Robust Stability Of System Research Articles

Robust-PID controller design for magnetic levitation system using parameter space approach

Recently, implementation of air magnetic suspension systems has become more challenging due to the growing demand for lightweight technologies, comfortable cabins, vehicle safety stability, and pollution control. Magnetic levitation, or Maglev, is the method of propelling a target into the air by adjusting different magnetic forces. The absence of contact and the avoidance of wear and friction phenomena are key considerations in the applications of magnetic levitation technology. Due to the high nonlinearity in the modelling process of such kind of systems, the stabilizing of magnetic levitation has been considered as a challenging task for many researchers in control engineering sector. The computation of all stabilizing PID gains controllers for the magnetic levitation benchmark ED-4810 (Maglev) is demonstrated in this paper using two different scenarios. In the first one, the tuning parameters of the classical PID controller (KP, KI, and KD) are assumed to be the uncertain parameters. The second scenario demonstrates the uncertainty in the transfer function of the system by using the resistance and the inductance as uncertain parameters. The characteristic polynomial of the linearized uncertain model is shown to be an unstable affine polynomial using the Zero Exclusion Theorem and the singular frequencies technique. The parameter space approach is used to illustrate the values of all PID parameters in order to achieve robust stability in the two scenarios. The effectiveness of the presented graphical technique has been verified through MATLAB simulation to obtain robust stability for magnetic levitation systems.

Disturbance observer-based delayed robust feedback control design for a class of uncertain variable fractional-order systems: Order-dependent and delay-dependent stability

This work addresses the stabilization of variable fractional-order (VFO) neutral-type systems with structure perturbations and unknown disturbance signals using the feedback control approach. The goal is to design disturbance-observer-based delayed state- and output-feedback controllers to achieve robust stability of such VFO systems. The proposed controller consists of two parts, namely a primary controller based on the linear feedback technique, and an auxiliary controller based on the disturbance observer. A disturbance observer is developed to estimate the disturbance signal, which is generated by an exogenous system. Based on matrix inequalities, order-dependent and delay-dependent conditions are formulated via FO Lyapunov theory that guarantee the robust stability of the closed-loop system. Simulations verify the main results.

Robust Stability Analysis of Smith Predictor Based Interval Fractional-Order Control Systems: A Case Study in Level Control Process

The robust stability study of the classic Smith predictor-based control system for uncertain fractional-order plants with interval time delays and interval coefficients is the emphasis of this work. Interval uncertainties are a type of parametric uncertainties that cannot be avoided when modeling real-world plants. Also, in the considered Smith predictor control structure it is supposed that the controller is a fractional-order proportional integral derivative (FOPID) controller. To the best of the authors' knowledge, no method has been developed until now to analyze the robust stability of a Smith predictor based fractional-order control system in the presence of the simultaneous uncertainties in gain, time-constants, and time delay. The three primary contributions of this study are as follows: i) a set of necessary and sufficient conditions is constructed using a graphical method to examine the robust stability of a Smith predictor-based fractional-order control system—the proposed method explicitly determines whether or not the FOPID controller can robustly stabilize the Smith predictor-based fractional-order control system; ii) an auxiliary function as a robust stability testing function is presented to reduce the computational complexity of the robust stability analysis; and iii) two auxiliary functions are proposed to achieve the control requirements on the disturbance rejection and the noise reduction. Finally, four numerical examples and an experimental verification are presented in this study to demonstrate the efficacy and significance of the suggested technique.

Approach to the synthesis of an aperiodic robust automatic control system based on the gradient-speed method of Lyapunov vector functions

One of the actual problems for the theory and practice of control of dynamic objects is the development of methods for research and synthesis of control systems of multidimensional objects. The paper proposes a universal approach to construct Lyapunov vector functions directly from the equation of state of control system and a new gradient-speed method of Lyapunov vector functions to study aperiodic robust stability of linear control system with m inputs and n outputs. The study of aperiodic robust stability of automatic control systems is based on the construction of Lyapunov vector functions and gradient-speed dynamic control systems. The basic statements of Lyapunov's theorem about asymptotic stability and notions of stability of dynamic systems are used. The representation of control systems as gradient systems and Lyapunov functions as potential functions of gradient systems from the catastrophe theory allow to construct the full-time derivative of Lyapunov vector functions always as a sign-negative function equal to the scalar product of the velocity vector on the gradient vector. The conditions of aperiodic robust stability are obtained as a system of inequalities on the uncertain parameters of the automatic control system, which are a condition for the existence of the Lyapunov vector-function. A numerical example of synthesis of aperiodic robustness of a multidimensional control object is given. The example shows the main stages of the developed synthesis method, the study of the system stability at different values of the coefficients k, confirming the consistency of the proposed method. Transients in the system satisfy all requirements

