Robust H ∞ Control of a Class of Switching Nonlinear Systems with Time-Varying Delay Via T–S Fuzzy Model

This paper considers H _∞ control of a class of switching nonlinear systems with time-varying delays via T–S fuzzy model based on piecewise fuzzy weighting-dependent Lyapunov–Krasovskii functionals (PFLKFs). The systems are switching among several nonlinear systems. The Takagi and Sugeno (T–S) fuzzy model is employed to approximate the sub-nonlinear dynamic systems. Thus, with two level functions, namely, crisp switching functions and local fuzzy weighting functions, we introduce a continuous-time switched fuzzy systems, which inherently contain the features of the switched hybrid systems and T–S fuzzy systems. Average dwell-time approach and PFLKFs methods are utilized for the stability analysis and controller design, and with free fuzzy weighting matrix scheme. Switching and control laws are obtained such that the H _∞ performance is satisfied. The conditions of stability and the control laws are given in the form of LMIs which can be obtained by solving a set of linear matrix inequalities (LMIs) that are numerically feasible. A numerical example and the control of an uncertain radio-controlled (R/C) hovercraft with time-varying delay are given to demonstrate the efficiency of the proposed method.     

Gain-scheduled robust control for lateral stability of four-wheel-independent-drive electric vehicles via linear parameter-varying technique

This paper proposes a robust gain-scheduled H_∞ controller for lateral stability control of four-wheel-independent-drive electric vehicles via linear parameter-varying technique. The controller aims at tracking the desired yaw rate and vehicle sideslip angle by controlling the external yaw moment. In the design of controller, uncertain factors such as vehicle mass and tire cornering stiffness in vehicle lateral dynamics are represented via the norm-bounded uncertainty. To address the importance of time-varying longitudinal velocity for vehicle lateral stability control, a linear parameter-varying polytopic vehicle model is built, and the built vehicle model depends affinely on the time-varying longitudinal speed that is described by a polytope with finite vertices. In order to reduce conservative, the hyper-rectangular polytope is replaced by a hyper-trapezoidal polytope. Simultaneously, the quadratic D-stability is also applied to improve the transient response of the closed-loop system. The resulting gain-scheduling state-feedback controller is finally designed, and solved utilizing a set of linear matrix inequalities derived from quadratic H_∞ performance and D-stability. Simulations using Matlab/Simulink-Carsim® are carried out to verify the effectiveness of the proposed controller with a high-fidelity, CarSim®, full-vehicle model. It is found from the results that the robust gain-scheduled H_∞ controller suggested in this paper provides improved vehicle lateral stability, safety and handling performance.     

Multi-objective control synthesis: an application to 4WS passenger vehicles

The vehicle dynamics and control play an important role in an automated highway system for passenger cars. This study addresses the problem of designing active controllers for four-wheel-steering (4WS) vehicles. We first obtain a set of linear maneuvering equations representing the four-wheel steering motions and independent wheel torques for lateral/directional plus roll dynamics. We then formulate simultaneous H₂ and H_∞ (sub)-optimal controls with a desired pole assignment via linear matrix inequalities (LMIs). The steering angles are actively controlled by steering wheel commands through the actuator mechanisms for the lateral/directional and roll motions. Further the wheel power and braking are directly controlled by independent torques. Numerical simulations are performed on a complex vehicle model in order to evaluate the vehicle performance (noise and disturbance attenuation), stability, and robustness under a given class of uncertainty. Finally, the presented autopilot controller provides greater maneuverability and improved directional stability for passenger vehicles.     

Fuzzy control of nonlinear electromagnetic suspension systems

This paper presents a T–S model-based fuzzy controller design approach for electromagnetic suspension systems. The T–S fuzzy model is firstly applied to represent the nonlinear electromagnetic suspension systems. Then, based on the obtained T–S fuzzy model, a fuzzy state feedback controller is used to ensure the required mixed ℓ₂–ℓ_∞ performance of original electromagnetic suspension system to be achieved. This controller is designed in a nonparallel-distributed compensation scheme. And sufficient conditions for the existence of such a controller are derived in terms of linear matrix inequalities. Finally, numerical simulation on an electromagnetic suspension system is performed to validate the effectiveness of the proposed approach.     

