Controller Design For Systems Research Articles

Data-based trackability criteria and control design for disturbed learning systems

This paper aims to establish a data-based control design framework for linear iterative learning control (ILC) systems subject to disturbances. Through the proper selection of the test inputs, some output data are collected to exploit two trackability criteria of the desired reference for ILC systems such that the implementability of the perfect tracking objective is ensured, where the persistent excitation condition may not be imposed. Furthermore, two classes of data-based ILC updating laws are presented by incorporating the design idea of the observer, for which the collected input and output data are only leveraged. It is shown that given any trackable desired reference, the perfect tracking objective can be realized for ILC systems under the proposed data-based ILC updating laws in the absence of any model information.

A dual robust control architecture with variable stiffness and damping parameters for switching task dominance in collaborative haptic systems

AbstractIn collaborative haptic training systems, a novice operator is interfaced with an expert operator and cooperatively performs some task on a real/virtual environment. Most control architectures for collaborative haptic training systems do not consider the switching task dominance together with investigating overall stability in the presence of nonlinear dynamics and uncertainty. In this paper, a theoretical framework is presented for switching task dominance in collaborative haptic training systems based on supervision and intervention of the expert operator. To that effect, the novice operator performs the operation with as little as possible interference haptic signals in the normal operational conditions. On the other hand, the expert operator is able to intervene the operation to guide the novice operator when it is necessary. The most challenging part of controller design for such systems is to provide the mentioned supervisory framework in a way that the stability of interaction between the operators and the system is ensured with acceptable task performance in various operational conditions. This work offers a variable‐gain dual robust control scheme to address the above problem. The key idea is that the tracking gain of each controller is adjusted in real‐time to switch the task authorities. It is verified that the input‐to‐state stability property is satisfied for each subsystem. Then, the overall stability is proved by leveraging the small gain theorem. Finally, the functionality and performance of the suggested control architecture is demonstrated through simulation and experimental studies.

Event-triggered [formula omitted] stabilization of networked cascade control systems under periodic DoS attack: A switching approach

This paper deals with the H∞ control design for the networked cascade control systems (NCCSs) subject to periodic denial-of-service (DoS) attack. The controller structure is based on the state-feedback controller for the both control loops. The communication network of the primary loop is equipped with an event-triggered mechanism while the network is under periodic DoS attack. For stability analysis and controller design, the mathematical model of the closed-loop system is formulated based on the switching systems approach. By using the piecewise Lyapunov-functional-based approach and average dwell time techniques, some stability and stabilization criteria are derived and presented in the form of linear matrix inequalities (LMIs). Finally, an steam temperature cascade control system is utilized as a practical example to demonstrate the effectiveness of the proposed method.

Improved Dynamic Event-Triggered Robust Control for Flexible Robotic Arm Systems with Semi-Markov Jump Process

In this paper, we investigate the problem of a dynamic event-triggered robust controller design for flexible robotic arm systems with continuous-time phase-type semi-Markov jump process. In particular, the change in moment of inertia is first considered in the flexible robotic arm system, which is necessary for ensuring the security and stability control of special robots employed under special circumstances, such as surgical robots and assisted-living robots which have strict lightweight requirements. To handle this problem, a semi-Markov chain is conducted to model this process. Furthermore, the dynamic event-triggered scheme is used to solve the problem of limited bandwidth in the network transmission environment, while considering the impact of DoS attacks. With regard to the challenging circumstances and negative elements previously mentioned, the adequate criteria for the existence of the resilient H∞ controller are obtained using the Lyapunov function approach, and the controller gains, Lyapunov parameters and event-triggered parameters are co-designed. Finally, the effectiveness of the designed controller is demonstrated via numerical simulation using the LMI toolbox in MATLAB.

