Atta Oveisi

Adaptive Sliding Mode Vibration Control of a Nonlinear Smart Beam: A Comparison with Self-Tuning Ziegler-Nichols PID Controller

This paper investigates the vibration control of geometrically nonlinear beam with Macro Fiber Composite (MFC) actuators using two different adaptive control algorithms. A complete mathematical modeling is presented in order to find the dynamic equation of motion. Then, a robust adaptive fuzzy control algorithm for controlling the proposed mechanical structure is introduced. This controller includes a fuzzy scheme and a robust controller. Based on sliding mode controller a fuzzy system is introduced to mimic an ideal controller. The robust controller is designed based on compensation of the difference between the fuzzy controller and the ideal controller. The parameters of the fuzzy system and uncertainty bound of the robust controller are adjusted adaptively. The adaptive laws are designed based on the Lyapunov stability theorem to reach the stability of the closed-loop system. Meanwhile, for comparison purposes the presented controller is compared with self tuning Ziegler-Nichols PID controller for both robustness and vibration suppression performance aspects. Effectiveness of these two control strategies is evaluated by numerical simulations. Detailed analysis for the closed-loop system is carried out to evaluate the vibration controlling performance under different output excitation, robustness of the closed-loop system under sudden loading and the effect of initial condition on vibration characteristic.

A path-following driver/vehicle model with optimized lateral dynamic controller

Reduction in traffic congestion and overall number of accidents, especially within the last decade, can be attributed to the enormous progress in active safety. Vehicle path following control with the presence of driver commands can be regarded as one of the important issues in vehicle active safety systems development and more realistic explanation of vehicle path tracking problem. In this paper, an integrated driver/DYC control system is presented that regulates the steering angle and yaw moment, considering driver previewed path. Thus, the driver previewed distance, the heading error and the lateral deviation between the vehicle and desired path are used as inputs. Then, the controller determines and applies a corrective steering angle and a direct yaw moment to make the vehicle follow the desired path. A PID controller with optimized gains is used for the control of integrated driver/DYC system. Genetic Algorithm as an intelligent optimization method is utilized to adapt PID controller gains for various working situations. Proposed integrated driver/DYC controller is examined on lane change manuvers andthe sensitivity of the control system is investigated through the changes in the driver model and vehicle parameters. Simulation results show the pronounced effectiveness of the controller in vehicle path following and stability.

Robust nonfragile observer-based H2/H∞ controller

A robust nonfragile observer-based controller for a linear time-invariant system with structured uncertainty is introduced. The H ∞ robust stability of the closed-loop system is guaranteed by use of the Lyapunov theorem in the presence of undesirable disturbance. For the sake of addressing the fragility problem, independent sets of time-dependent gain-uncertainties are assumed to be existing for the controller and the observer elements. In order to satisfy the arbitrary H2-normed constraints for the control system and to enable automatic determination of the optimal H 2 / H ∞ bound of the performance functions in disturbance rejection control, additional necessary and sufficient conditions are presented in a linear matrix equality/inequality framework. The H 2 / H ∞ observer-based controller is then transformed into an optimization problem of coupled set of linear matrix equalities/inequality that can be solved iteratively by use of numerical software such as Scilab. Finally, concerning the evaluation of the performance of the controller, the control system is implemented in real time on a mechanical system, aiming at vibration suppression. The plant under study is a multi-input single-output clamped-free piezo-laminated smart beam. The nominal mathematical reduced-order model of the beam with piezo-actuators is used to design the proposed controller and then the control system is implemented experimentally on the full-order real-time system. The results show that the closed-loop system has a robust performance in rejecting the disturbance in the presence of the structured uncertainty and in the presence of the unmodeled dynamics.

Semi-Analytical Modeling and Vibration Control of a Geometrically Nonlinear Plate

This paper presents the dynamic modeling of a piezolaminated plate considering geometrical nonlinearities. The piezo-actuator and piezo-sensor are connected via proportional derivative feedback control law. The Hamilton’s principle is used to extract the strong form of the equation of motion with the reflection of the higher order strain terms by means of the strain–displacement relationship of the von Karman type. Then the nonlinear partial differential equation (PDE) obtained is converted to a nonlinear algebraic equation by employing the combination of harmonic balance method and single-mode Galerkin’s technique. Finally, the vibration suppression performance and sensitivity of the dynamic response is evaluated for various control parameters and magnitudes of external disturbance.

Liquid Sloshing in a Horizontal Circular Container with Eccentric Tube under External Excitation

Appropriate conformal mapping transformation in combination with the linear potential theory is employed to develop mathematical model for two-dimensional sloshing in horizontal circular cylindrical containers with overall eccentric hole. The tube-type tank is filled with inviscid incompressible fluid up to its half depth and subjected to lateral accelerations. A ramp-step excitation encountered in a road turning maneuver as well as real seismic event is used to simulate the lateral acceleration excitation. The resulting linear sets of ordinary differential equations are truncated and then solved numerically by employing Laplace transform technique followed by Durbin’s numerical inversion pattern. The effects of excitation input time, eccentricity, and radii ratio on the hydrodynamic responses and suppression of the induced destabilizing lateral forces are examined. Limiting cases are considered and good agreements with available analytic and numerical solutions as well as the simulations performed by using a commercial FEM software package are obtained.

