Controller Design Problem Research Articles

Adaptive fixed-time fuzzy control for delayed recycling continuous stirred tank reactor with asymmetric time-varying full-state constraints

Recently, there are some results concerning stability and finite-time stability control for continuous stirred tank reactors (CSTR). However, when considering the control of time-delay CSTR systems or fixed-time stability of CSTR systems, there are relatively few articles involved. In this paper, we first consider the CSTR system that includes both of the above factors simultaneously, that is, the adaptive fixed-time fuzzy control design problem for a CSTR with a delayed recycle stream and asymmetric time-varying full-state constraints. Firstly, based on existing works, we present an improved practical fixed-time stability criterion, which can be applied to more complex nonlinear systems. Then, we construct time-varying asymmetric integral barrier Lyapunov functions to handle asymmetric time-varying full-state constraints. Next, fuzzy logic systems are used to approximate the unknown functions of the system, and a sliding mode differentiator is introduced to avoid the “explosion of complexity” of the time derivative of the virtual controller. Furthermore, using the improved practical fixed-time stability criterion, we present the adaptive fixed-time fuzzy controller design processes that can ensure tracking performance in a fixed-time, and states of the system never violate their constraint bounds. Finally, a simulation example is provided to verify the effectiveness of the proposed control strategy.

A Data-driven Modeling and Control Method for CO2 Expanding Tobacco Production Line

Abstract An expanded tobacco production line is a typical industrial process with a large time lag, nonlinearity and time-varying nature. Aiming at the controller design problem of this industrial process, this paper proposes a control scheme that adopts the Dalin control algorithm based on a data-driven model. The scheme first regards the industrial process of expanding tobacco as a dynamic object that can be linearized near the working point, then calculates the parameters of the dynamic linearized model by using the Kaczmarz projection algorithm, and finally obtains the controller parameters according to the Dahlin control algorithm. The simulation and calculation results show that the scheme can extract an effective data-driven model from the production data and design reliable controller parameters.

Chaotic-Based Improved Henry Gas Solubility Optimization Algorithm: Application to Electric Motor Control

This study presents a novel meta-heuristic optimization method that combines the Henry Gas Solubility Optimization (HGSO) technique with symmetric chaotic systems. By leveraging the randomness of chaotic systems, the parameters of the HGSO algorithm that require random generation are produced through chaotic processes, allowing the algorithm to exhibit chaotic behavior in its pursuit of optimal values. This innovative approach is termed Chaotic Henry Gas Solubility Optimization (CHGSO), with the primary objective of enhancing the performance of the HGSO method. The randomness of the data obtained from chaotic systems was validated using NIST-800-22 tests. The CHGSO method was applied to both 47 benchmark functions and the optimization of parameters for a PID controller utilized in the speed control of a DC motor. To evaluate the effectiveness of the proposed method, it was compared with several widely recognized algorithms in the literature, including PSO, WOA, GWO, EA, SA, and the original HGSO algorithm. The results demonstrate that the proposed method achieved the best performance in 43 of the benchmark functions, outperforming the other algorithms. In the context of controller design, the PID parameters were optimized using the error-based ITSE objective function. According to the controller responses, the proposed method has achieved the best results in the simulation studies, with a settling time of 0.035 and a rise time of 0.014 without overshooting, and in the experimental studies, with a settling time of 0.15 and a settling time of 1.4%. When the results are examined, it is observed that it has achieved successful results in the controller design problem.

A directional-performance control design for articulated heavy vehicles with extendable-trailers

Articulated heavy vehicles (AHVs) with extendable-trailers cost-effectively transport freight under varying operating conditions, and they are well-suited for delivering cargos with varying sizes. These AHVs face a challenging issue of varying performance in steady-state handling characteristics, lateral-stability, and manoeuvrability under various conditions. To address this issue, a control design with a fuzzy-PID (proportional, integral, and derivative) controller-based differential-braking system is proposed to improve the directional-performance of these AHVs. To examine the varying performance of a tractor/semi-trailer with extendable-trailer, simulations are conducted. Built upon the knowledge gained from the simulations, the control design problem is formulated; the control design is then evaluated using co-simulations in a Matlab/Simulink-TruckSim environment. The co-simulations demonstrate the effectiveness of the proposed control design.