H ∞ Control of Piecewise-Linear Systems Under Unreliable Communication Links

This paper considers the problem of H _∞ control of piecewise-linear control systems under unreliable communication links. Due to the limited bandwidth of the channels, signal transmission delays and data packet losses can occur between the plant and the controller. In the presence of random signal transmission delays and data packet losses, a piecewise controller is designed to stabilize the piecewise-linear system in the sense of mean square and also achieve a prescribed H _∞ disturbance attenuation performance based on piecewise-quadratic Lyapunov–Krasovskii functionals. It is shown that the H _∞ controllers can be designed by solving a set of linear matrix inequalities (LMIs) that are numerically feasible. Moreover, the controller design method is further extended to uncertain case where the system matrices’ uncertainties are represented in polytopic frameworks. Finally, an example is provided to illustrate the effectiveness of the developed theoretical results.     

Controller design and analysis for automatic steering of passenger cars

This paper deals with a lateral controller design for active 2WS vehicles in ITS applications. First, the vehicle dynamics for typical lateral maneuvers are rigorously described by Newton's formulation. Next, based on a linear perturbed model, a robust controller via μ (mu)-synthesis is designed. Due to the characteristics of D–K iteration, the resulting high-order controller has to be reduced for implementation. Then the frequency- and time-domain responses of the robust controller are extensively evaluated through numerical simulations. Further, we present performance comparisons between full-order controller and reduced-order controller. Finally, the automated steering control presented here is shown to be robust to the prescribed levels of uncertainty for highway maneuvers.     

H ∞ Filtering of Two-Dimensional T-S Fuzzy Systems

The H _∞ filtering problem for two-dimensional Takagi–Sugeno fuzzy systems described by the Fornasini–Marchesini (FM) model is studied. Attention is focused on the design of an H _∞ fuzzy filter such that the filter error system is asymptotically stable and preserves a guaranteed H _∞ performance. By using basis-dependent Lyapunov functions and adding slack matrix variables, the coupling between the Lyapunov matrix and the system matrices is eliminated. Then, a linear matrix inequality (LMI)-based approach is developed for designing the H _∞ fuzzy filter. Finally, an illustrative example is provided to show the effectiveness of the proposed approach and less conservatism.     

Design and control of a mechanical rotary variable impedance actuator

To realize different tasks in human-robotic interaction, various mechanical variable stiffness actuators are being investigated. A mechanical-rotary impedance actuator (the MeRIA) is presented that is based on the controllable effective length of a mechanical bending bar, which can be implemented into an orthosis for future research on rehabilitation training. The actuator provides joint motion and variable stiffness, simultaneously. The control task can be decoupled to be a decentralized control structure for which the controller of the two motor power sources can be designed respectively. For the movement control-loop, a cascaded impedance controller with position-torque-velocity control-loops are designed to maintain a stable and safe working environment. Using an H_∞ loop-shaping methodology, a robust stabilization torque controller is achieved. The trade-off between the actuators performance and stability is taken into account to obtain a desired shape as a precondition of an H_∞ controller synthesis. The actuator is tested on a test bench using rapid control prototyping. A model reduction algorithm is implemented to simplify the controller, and a prefilter design reduces the control-loop overshoot, thereby improving the robust stability and tracking performance during application. Experiments show that the MeRIA meets all the requirements for a mechanical device attached to the body.     

Exponential l 2–l ∞ Control for Discrete-Time Switching Markov Jump Linear Systems

The problem of exponential l ₂–l _∞ control is considered in this paper for a class of discrete-time switching Markov jump linear systems. First, the definition of exponential l ₂–l _∞ mean square stability for discrete-time switching Markov jump linear systems is introduced. Then, by resorting to the average dwell time approach, the mean square exponential stability criteria are presented with an exponential l ₂–l _∞ performance index and a decay rate, and the corresponding controller is also designed. Finally, numerical and application examples are provided to demonstrate the effectiveness of the obtained results.     

H∞ control of electrorheological suspension system subjected to parameter uncertainties

Vehicle suspension is normally used to attenuate unwanted vibration from various road conditions. The successful suppression of the vibration leads to the improvement of ride comfort as well as steering stability of the vehicle. One of attractive candidates to formulate successful vehicle suspension is to use electrorheological (ER) damper. This paper presents robust control performances of ER suspension system subjected to parameter uncertainties associated with sprung mass of the vehicle and time constant of the ER damper. After identifying dynamic bandwidth of a cylindrical ER damper operated with two different ER fluids (one has fast response characteristic, while the other slow response characteristic), a quarter car model is established by incorporating with time constant of the damping force. A robust H_∞ controller, which compensates the sprung mass and time constant uncertainties, is designed in order to suppress unwanted vibration of the vehicle. Control responses such as vertical acceleration of the sprung mass are presented in time and frequency domains. In addition, the effect of time constant of the damping force on the vibration control performance is investigated by undertaking a comparative work between fast and slow dynamic characteristics of the ER damper.     