An Adaptive Controller Design for Nonlinear Active Air Suspension Systems with Uncertainties

Active air spring suspensions can improve the vehicle ride comfort and meanwhile realize the vehicle height regulation, and therefore, they have been widely used and studied. However, to achieve better ride comfort and a satisfactory vehicle body height adjustment, the active air suspension controller becomes an indispensable and significant part of the system. Since the nonlinear suspension system possesses uncertainties, it is difficult to take into account both ride comfort and height regulation. This study innovatively proposes an adaptive control algorithm to specifically address the problem of vehicle height regulation and ride comfort for nonlinear active air suspension systems with uncertainties. The accurate tracking to reference vehicle body height curves is realized, and the ride comfort is also improved. Through simulations with two scenarios, it is illustrated that the active air suspension controller owns better control effectiveness than the PID controller. Compared with the PID controller, the designed controller can track the reference vehicle body height curves faster and more accurately. The result also verifies the priority of the designed controller.

An improved event-triggered control method for fuzzy systems under membership functions online learning

This paper is concerned with the problem of adaptive event-triggered (AET) based optimal fuzzy controller design for nonlinear networked control systems (NCSs) characterized by Takagi–Sugeno (T–S) fuzzy models. An improved AET communication scheme with a memory adaptive rule is proposed to enhance the utilization of the state response vertex data. Different from the existing ET based results, the improved AET scheme can save more communication resources and acquire better system performance. The sufficient criteria of performance analysis and controller design are presented for the closed-loop control system subject to mismatched membership functions (MFs) and AET scheme. And then, a new MFs online learning algorithm on the basis of the gradient descent approach is employed to optimize the MFs of fuzzy controller and obtain optimal fuzzy controller for further improving system performance. Finally, two simulation examples are presented to verify the advantage and effectiveness of the provided controller design technique.

Homogeneous systems stabilization based on convex embedding

The paper develops control algorithms for a class of affine nonlinear systems using the so-called canonical homogeneous representation. It is demonstrated that such a representation exists for any homogeneous vector field bounded on the unit sphere. It is shown that canonical homogeneous representation is useful for LMI-based control design and stability analysis of nonlinear systems. Theoretical results are supported by numerical examples.

Polynomial Design of Low-Order Controllers for SISO DAE Systems

Polynomial Design of Low-Order Controllers for SISO DAE Systems

Adaptive Asymptotic Tracking Control for Flexible-Joint Robots With Prescribed Performance: Design and Experiments

This study reports the adaptive asymptotic tracking control problem for flexible-joint (FJ) robot systems, the output tracking error can be kept within the prescribed range in the initial stage of system operation, as time approaches infinity, the asymptotic tracking result can be obtained. The prescribed performance function and the positive integrable time-varying function are introduced simultaneously in the control design of FJ robot systems for the first time. The control scheme is designed under the frame of the adaptive backstepping method and command filtered technique, which successfully avoids the problem of complexity explosion. The radial basis function neural networks are used to deal with unknown uncertainties and the adaptive laws are designed to approximate the norms of weight vectors and approximation errors. Finally, the feasibility of the proposed scheme is proved by the simulation and the experiment of the 2-link FJ robot on the Quanser platform.

Robust Output Feedback Control Design in the Presence of Sporadic Measurements

Output feedback control design for linear time-invariant systems in the presence of sporadic measurements and exogenous perturbations is addressed. To cope with the sporadic availability of measurements of the output, a hybrid dynamic output feedback controller equipped with a holding device whose state is reset when a new measurement is available is designed. The closed-loop system, resulting from the interconnection of the controller and the plant, is augmented with a timer variable triggering the arrival of new measurements and its properties are analyzed using hybrid system tools. Building upon Lyapunov theory for hybrid systems, sufficient conditions for internal and L2 input-to-output stability are proposed. An LMI-based design methodology for the co-design of the gains of the controller and the parameters of the holding device is presented. The effectiveness of the proposed LMI-based design approach is showcased in a numerical example.

Distributed MPC-ILC Thermal Control Design for Large-Scale Multi-Zone Building HVAC System

With building heating, ventilation, and air conditioning (HVAC) systems accounting for 50% the energy consumption in the building sector in the United States, there is a need to develop and implement optimal control strategies for building HVAC systems that reduce energy consumption while achieving thermal comfort for users. In the author's previous work, an integrated model predictive control (MPC) and iterative learning control (ILC) design approach was presented that took advantage of both controllers. It did not rely on model accuracy compared to conventional MPC and reduced the learning curve compared to conventional ILC. Albeit the previous numerical results showed fast convergence in most of the VAV subsystems, the gap between room air temperature and its set point remains noticeable in several zones. This paper further proposes an approach to extend the centralized MPC-ILC controller to take into account the distributed factor and the spatial distribution of the thermal zones of the VAV system. The improved control strategy allows all VAVs to interact with each other and contribute collectively to the overall convergence of the whole system. The proposed controller is implemented on a thirty-two zone VAV reheat system and compared with different controllers, including our previous MPC-ILC design. The outcomes show that the proposed controller results in faster and closer convergence among all zones even when the number of subsystems is large.