Global fractional Halanay inequalities approach to finite-time stability of nonlinear fractional order delay systems

In this paper, we investigate the robust finite time stability of fractional order systems with time varying delay and nonlinear perturbation. We improve the sufficient condition for general fractional delay systems by utilizing the special structure of a singular Gronwall inequality. For stable fractional delay systems, our approach bases on a global Halanay type inequality in differential and integral forms. A sharper delay dependent sufficient condition for robust finite time stability of such systems is formulated in terms of the Mittag-Leffler functions and the delayed size. The connection between the new sufficient condition and the previous results is compared and discussed thoroughly.

Reduction of Conservativeness of Robust PID Control System Design Method: An Approach Using the Mapping Theorem and the Cremer–Leonhard–Mikhailov Criterion

This paper gives a novel method to design less‐conservative robust PID control systems. The partial model matching method is a design method for PID control systems. That is a method to design a control system that matches a reference model as closely as possible. This method does not guarantee robust stability of a PID control system because it is assumed that there are no uncertainties on the coefficients of the lower‐order terms of the plant. Therefore, in our previous work, a robust design method based on the partial model matching method was proposed. However, the drawback of this conventional method is that the results of stability analysis are conservative. In this paper, we aim to reduce the conservativeness caused by the conventional method. To achieve this goal, we use a robust stability analysis method based on the Cremer–Leonhard–Mikhailov criterion and the mapping theorem. Moreover, we also propose a new method to update the value of a design parameter. A numerical example shown in this paper implies that the conservativeness is reduced by the proposed method. © 2023 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

Pantograph Catenary Contact Force Regulation Based on Modified Takagi-Sugeno Fuzzy Models

In this paper, a new contact force control technique, based on the modified Takagi-Sugeno model and the parallel distributed compensation concept is developed to suppress vibrations between the pantograph and the catenary by regulating the contact force to a reference value, thereby achieving stable current collection. The proposed method uses simple and standard PID and modified Takagi-Sugeno fuzzy controllers. The two controllers guarantee the designed system's robust stability. Furthermore, based on a simplified pantograph–catenary system model, the comparative simulation results show that variations of the contact force can be almost attenuated. As a result, the system stability is guaranteed, and the performance robustness is verified.

Fault-Tolerant Tracking Control Optimization of Constrained LPV Systems Based on Embedded Preview Regulation and Reference Governance

This article presents some new improvements to the relevant constrained predictive fault-tolerant tracking control (FTTC) methods through embedding optimal preview regulation and reference governance. The main novelty of such a strategy is that some valuable information of finite future references can be adequately scheduled to optimize the robust tracking performance and significantly enlarge the fault-tolerant admissible region. In order to better describe the wide applicability of the proposed strategy, the robust FTTC problem for a class of LPV systems with state/input constraints is considered. Overall, the involved key designs consist of three parts. First, an unconstrained FTTC component is constructed by combining tracking error feedback, reference input regulation, and fault signal compensation. It is used to guarantee the robust tracking stability of closed-loop systems when the constraints are not activated. Second, a tube-based predictive FTTC policy with an embedded optimal preview regulator is designed to achieve the robust constraint satisfaction and transient response improvement. Third, an embedded reference governor is additionally integrated to significantly enlarge the size of the fault-tolerant admissible region. This design further reinforces the feasibility of constrained FTTC optimization. The effectiveness of these results is finally validated by a case study of a single transistor dc/dc Forward converter.

An Output-Feedback Design Approach for Robust Stabilization of Linear Systems With Uncertain Time-Delayed Dynamics in Sensors and Actuators

In this paper, we propose a control approach for the robust stabilization of linear time-invariant (LTI) systems with non-negligible sensor and actuator dynamics subject to time-delayed signals. Our proposition is based on obtaining an augmented model that encompasses the plant, sensor, and actuator dynamics and also the time-delay dynamic effect. We make use of the Padé Approximation for modeling the time-delay impact on the feedback loop. Since the actual plant state variables are not available for feedback, the sensor outputs, which represent a subset of the augmented system state variables, are used for composing a static output-feedback control law. The robust controller gains are computed by means of a two-stage strategy based on linear matrix inequalities (LMI). For obtaining less conservative conditions we consider the use of homogeneous-polynomial Lyapunov functions (HPLF)– and other decision variables– of arbitrary degree. In our proposition, we also take into account the inclusion of a minimum decay rate criterion in order to improve closed-loop system transient response. Disturbance rejection is also addressed through extensions to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathscr {H}_{2}$ </tex-math></inline-formula> guaranteed cost minimization. The effectiveness of the proposed strategy is attested in the design of a controller for the lateral axis dynamics of an aircraft and other academic examples.