Adaptive sliding controller with self-tuning fuzzy compensation for vehicle suspension control

Since the hydraulic actuating suspension system has nonlinear and time-varying behavior, it is difficult to establish an accurate dynamic model for a model-based sliding mode control design. Here, a novel model-free adaptive sliding controller is proposed to suppress the position oscillation of the sprung mass in response to road surface variation. This control strategy employs the functional approximation technique to establish the unknown function for releasing the model-based requirement. In addition, a fuzzy scheme with online learning ability is introduced to compensate the functional approximation error for improving the control performance and reducing the implementation difficulty. The important advantages of this approach are to achieve the sliding mode controller design without the system dynamic model requirement and release the trial-and-error work of selecting approximation function. The update laws for the coefficients of the Fourier series functions and the fuzzy tuning parameters are derived from a Lyapunov function to guarantee the control system stability. The experimental results show that the proposed control scheme effectively suppresses the oscillation amplitude of the vehicle sprung mass corresponding to the road surface variation and external uncertainties, and the control performance is better than that of a traditional model-based sliding mode controller.     

Joint optimization approach to building vibration control via multiple active tuned mass dampers

This paper puts forward a novel optimization approach for Multiple Active Tuned Mass Dampers (MATMDs) system under seismic and wind-induced building vibration. A model of an n-storey building with MATMD system is established and a joint optimization method is used to obtain an optimal state-feedback controller gain and the parameters of the MATMD system. A mixed H₂/H_∞/GH₂ control is employed to attenuate the seismic and wind-induced vibration of the building with the constraints of the actuating forces and strokes of the masses. Genetic algorithm (GA) is used to search for the optimal parameters and obtain the corresponding controller gain. Two illustrative examples are presented in this paper. In the first comparison, the GA-based approach can obtain a better set of parameters and achieve better control performance. When comparing with an Active Tuned Mass Damper (ATMD), an MATMD system can achieve similar control effects with much smaller acting forces.     

Robust Nonlinear H ∞ State Feedback Control of Polynomial Discrete-Time Systems: An Integrator Approach

This paper investigates the problem of designing a nonlinear H _∞ state feedback controller for polynomial discrete-time systems with norm-bounded uncertainties. In general, the problem of designing a controller for polynomial discrete-time systems is difficult, because it is a nonconvex problem. More precisely, in general, its Lyapunov function and control input are not jointly convex. Hence, it cannot be solved by semidefinite programming. In this paper, a novel approach is proposed, where an integrator is incorporated into the controller structure. In doing so, a convex formulation of the controller design problem can be rendered in a less conservative way than the available approaches. Furthermore, we establish the interconnection between robust H _∞ control of polynomial discrete-time systems with norm-bounded uncertainties and H _∞ control of scaled polynomial discrete-time systems. This establishment allows us to convert the robust H _∞ control problems to H _∞ control problems. Then, based on the sum of squares (SOS) approach, sufficient conditions for the existence of a nonlinear H _∞ state feedback controller are given in terms of solvability of polynomial matrix inequalities (PMIs), which can be solved by the recently developed SOS solvers. A tunnel diode circuit is used to demonstrate the validity of this integrator approach.     

Fuzzy Sliding-Mode Control of Active Suspensions

In this paper, a robust fuzzy sliding-mode controller for active suspensions of a nonlinear half-car model is introduced. First, a nonchattering sliding-mode control is presented. Then, this control method is combined with a single-input–single-output fuzzy logic controller to improve its performance. The negative value of the ratio between the derivative of error and error is the input and the slope constant of the sliding surface of the nonchattering sliding-mode controller is the output of the fuzzy logic controller. Afterwards, a four-degree-of-freedom nonlinear half-car model, which allows wheel hops and includes a suspension system with nonlinear spring and piecewise linear damper with dry friction, is presented. The designed controllers are applied to this model in order to evaluate their performances. It has been shown that the designed controller does not cause any problem in suspension working limits. The robustness of the proposed controller is also investigated for different vehicle parameters. The results indicate the success of the proposed fuzzy sliding-mode controller.      

