A linear approach to generalized minimum variance controller design for MIMO nonlinear systems

Designing minimum variance controllers (MVC) for nonlinear systems is confronted with many difficulties. The methods which are able to identify MIMO nonlinear systems are scarce, and linear models are not accurate in modeling nonlinear systems. In this paper, Vector ARX (VARX) models are proposed for designing MVC and generalized minimum variance controller (GMVC) for linear and nonlinear systems, and the accuracy of these models in approximating the nonlinear MIMO system is studied. However, the VARX is a linear model. It is shown that this model can identify some kinds of nonlinear systems with any desired accuracy. Therefore, the controller designed by the VARX is accurate, even for these nonlinear systems. The proposed controller is tested on a both linear system and a nonlinear four-tank benchmark process. In spite of the simplicity of designing GMVCs for the VARX models, the results show that the proposed method is accurate and implementable.     

Dissipativity-based stable controller redesign for nonlinear MIMO switched systems in the presence of perturbations

This paper offers a control redesign method for a class of nonlinear MIMO perturbed dissipative switched systems. The controller for the nominal switched system without perturbation is considered to have been designed based on dissipativity. The nominal model is considered affine with perturbations in both nonlinear terms. The controller is then redesigned such that the dissipativity of the switched system with perturbations is maintained by including a robustifying term in the control law. The design is developed for the two cases of 2-norm and infinity-norm bounded perturbations. The proposed method is applied to a nonlinear MIMO switched system to verify the convergence of the state vector to the origin in the presence of perturbations.     

Parametric identification of nonlinear hysteretic systems

Nonlinear Dynamics - The hysteretic behavior is an essential feature of many physical systems (e.g. mechanical structures, buildings dampers). Such a feature is conveniently accounted for in...     

The effect of time-delayed feedback controller on an electrically actuated resonator

This paper presents a study of the effect of a time-delayed feedback controller on the dynamics of a Microelectromechanical systems (MEMS) capacitor actuated as a resonator by DC and AC voltage loads. A linearization analysis is conducted to determine the stability chart of the linearized system equations as a function of the time delay period and the controller gain. Then the method of multiple-scales is applied to determine the response and stability of the system for small vibration amplitude and voltage loads. It is shown that negative time-delay feedback control gain can lead to unstable responses, even if AC voltage is relatively small compared to the DC voltage. On the other hand, positive time delay can considerably strengthen the system stability even in fractal domains. We also show how the controller can be used to control damping in MEMS, increasing or decreasing, by tuning the gain amplitude and delay period. Agreements among the results of a shooting technique, long-time integration, basin of attraction analysis with the perturbation method are achieved.     

Robust tracking controller for multivariable delayed systems with input saturation via composite nonlinear feedback

In this paper, the composite nonlinear feedback (CNF) method for robust tracking control of multivariable time-delayed systems with input saturation is proposed. By constructing an appropriate Lyapunov–Krasovskii functional and using the linear matrix inequality (LMI) technique, the asymptotic tracking criteria is derived in terms of LMI, which can be solved numerically using the LMI^® toolbox of MATLAB. Unlike the previous robust tracking controller design methods, which need restrictive assumptions, less conservative design conditions are obtained using this approach. The proposed CNF-based robust tracking controller improves the transient performance and steady state accuracy simultaneously. Simulation results are included to demonstrate the effectiveness of the proposed method.     

An adaptive delayed feedback control method for stabilizing chaotic time-delayed systems

This paper addresses a new adaptive delayed feedback control technique for stabilizing a class of chaotic time-delayed systems with a variable parameter. In the proposed scheme, the feedback gain of a delayed feedback controller is automatically tuned according to an adaptation law in order to stabilize unstable fixed points of the system. Such a mechanism provides a way to cope with unexpected changes in the parameters of the system. The adaptation algorithm is constructed based on the Lyapunov?CKrasovskii??s stability theorem. The control technique provides the advantages of increased stability and optimality, adaptability to the changes in the parameters, high privacy, simplicity, and noninvasiveness. The effectiveness of the control scheme is demonstrated using numerical simulations for a well-known chaotic time-delayed system.     

Output feedback stabilization based on dynamic surface control for a class of uncertain stochastic nonlinear systems

In this paper, the dynamic surface control (DSC) algorithm is proposed for a class of stochastic nonlinear systems with nonminimum phase and the standard output-feedback form. The proposed algorithm is a stochastic vision by combining the traditional back-stepping together with the DSC technique, which can overcome the problem of ‘explosion of complexity’ in the back-stepping designing procedure for the stochastic nonlinear systems. Thus, it can reduce the computation complexity and is easy to be used in the actual implementation. It is shown that all the signals of the resulting closed-loop system are uniformly ultimately bounded.     

