the velocity equation. Fuzzy logic controllers (FLCs) are optimized with ACO and PSO, respectively, to prove the performance of the proposed approach. The particular benchmark problems considered to test the proposed methods are the water level control in a tank and temperature control in a shower. Therefore, PSO and ACO algorithms are applied in the optimization of the parameters of the FLCs. The achievement of the proposed fuzzy ACO and PSO algorithms is compared with the original results of each benchmark control problem.

Nonlinear finite element modeling of vibration control of plane rod-type structural members with integrated piezoelectric patches

This paper addresses modeling and finite element analysis of the transient large-amplitude vibration response of thin rod-type structures (e.g., plane curved beams, arches, ring shells) and its control by integrated piezoelectric layers. A geometrically nonlinear finite beam element for the analysis of piezolaminated structures is developed that is based on the Bernoulli hypothesis and the assumptions of small strains and finite rotations of the normal. The finite element model can be applied to static, stability, and transient analysis of smart structures consisting of a master structure and integrated piezoelectric actuator layers or patches attached to the upper and lower surfaces. Two problems are studied extensively: (i) FE analyses of a clamped semicircular ring shell that has been used as a benchmark problem for linear vibration control in several recent papers are critically reviewed and extended to account for the effects of structural nonlinearity and (ii) a smart circular arch subjected to a hydrostatic pressure load is investigated statically and dynamically in order to study the shift of bifurcation and limit points, eigenfrequencies, and eigenvectors, as well as vibration control for loading conditions which may lead to dynamic loss of stability.