A Framework for Decentralized Equilibrium Seeking in Networked Sampled-Data Games using Hybrid Control Tools*

We study the steady-state Nash equilibrium-seeking problem for sampled-data games with LTI dynamics and quadratic costs. The key challenge is to guarantee the robust stability and convergence properties of the closed-loop system in the presence of local individual sampling mechanisms assigned to each of the players in the game. This problem is non-trivial due to the unstable behaviors that can arise when sequential control updates (rather than parallel) emerge in the closed-loop system because of the existence of local control triggering mechanisms in each node of the network. To address this issue, we introduce a controls framework based on tools from hybrid dynamical systems theory. Our results are illustrated via numerical examples.

Robust Global Asymptotic Stabilization of Linear Cascaded Systems With Hysteretic Interconnection

We address the problem of setpoint regulation for cascaded minimum-phase linear systems interconnected through a scalar hysteresis, modeled as a Prandtl-Ishlinskii operator. Employing well-posed constrained differential inclusions to represent the hysteretic dynamics, we formulate the control problem in terms of stabilization of a compact set of equilibria depending on the hysteresis states. For our design, we firstly consider a proportional-integral controller for linear systems with hysteretic input, and provide model-free sufficient conditions based on high-gain arguments for closed-loop stability. Then, the controller is dynamically extended to obtain an inversion-free stabilizer of the overall cascade. For the presented schemes, we prove robust global asymptotic stability of a compact set that ensures setpoint regulation, regardless of the hysteresis states.

Robust stability and boundedness of uncertain conformable fractional-order delay systems under input saturation

&lt;abstract&gt;&lt;p&gt;In this article, a class of uncertain conformable fractional-order delay systems under input saturation is considered. By establishing the Lyapunov boundedness theorem for conformable fractional-order delay systems, some sufficient conditions for robust stability and boundedness of the systems are obtained. Examples are given to illustrate the obtained theory.&lt;/p&gt;&lt;/abstract&gt;

Robust Local Stabilization of Nonlinear Systems With Controller-Dependent Norm Bounds: A Convex Approach With Input-Output Sampling

This letter presents a framework for synthesizing a robust full-state feedback controller for systems with unknown nonlinearities. Our approach characterizes input-output behavior of the nonlinearities in terms of local norm bounds using available sampled data corresponding to a known region about an equilibrium point. A challenge in this approach is that if the nonlinearities have explicit dependence on the control inputs, an a priori selection of the control input sampling region is required to determine the local norm bounds. This leads to a “chicken and egg” problem, where the local norm bounds are required for controller synthesis, but the region of control inputs needed to be characterized cannot be known prior to synthesis of the controller. To tackle this issue, we constrain the closed-loop control inputs within the sampling region while synthesizing the controller. As the resulting synthesis problem is non-convex, three semi-definite programs (SDPs) are obtained through convex relaxations of the main problem, and an iterative algorithm is constructed using these SDPs for control synthesis. Two numerical examples are included to demonstrate the effectiveness of the proposed algorithm.

Robust and minimum norm stabilization for uncertain singular second-order vibration systems

Robust and minimum norm stabilization for uncertain singular second-order vibration systems

A novel approach for robust model predictive control applied to switched linear systems through state and output feedback

This paper proposes a robust switched model-based predictive controller design for discrete linear systems with state constraints, inputs, and disturbances limited in norm. Modeled via linear matrix inequalities, the online and offline designs of the proposed control aim at minimizing the upper bound of the quadratic performance index for a horizon of infinite prediction associated with the state estimator and the switching rule, seeking to guarantee the robust stability for closed-loop systems. To this end, three theorems are formulated. To demonstrate the effectiveness of the control strategy, a comparative analysis is performed between the performance of the proposed model and a benchmark method. From the results, it is possible to conclude that the proposed method is promising in the scope of control of linear systems subject to switching, being more efficient than the benchmark for the stabilization and control of both numerical examples.