Event-triggered fuzzy adaptive control for a class of MIMO discrete-time nonlinear systems with uncertain control gains

ABSTRACT An event-triggered output control technique is devised for the output anticipated trajectory tracking controller design problem for a class of unknown multiple-input-multiple-output (MIMO) discrete-time nonlinear systems. A parameterized state observer is established to estimate the non-measurable states accurately by utilizing the filter states and the gradient-based fuzzy parameter updated laws. A series of fuzzy filters are proposed to evaluate the immeasurable states, and a filter state observer is constructed to overcome the state estimation that is triggered by the unknown control gains and the coupling of control input. One non-zero parameter is added to a fuzzy logic system (FLS) to reduce the computed burden of the controller with several updating laws. A FLS with one non-zero parameter is introduced to reduce the calculated burden of the controller with fewer updating laws. The proposed method reduces the computed burden and communication consumption while realizing the immeasurable state estimations, guaranteeing the ultimately uniformly bounded (UUB) of the closed-loop system, and achieving a good tracking impact. Finally, simulation analyses are used as a numerical example to confirm that the proposed control strategy is valid.

Strategy for obtaining robust solutions in multi-objective design with uncertainties

This paper proposes a novel definition of robustness for multi-objective optimization problems. This definition underpins an innovative strategy for obtaining robust solutions in the presence of uncertainty; it involves formulating the cost function under uncertainties as conflicting objectives during optimization. This approach aims to define the decision vectors that are not dominated in all scenarios simultaneously by any other. These solutions exhibit both optimality and robustness properties, aligning with conventional and unconventional multi-objective methods. This approach enables the implicit definition of the Pareto-optimal solutions for each scenario and robust solutions that optimize performance in worst-case scenarios. Additionally, the set of robust solutions that optimize the global performance concerning the utopian points of all uncertainty scenarios is also defined.To demonstrate the effectiveness of this method, this paper addresses two control design problems. The first example, a first-order process, illustrates the advantages and aspects of the optimization strategy. The second problem, multi-loop temperature control design of a proton exchange membrane fuel cell stack, is a more complex engineering problem involving results from previous research.

Observer-based control for time-delayed quasi-one-sided Lipschitz nonlinear systems under input saturation

This paper addresses the observer-based controller design problem for nonlinear time-delayed systems under input saturation. The nonlinearities are supposed to satisfy the quasi-one-sided Lipschitz condition, which is less conservative than the one-sided Lipschitz condition. Based on the nonlinear matrix inequalities, control law for nonlinear systems subject to input saturation, time delays, and unavailable states, some sufficient conditions have been developed for an augmented system containing the system state vector and the error vector to ensure the convergence of all states to zero. The paper used a decoupling approach to reduce the complexity of the corresponding observer and controller gain computations. Finally, the effectiveness of the developed results is validated using suitable examples.

Relaxed conditions for parameterized linear matrix inequality in the form of nested fuzzy summations

The aim of this study is to investigate less conservative conditions for parameterized linear matrix inequalities (PLMIs) that are formulated as nested fuzzy summations. Such PLMIs are commonly encountered in stability analysis and control design problems for Takagi-Sugeno (T-S) fuzzy systems. Utilizing the weighted inequality of arithmetic and geometric means (AM-GM inequality), we develop new, less conservative linear matrix inequalities for the PLMIs. This methodology enables us to efficiently handle the product of membership functions that have intersecting indices. Through empirical case studies, we demonstrate that our proposed conditions produce less conservative results compared to existing approaches in the literature.

Feedback control for plants with time delay

Abstract The paper considers the problem of feedback control design for plants with time delay. The role of the feedback is presented showing its ability to restrict the uncertainty in the plant model. The conditional feedback control structure is introduced and its properties for restricting model uncertainty are discussed. The presence of local feedback makes the conditional feedback structure pertinent for its usage when the plant contains a time delay element. The time delay model is replaced by its Pade series approximation. The key idea is to consider the time delay model as perturbation around its Pade series approximation. This fact allows utilizing the rational function expression in the procedure of controller design, thus avoiding using the irrational function of the time delay for this purpose. It is shown that the conditional feedback control structure gives an alternative than the Smith predictor method for controller design of plants with time delay e −θs in their structure. The efficiency of the presented method is demonstrated by a numerical example.

Polynomial Fuzzy Observer-Based Feedback Control for Nonlinear Hyperbolic PDEs Systems.

This article explores the observer-based feedback control problem for a nonlinear hyperbolic partial differential equations (PDEs) system. Initially, the polynomial fuzzy hyperbolic PDEs (PFHPDEs) model is established through the utilization of the fuzzy identification approach, derived from the nonlinear hyperbolic PDEs model. Various types of state estimation and controller design problems for the polynomial fuzzy PDEs system are discussed concerning the state estimation problem. To investigate the relaxed stability problem, Euler's homogeneous theorem, Lyapunov-Krasovskii functional with polynomial matrices (LKFPM), and the sum-of-squares (SOSs) approach are adopted. The exponential stabilization condition is formulated in terms of the spatial-derivative-SOSs (SD-SOSs). Additionally, a segmental algorithm is developed to find the feasible solution for the SD-SOS condition. Finally, a hyperbolic PDEs system and several numerical examples are provided to illustrate the validity and effectiveness of the proposed results.