입력 포화를 고려한 모핑 쿼드로터의 T‒S 퍼지 모델 기반 강인 제어기 설계

In this paper, we propose a Takagi‒Sugeno (T‒S) fuzzy-model-based robust controller design of a morphing quadrotor system by considering input saturation. First, the closed-loop control system is expressed as the T‒S fuzzy model by considering the input saturation characteristics of the actuator of a morphing quadrotor. Then, we derive the robust controller design condition as linear matrix inequalities (LMIs) to enable the designed controller to become robust to parameter uncertainties and the input saturation characteristics of the control system. Finally, in the simulation example, we verify the validity of the proposed method by showing that the designed controller successfully stabilizes the attitude system of the quadrotor.

Admissibility and robust H∞ controller design for uncertain 2D singular discrete systems with interval time‐varying delays

SummaryAdmissibility and robust controller design is considered here as uncertain 2‐D discrete singular systems with interval time‐varying delays and norm‐bounded parameter uncertainties. By employing an augmented Lyapunov‐Krasovskii's functional and then using a new version of Jensen inequality combined with an improved reciprocally convex approach, a new delay‐dependent admissibility condition is obtained, consequently the robust controller is designed in terms of linear matrix inequality. Numerical examples are proposed to demonstrate the efficiency of the proposed methods.

State Feedback Controller Design for a Class of Generalized Proportional Fractional Order Nonlinear Systems

The state feedback controller design for a class of Generalized Proportional Fractional Order (GPFO) Nonlinear Systems is presented in this paper. The design is based on the combination of the One-Sided Lipschitz (OSL) system class with GPFO modeling. The main contribution of this study is that, to the best of the authors’ knowledge, this work presents the first state feedback control design for GPFO systems. The suggested state feedback controller is intended to ensure the system’s generalized Mittag Leffler (GML) stability and to deliver optimal performance. The findings of this paper show that the proposed strategy is effective in stabilizing Generalized Proportional Fractional Order Nonlinear Systems. A numerical example is presented to demonstrate the usefulness of the stated theoretical conclusions.

Relaxed nonquadratic H∞ robust constrained event-triggered fuzzy controller design for discrete-time nonlinear systems

This paper introduces an [Formula: see text] robust constrained event-triggered fuzzy controller for discrete-time nonlinear systems in the presence of system parameter uncertainties, the parameter uncertainties of the output matrices and the disturbances, simultaneously. To reduce the communication resources and improve the robust performance, the event-triggered mechanism is incorporated with the [Formula: see text] robust fuzzy controller design. Moreover, by employing the fuzzy modeling of the actuator saturation and a nonquadratic Lyapunov function (NQLF), the ultimate bounded stability (UBS) of the closed-loop system is guaranteed subject to the amplitude limitations of the control signal. This means, a new linear matrix inequality (LMI) problem is derived to ensure the robustness and constraints in an offline scheme based on the event-triggered strategy. Besides, to meet the practical problem to further improve the controlled system performance, the control input rate constraint is also considered and a new LMI condition is provided with no online computational burden. Therefore, the computational burden of the proposed controller is greatly reduced with less conservatism. Two simulation examples including a numerical dynamic system and a truck–trailer system are employed to illustrate the less conservatism and computational complexity of the proposed method compared with the existing approaches.