A Genetic Fuzzy Controller for Vehicle Automatic Steering Control

This paper presents the design and experimental implementation of a genetic fuzzy controller for automatic steering of a small-scaled vehicle. We first derive a dynamic model of the vehicle via system identification and show that the model exhibits similar characteristics to full-sized vehicles. Subsequently, a stable fuzzy proportional-derivative controller is designed and optimized by genetic algorithms. The control system is transformed into a Lureacute system, and Lyapunov's direct method is used to guarantee the stability of the control system. Experimental studies suggest that the control system is insensitive to parametric uncertainty, load, and disturbances. The performance of the proposed controller is also compared against a conventional proportional derivative (PD) controller. Experimental results confirm that it outperforms the conventional PD controller, particularly in terms of robustness     

Position control of a pneumatic surgical robot using PSO based 2-DOF H∞ loop shaping structured controller

This research proposed novel development of a 2-DOF H_∞ loop shaping structured controller based on Particle Swarm Optimization (PSO) that considers the closed-loop dynamic response, robustness, stability, and minimal control input in design criteria to control position of 3-DOF pneumatic surgical robot. Unlike other conventional H_∞ controllers, the proposed controller offers robustness, high performance, but cost-effective simple structure, which has recently received attention from several researchers and preferred in industrial applications. The proposed technique is simulated and experimented on a nonlinear system of a pneumatic 3-DOF surgical robot for a Minimally Invasive Surgery (MIS). Mechanical design, dynamics modeling, and system identification of the surgical robot are conducted. The simulation results verify that the proposed controller can gain a better H_∞ sub-optimal solution than the conventional 2-DOF H_∞ loop shaping controller. Also, the experiments confirm that the proposed controller is capable to tolerate the perturbed conditions and can be alternative to the conventional controllers in pneumatic controlled system     

A fuzzy logic sliding mode controlled electronic differential for a direct wheel drive EV

In this study, a direct wheel drive electric vehicle based on an electronic differential system with a fuzzy logic sliding mode controller (FLSMC) is studied. The conventional sliding surface is modified using a fuzzy rule base to obtain fuzzy dynamic sliding surfaces by changing its slopes using the global error and its derivative in a fuzzy logic inference system. The controller is compared with proportional–integral–derivative (PID) and sliding mode controllers (SMCs), which are usually preferred to be used in industry. The proposed controller provides robustness and flexibility to direct wheel drive electric vehicles. The fuzzy logic sliding mode controller, electronic differential system and the overall electrical vehicle mechanism are modelled and digitally simulated by using the Matlab software. Simulation results show that the system with FLSMC has better efficiency and performance compared to those of PID and SMCs.     

H ∞ Control of T-S Fuzzy Singularly Perturbed Systems Using Multiple Lyapunov Functions

In this paper, H _∞ controller synthesis of T-S fuzzy singularly perturbed systems based on fuzzy and non-fuzzy multiple Lyapunov functions is discussed. By assuming some lower bounds for the grades of fuzzy membership functions and using the elimination lemma, the design conditions are presented in the form of linear matrix inequalities (LMIs). Considering ε as the singular perturbation parameter, it is shown that the ε-dependent controller in the absence of disturbances, results in an asymptotically stable closed-loop system, and in the presence of disturbances, satisfies the H _∞-norm condition for all ε∈(0,ε ^?]. The resulting LMIs are feasible for larger values of ε ^? compared to those of the previous methods. Moreover, for the case that the value of ε is not available for feedback, Finsler’s lemma is used to separate the controller gains and the ε-dependent Lyapunov matrix, and to achieve an ε-independent control. An example is presented to illustrate the validity of the design techniques.     

H∞ loop shaping for the torque-vectoring control of electric vehicles: Theoretical design and experimental assessment

This paper presents an H_∞ torque-vectoring control formulation for a fully electric vehicle with four individually controlled electric motor drives. The design of the controller based on loop shaping and a state observer configuration is discussed, considering the effect of actuation dynamics. A gain scheduling of the controller parameters as a function of vehicle speed is implemented. The increased robustness of the H_∞ controller with respect to a Proportional Integral controller is analyzed, including simulations with different tire parameters and vehicle inertial properties. Experimental results on a four-wheel-drive electric vehicle demonstrator with on-board electric drivetrains show that this control formulation does not need a feedforward contribution for providing the required cornering response in steady-state and transient conditions.     

基于单片机的双模糊温度控制器设计

传统的温度控制存在难以建立精确的数学模型以及控制性能较差等缺点,为此,在基本模糊控制理论基础上提出一种双输入单输出的双模糊温度控制器,根据系统不同的工作状态采用不同的模糊温度控制器。并结合单片机技术,设计了体积小、功能强的双模糊温度控制器,给出了温度控制器的硬件及软件设计思想与方法。该控制器简单易行,能有效改善温度控制性能,提高温度控制的稳定性。