ROBUST OUTPUT FEEDBACK CONTROL FOR HETEROGENEOUS AUTONOMOUS VEHICLE PLATOONS

An heterogeneous vehicle platoon controller for autonomous vehicles is proposed in this paper. The traction force of each vehicle is controlled according to the state of the predecessor vehicle, which can be known by LiDAR/RADAR, and the state of the leader vehicle, which is received by vehicle-to-vehicle (V2V) communication. Platoon string stability is evaluated under Lyapunov and H8 conditions. An iterative procedure is proposed in order to deal with the non-convexity of the static output feedback control design problem. Simulation results demonstrate that the proposed heterogeneous vehicle platoon controller achieves a good overall performance without compromising the safety of any vehicle. The separation between each follower and its predecessor is kept in appropriate ranges, always close to the desired reference. Furthermore, the transient errors are not amplificated when propagated downstream the platoon, therefore string stability is assured. Keywords: Autonomous vehicles, heterogeneous vehicle platoon, vehicle platoon control, string stability, output feedback control, robust control, Linear Matrix Inequality

A Gradient Dynamics-Based Singularity Avoidance Method for Backstepping Control of Underactuated TORA Systems.

In this paper, a gradient dynamics-based control method is proposed to directly tackle the singularity problem in the backstepping control design of the TORA system. This method is founded upon the construction of an energy-like positive function, which includes an auxiliary variable in terms of the intermediate virtual control law. On this basis, a gradient dynamics is created to obtain a new virtual control command, which is capable of making the auxiliary variable gradually approach zero, thereby mitigating the issue of division by zero. The core innovation is the integration of the gradient dynamics into the recursive backstepping design to overcome the singularity problem and stabilize the system at the equilibrium quickly. In addition, it rigorously proves that all the signals in the closed-loop control system are uniformly ultimately bounded, and the tracking errors converge to a small neighborhood around zero through a Lyapunov-based stability analysis. Comparative simulations demonstrate that the proposed approach not only avoids the singularity issue, but also achieves a better transient performance over other methods.

Protocol-based secure guaranteed cost control of sampled-data T-S fuzzy system with denial-of-service attack and input saturation

This paper proposes a protocol-based secure guaranteed cost sampled-data controller design problem of Takagi-Sugeno (T-S) fuzzy system under denial-of-service (DoS) attack and input saturation. First, in the absence of an effective description for the characteristics of received signals on controller, a novel scheduling protocol is proposed according to the characteristics of the round-robin protocol and DoS attack, which can guarantee the specific sequence characteristic for control updates. Then, via introducing input delay approach and switched system modeling method, a time-delay switched system with fixed switching sequence is introduced to describe the considered system with DoS phenomenon. Moreover, some novel control criteria are presented to ensure the resulting closed-loop system reaches a required cost level under the obtained control law. And an optimization problem is proposed to compute the optimal upper of the specified cost level. Finally, a simulation example is presented to demonstrate the effectiveness of the algorithm.

Practical output regulation of uncertain Euler–Lagrange systems

This paper deals with the problem of robust output regulation of uncertain Euler–Lagrange systems. An internal model controller is synthesized by a systematic framework that considers polynomial mappings of the steady-state trajectory. The closed-loop stabilization is guaranteed by using a descriptor differential–algebraic representation of the system. This methodology allows the controller design problem to be cast as a convex optimization problem subject to linear matrix inequalities. Simulations considering a two-link robotic manipulator illustrate the method.

State Observer-Based Iterative Learning Control Design for Discrete Systems Using the Heavy Ball Method

The paper considers a state observer-based iterative learning control design problem for discrete linear systems. To accelerate the convergence of the learning error, a combination of the heavy ball method from optimization theory and the vector Lyapunov function method for a class of two-dimensional systems known as repetitive processes is used to develop a new design. A supporting numerical example is given, including a comparison with an existing design.

Anti-Disturbance Bumpless Transfer Control for a Switched Systems via a Switched Equivalent-Input-Disturbance Approach

This paper concentrates on the issue of anti-disturbance bumpless transfer (ADBT) control design for switched systems. The ADBT control design problem refers to designing a continuous controller and a switching rule to ensure the switched system satisfies the ADBT property. First, the concept of the ADBT property is introduced. Then, via a switched equivalent-input-disturbance (EID) methodology, a switched EID estimator is formulated to estimate the impact of external disturbances within the switched system. Second, a bumpless transfer control is then constructed via a compensator integrating an EID estimation. Finally, the effectiveness of the presented control scheme is verified by controlling a switching resistor–inductor–capacitor circuit on the Matlab platform. Above all, a new configuration for ADBT control of switched systems is established via a switched EID methodology.