Dynamic Response of a Thick Piezoelectric Circular Cylindrical Panel: An Exact Solution

One of the interesting fields that attracted many researchers in recent years is the smart structures. The piezomaterials, because of their ability in converting both mechanical stress and electricity to each other, are very applicable in this field. However, most of the works available used various inexact two-dimensional theories with certain types of simplification, which are inaccurate in some applications such as thick shells while, in some applications due to request of large displacement/stress, thick piezoelectric panel is needed and two-dimensional theories have not enough accuracy. This study investigates the dynamic steady state response and natural frequency of a piezoelectric circular cylindrical panel using exact three-dimensional solutions based on this decomposition technique. In addition, the formulation is written for both simply supported and clamped boundary conditions. Then the natural frequencies, mode shapes, and dynamic steady state response of the piezoelectric circular cylindrical panel in frequency domain are validated with commercial finite element software (ABAQUS) to show the validity of the mathematical formulation and the results will be compared, finally.

Standing Gravity Waves in a Horizontal Circular Eccentric Annular Tank

Standing gravity waves in half-full horizontal cylindrical containers with eccentric tube are analyzed using the linear theory of water waves. The problem solution is obtained by the method of conformal coordinate transformation, leading to standard truncated matrix Eigen-value problem from which fluid motion characteristics (Eigen-frequencies and wave modes) are calculated. The effects of tube eccentricity and radius ratio upon the three lowest antisymmetric and symmetric sloshing frequencies and the associated hydrodynamic pressure mode shapes are examined. Also, convergence of the adopted approach with respect to the eccentricity condition, and radius ratio is discussed. Accuracy of the present analysis is checked by comparison with the known results of the limiting cases.

Robust Linear Output Regulation Using Extended State Observer

This paper presents a disturbance rejection-based solution to the problem of robust output regulation. The mismatch between the underlying plant and its nominal mathematical model is formulated by two disturbance classes. The first class is assumed to be generated by an autonomous linear system while for the second class no specific dynamical structure is considered. Accordingly, the robustness of the closed-loop system against the first disturbance class is achieved by following the internal model principle. On the other hand, in the framework of disturbance rejection control, an extended state observer (ESO) is designed to approximate and compensate for the second class, i.e., unstructured disturbances. As a result, the proposed output regulation method can deal with a vast range of uncertainties. Finally, the stability of the closed-loop system based on the proposed compound controller is carried out via Lyapunov and center manifold analyses, and some results on the robust output regulation are drawn. A representative simulation example is also presented to show the effectiveness of the control method.

Nonlinear observer-based recurrent wavelet neuro-controller in disturbance rejection control of flexible structures

Abstract In this paper, a model-based output feedback recurrent wavelet neural network (RWNN) controller is proposed for a class of nonlinear MIMO systems with time-varying matched/mismatched uncertainties. The proposed RWNN emulator adaptively trains to follow an ideal state-feedback controller which is designed on the underlying linear model (ULM) of the plant. Simultaneously, the control system employs an adaptive neural network (NN) mechanism to estimate the mismatch between the RWNN controller and this ideal control law. As a result, the conservatism associated with the classical robust control methods where the controller is synthesized based on worst-case bounds is addressed. Moreover, in order to generalize the subjected class of the investigatable plants, the echo-state feature of adaptive RWNN is used to contribute to the performance of nonminimum phase systems. Accordingly, in the context of flexible smart structures with non-collocated sensor/actuator configuration, a delayed feedback is added in the network which brings about a better match between the model output and the measured output. As a result, even for systems with an unknown Lipschitz constant of lumped uncertainty, the controller can be trained online to compensate with an additional revision of the control law following some Lyapunov-based adaptive stabilizing rules. Additionally, the current approach is proposed as an alternative to the hot topic of nonlinear system identification-based control synthesis where the exact structure of the nonlinearity is required.

Disturbance Rejection Control Based on State-Reconstruction and Persistence Disturbance Estimation

Abstract In this note, disturbance rejection control (DRC) based on unknown input observation (UIO), and disturbance-observer based control (DOBC) methods are revisited for a class of MIMO systems with mismatch disturbance conditions. In both of these methods, the estimated disturbance is considered to be in the feedback channel. The disturbance term could represent either unknown mismatched signals penetrating the states, or unknown dynamics not captured in the modeling process, or physical parameter variations not accounted for in the mathematical model of the plant. Unlike the high-gain approaches and variable structure methods, a systematic synthesis of the state/disturbance observer-based controller is carried out. For this purpose, first, using a series of singular value decompositions, the linearized plant is transformed into disturbance-free and disturbance-dependent subsystems. Then, functional state reconstruction based on generalized detectability concept is proposed for the disturbance-free part. Then, a DRC based on quadratic stability theorem is employed to guarantee the performance of the closed-loop system. An important contribution offered in this article is the independence of the estimated disturbance from the control input which seems to be missing in the literature for disturbance decoupling problems. In the second method, DOBC is reconsidered with the aim of achieving a high level of robustness against modeling uncertainties and matched/mismatched disturbances, while at the same time retaining performance. Accordingly, unlike the first method, DRC, full information state observation is developed independent of the disturbance estimation. An advantage of such a combination is that disturbance estimation does not involve output derivatives. Finally, the case of systems with matched disturbances is presented as a corollary of the main results.