Control Design for Fractional Order Leader and Follower Systems with Mixed Time Delays: A Resilience-Based Approach

In this article, we consider the problem of resilient base containment control for fractional-order multi-agent systems (FOMASs) with mixed time delays using a reliable and simple approach, where the communication topology among followers is a weighted digraph. A disturbance term is introduced into the delayed and non-delayed controller part to make it more practical. Our method involves proposing algebraic criteria by utilizing non-delayed and delayed protocols, applying the Razumikhin technique and graph theory respectively. The presented method can well overcome the difficulty resulting from fractional calculus, time delays and fractional derivatives. To demonstrate the validity and effectiveness of our findings, we provide an example at the end of our study.

Non-Gaussian disturbance rejection control for multivariate stochastic systems using moment-generating function

In this paper, a non-Gaussian disturbance rejection control algorithm for a class of nonlinear multivariate stochastic systems is studied. Based on the moment-generating functions obtained from the deduced probability density functions of the output tracking errors, a new criterion representing the stochastic properties of the system is proposed, motivated by a minimum entropy design. A time-variant linear model can be established by the sampled moment-generating functions. Using this model, a control algorithm is developed that minimizes the newly developed criterion. Moreover, a stability analysis is performed for the closed-loop control system. Finally, simulation results of a numerical example demonstrate the effectiveness of the presented control algorithm. The contribution and novelty of this work can be summarized as follows: (1) a novel non-Gaussian disturbance rejection control scheme is proposed based on the minimum entropy principle, (2) the randomness of the multi-variable non-Gaussian stochastic nonlinear system is attenuated based on the new performance criterion, (3) a theoretical convergence analysis has been given for the proposed control system, and (4) a potential framework has been established for the design of a general stochastic system control.

Sub-optimal controller design for time-delay nonlinear partial differential equation systems: an extended state-dependent differential Riccati equation approach

ABSTRACT In this article, a sub-optimal controller based on Extended State-Dependent Differential Riccati Equation (ESDDRE) is suggested for a class of time-delay nonlinear Partial Differential Equation (PDE) systems. At first, an extended pseudo linearisation presentation for parameterisation form using State-Dependent Coefficients (SDC) is proposed. In this presentation, all the time-delay parts are placed in system matrices as well as in input vectors. By defining a cost function and a Hamiltonian related to the PDE systems, the sub-optimal control law regarded on the ESDDRE is obtained. The stability of the closed-loop system based on the ESDDRE control approach is ensured by using a proper Lyapunov function and also Poincaré inequality. Numerical simulation results for three time-delay nonlinear PDE systems illustrate the appropriate performance of the proposed control approach.

ℒ1 Adaptive Path-Following of Airships in Wind

This paper proposes an adaptive, three-dimensional (3D) path-following controller for airships in the presence of wind disturbances, which explicitly considers that wind speed is time-varying. The main idea is to formulate airship path-following as control design for systems in the presence of parametric uncertainties and external disturbances. Assuming that there is no prior information on wind, the proposed solution is based on the [Formula: see text] adaptive controller. This approach makes clear statements for performance specifications of the controller and relaxes the common assumption that wind speed is constant. This makes the design more realistic and the analysis more rigorous, because in practice, the wind speed may be time-varying. The results of the simulation indicate that the path following system has a good performance and is robust against wind disturbances.

A distributed delay based controller for simultaneous periodic disturbance rejection and input-delay compensation

The paper presents a controller design for systems suffering from multi-harmonic periodic disturbance and substantial input time-delay. It forms an alternative approach to Repetitive Control where the goal is to stabilize a close-loop that encapsulates an explicit time-delay model of the periodic signal. The proposed controller design is based on the Internal Model Control (IMC) framework, and it consists of the inverse system model and a tuneable distributed delay with an overall length related to the period of the disturbance. The properness of the controller can be ensured by utilizing a low-pass filter, however, such a component is shown to be unnecessary when the relative order of the system model is one. This fact makes the alternative approach especially suitable for systems approximated by a first-order model with input time-delay, leading to a straightforward controller design thanks to its simple structure and attainable conditions. Stability of the configuration is guaranteed by an ideal IMC framework. For further performance and robustness requirements for the non-ideal case the tuning of the controller is posed as a weighted-H∞ optimization problem where frequency-, spectral- and time-domain requirements are formulated as constraints. The overall control design is experimentally verified on a laboratory setup that has high-order dynamics approximated by a first-order model with input delay.