LQR controller performance via particle swarm optimization and neural networks

AbstractThe inverted pendulum‐cart (IPC) control problem has long been a benchmark in the field of control systems due to its inherent instability and nonlinear dynamics. The linear quadratic regulator (LQR) control technique has been proven to be effective in stabilizing the inverted pendulum; however, the challenge lies in finding the optimal control gains that provide the best performance. This article presents a method to address the LQR control design problem for the IPC system which is compared against a particle swarm optimization based LQR and a neural network optimized LQR. The method provides a deterministic approach to finding the weighing matrices Q and R in accordance with the time domain characteristics chosen by the designer, such as settling time and maximum peak overshoot. Results from MATLAB simulations indicate that the suggested strategy has good performance.

Indirect adaptive observer control (I-AOC) design for truck–trailer model based on T–S fuzzy system with unknown nonlinear function

Tracking is a crucial problem for nonlinear systems as it ensures stability and enables the system to accurately follow a desired reference signal. Using Takagi–Sugeno (T–S) fuzzy models, this paper addresses the problem of fuzzy observer and control design for a class of nonlinear systems. The Takagi–Sugeno (T–S) fuzzy models can represent nonlinear systems because it is a universal approximation. Firstly, the T–S fuzzy modeling is applied to get the dynamics of an observational system in order to estimate the unmeasurable states of an unknown nonlinear system. There are various kinds of nonlinear systems that can be modeled using T–S fuzzy systems by combining the input state variables linearly. Secondly, the T–S fuzzy systems can handle unknown states as well as parameters known to the indirect adaptive fuzzy observer. A simple feedback method is used to implement the proposed controller. As a result, the feedback linearization method allows for solving the singularity problem without using any additional algorithms. A fuzzy model representation of the observation system comprises parameters and a feedback gain. The Lyapunov function and Lipschitz conditions are used in constructing the adaptive law. This method is then illustrated by an illustrative example to prove its effectiveness with different kinds of nonlinear functions. A well-designed controller is effective and its performance index minimizes network utilization—this factor is particularly significant when applied to wireless communication systems.

RL-based adaptive control for a class of non-affine uncertain stochastic systems with mismatched disturbances

This paper investigates the reinforcement learning (RL) adaptive tracking control design problem for a class of mismatched stochastic nonlinear systems with non-affine structure. The stochastic system studied in this paper is more generally representative due to the presence of non-affine inputs, internal uncertainties, and mismatched external disturbances. Firstly, in order to solve the non-affine structure of stochastic systems, an extended stochastic differential equation is constructed. Based on the actor–critic framework, by generating reinforcement signals, the network is stimulated to evolve more quickly towards the desired direction, while compensating internal uncertainties and induced uncertainties in the stochastic system. Furthermore, aiming at the approximation errors and external disturbances, while satisfying stochastic stability, the adaptive laws for disturbances boundary estimator are established with the usage of higher powers of tracking errors. As a result, a novel non-affine adaptive tracking controller has been proposed by integrating RL, disturbances boundary estimation, and dynamic surface method. Through the stability analysis, it is proved that all closed-loop signals are bounded in probability, and the system output converges to a small neighborhood near the desired trajectory. Numerical simulations demonstrate the effectiveness and superiority of the proposed controller.

Adaptive event-triggered optimal [formula omitted] tracking control for uncertain nonlinear systems: Comparative analysis applied to autonomic tractor-trailer system

In this paper, an event-triggered tracking optimization control method is proposed for nonlinear uncertain systems with H∞ discounted cost. First, the linearization method using the infinite series expansion theorem is given. And the tracking control design problem is solved by appropriate state augment. Secondly, the zero sum differential game strategy is introduced to address the control design problem of uncertain systems with event-triggered inputs. The actor-critic-disturbance networks framework is used to approximate the optimization of event- triggered controller strategy, optimization costs, and the disturbance strategy, respectively. Due to the consideration of discrete time and continuous time dynamics, we put the impulsive system method to use and choose appropriate Lyapunov functions to prove stability and boundedness, at the same time, there will be no infinite triggering situation. Finally, the effectiveness of the proposed scheme is demonstrated by an example of a practical tractor system with n trailers through simulation compared with another typical design method.