Linear feedback controller design method for time-delay chaotic systems

Based on the stability theory of time-delay systems, this paper discusses chaos control and synchronization problem of time-delay chaotic systems. Through the combining of a new theorem and the characters of the chaotic system, we have designed a linear controller to realize chaos control and synchronization for Lorenz system with time-varying lags. Finally, numerical simulations are provided to verify the effectiveness and feasibility of the developed method.     

Adaptive fuzzy backstepping output feedback control for a class of MIMO time-delay nonlinear systems based on high-gain observer

In this paper, an adaptive fuzzy backstepping output feedback control approach is developed for a class of multiinput and multioutput (MIMO) nonlinear systems with time delays and immeasurable states. Fuzzy logic systems are employed to approximate the unknown nonlinear functions, and an adaptive fuzzy high-gain observer is developed to estimate the unmeasured states. Using the designed high-gain observer, and combining the fuzzy adaptive control theory with the backstepping approach, an adaptive fuzzy output feedback control is constructed recursively. It is proved that all the signals of the closed-loop adaptive control system are semiglobally uniformly ultimately bounded (SUUB) and the tracking error converges to a small neighborhood of the origin.     

Output frequency properties of nonlinear systems

Nonlinear systems usually have complicated output frequencies. For the class of Volterra systems, some interesting properties of the output frequencies are studied in this paper. These properties show theoretically the periodicity of the output super-harmonic and inter-modulation frequencies and clearly demonstrate the mechanism of the interaction between different output harmonics incurred by different input nonlinearities in system output spectrum. These new results have significance in the analysis and design of nonlinear systems and nonlinear filters in order to achieve a specific output spectrum in a desired frequency band by taking advantage of nonlinearities. Examples and discussions are given to illustrate these new results.     

Output regulation distributed formation control for nonlinear multi-agent systems

In this paper, the distributed formation control problem for multi-agent systems with affine nonlinear dynamic is considered. In order to solve the problem, we generalize the output regulation problem of nonlinear systems to multi-agent systems and design a distributed control scheme. Based on the internal model principle, the distributed output regulation formation control problem can be solved by solving the regulator equations. Moreover, the simulation example is provided to demonstrate the effectiveness of the main results.     

Output feedback regulation of time-delay nonlinear systems with unknown continuous output function and unknown growth rate

Nonlinear Dynamics - This paper is concerned with the global regulation via output feedback for the time-delay nonlinear systems with unknown continuous output function and unknown growth rate....     

Variable structure based robust backstepping controller design for nonlinear systems

This study presents robust control architecture in the sense of variable structure control via a backstepping design. By using systematic backstepping design techniques, closed-loop behavior of an n-order nonlinear system can be transformed into a stability and convergence problem of a fast switched 2nd order system. There are two main parts contained within the proposed control algorithm; one is a nominal control effort generated according to the Lyapunov stability criterion during recursive backstepping processes, and the other belongs to a smooth robust control law designed to eliminate the effects of unknown lumped perturbations. Finally, a Genesio system is used as an illustrated example to demonstrate the robustness of the control algorithm. The feasibility and properties of the proposed method are given by numerical simulations.     

SDRE-based near optimal nonlinear controller design for unified chaotic systems

This paper proposes a near optimal controller design method for unified chaotic systems based on state-dependent Riccati equation (SDRE) approach. A parameterization of the optimal nonlinear control gain is given in terms of the solution matrix of an SDRE. A simple algorithm to compute the near optimal control gain is proposed. The proposed near optimal control design method is also extended to the synchronization problem for unified chaotic systems. Finally, the effectiveness of the proposed design method is verified via numerical simulations.     

Nonlinear integral resonant controller for vibration reduction in nonlinear systems

A new nonlinear integral resonant controller (NIRC) is introduced in this paper to suppress vibration in nonlinear oscillatory smart structures. The NIRC consists of a first-order resonant integrator that provides additional damping in a closed-loop system response to reduce high-amplitude nonlinear vibration around the fundamental reso-nance frequency. The method of multiple scales is used to obtain an approximate solution for the closed-loop system. Then closed-loop system stability is investigated using the resulting modulation equation. Finally, the effects of different control system parameters are illustrated and an approximate solution response is verified via numerical simulation results. The advantages and disadvantages of the proposed controller are presented and extensively discussed in the results. The controlled system via the NIRC shows no high-amplitude peaks in the neighboring frequencies of the resonant mode, unlike conventional second-order compensation methods. This makes the NIRC controlled system robust to excitation frequency variations.