Reinforcement learning for robust stabilization of nonlinear systems with asymmetric saturating actuators

We study the robust stabilization problem of a class of nonlinear systems with asymmetric saturating actuators and mismatched disturbances. Initially, we convert such a robust stabilization problem into a nonlinear-constrained optimal control problem by constructing a discounted cost function for the auxiliary system. Then, for the purpose of solving the nonlinear-constrained optimal control problem, we develop a simultaneous policy iteration (PI) in the reinforcement learning framework. The implementation of the simultaneous PI relies on an actor–critic architecture, which employs actor and critic neural networks (NNs) to separately approximate the control policy and the value function. To determine the actor and critic NNs’ weights, we use the approach of weighted residuals together with the typical Monte-Carlo integration technique. Finally, we perform simulations of two nonlinear plants to validate the established theoretical claims.

Novel robust stability conditions of fractional-order systems with structured uncertain parameters based on parameter-dependent functions: the 0

ABSTRACT In this paper, the robust stability of fractional-order systems with fractional order and structured uncertain parameters is considered. Firstly, novel robust stability conditions of the above systems are presented based on the parameter-dependent polynomial functions. Secondly, the existence of the parameter-dependent polynomial functions is transformed into linear matrix inequalities via the generalized Kalman-Yakubovič-Popov lemma. In addition, the above methods can also be applied to solve the robust stability of fractional-order systems with structured uncertainties or polytopic uncertainties. Finally, numerical examples are presented to show the proposed methods are less conservative than the existing methods.

Observer-based adaptive ISMC for connected vehicles against cyber-attacks

This paper concentrates on decentralized variable structure adaptive integral sliding mode control (ISMC) for connected vehicles (CV) against cyber-attacks. First of all, a novel vehicle leader-follower model is established by jointly considering the cyber-attacks which involve replay attack and DoS attack simultaneously. Secondly, a decentralized control scheme is designed on the basis of the variable structure observer and adaptive integral sliding mode technique. The Lyapunov-Razumikhin method is adopted such that the state estimation error of CV system is asymptotically converged to zero, which can overcome the replay attack, DoS attack, and measurement delays, then a corrective signal is designed for the deception attack to eliminate the influence of deception attack on the CV system. Furthermore, the robust asymptotic stability of CV system is guaranteed by exploiting the emerging technique of robust control for time-delay systems. Meanwhile, the string stability of CV is guaranteed, even under the condition of heterogeneous vehicles. Finally, extensive simulations are conducted to verify the theoretical analysis and demonstrate the effectiveness and superiority of the proposed method.

Simultaneous HPLC Determination of Clindamycin Phosphate, Tretinoin, and Preservatives in Gel Dosage Form Using a Novel Stability-Indicating Method

The most well-known, effective medicines for acne therapy are clindamycin phosphate and tretinoin. For the first time, we have developed and validated a reversed-phase HPLC stability-indicating technique for the detection of clindamycin phosphate (CLP), tretinoin (TRN), and two preservatives, methylparaben (MP) and imidazolidinyl urea (IU), simultaneously in this work. Most of the chromatographic conditions in the present study were optimized to achieve better separation. The best separation results were obtained using gradient elution on a C-18 (250 × 4.6 mm), 5 µm column, with a mobile phase consisting of solution A (1 mL/L ortho-phosphoric acid in water) and solution B (methanol), at a flow rate of 1.0 mL/min, with UV detection at wavelengths of 200 nm and 353 nm. Standard parameters such as system suitability, precision, accuracy, specificity, robustness, linearity, range, detection limit, quantification limit, and reagent stability were used to validate the developed technique. According to the standards of the International Council for Harmonization, all of the experimental parameters were found to be within allowable bounds (ICH). The simultaneous concentrations of clindamycin phosphate, tretinoin, methylparaben, and imidazolidinyl urea in pharmaceutical formulations were successfully determined using the suggested approach. The proposed RP-HPLC method detected no interfering peaks in the chromatogram. We may conclude from the data that the new RP-HPLC method can be utilized in pharmaceutical laboratories to simultaneously assess clindamycin phosphate, tretinoin, and two preservatives, methylparaben and imidazolidinyl urea, for both qualitative and quantitative analyses.

Robust Stability and Stable Member Problems for Multilinear Systems

In this paper, we consider robust stability and stable member problems for linear systems whose characteristic polynomials are nonmonic polynomials with multilinear uncertainty. For both problems, the results are given by using the reflection (box) coefficients and the extreme point property of multilinear functions defined on the box. Finding stable member in a polynomial family is one of the hard problems of linear control theory. This issue is considered by visualizing the cases n-l=2 and n-l=3. Necessary and sufficient conditions for robust stability and the existence of a stable member of the multilinear polynomial family using the reflection coefficients are obtained. Several examples are provided.