Linear Control Term Research Articles

Robust control design of uncertain nonlinear systems: a self-compensating and self-tuning approach

ABSTRACT The problem of robust stabilisation is considered for a class of uncertain nonlinear systems with linear control term. It is not required that the unforced nominal (nonlinear) system has to be stable and/or has to be known, which means that its Lyapunov function need not be known and/or found for designing a stabilising control scheme to compensate the effect of uncertainty on the systems like some traditional control design approaches. For such a class of uncertain nonlinear systems, a design approach, called a self-compensating and self-tuning one, is presented whereby some robust state feedback control schemes can be easily synthesised. The proposed design approach can result in a linear state feedback control scheme with a time-varying control gain for such a class of uncertain nonlinear systems, which implies the simplicity of the design approach and control results. In addition, the system uncertainty is also not required to have to satisfy the matching conditions.

Finite-time extended state observer based nonsingular fast terminal sliding mode control of autonomous underwater vehicles

In this paper, a finite-time extended state observer-based nonsingular fast terminal sliding mode control (NFTSMC) is proposed for the trajectory tracking of autonomous underwater vehicles (AUVs) with various hydrodynamic uncertainties and external disturbances. First, a proportional–integral velocity variable based third-order fast finite-time extended state observer is designed to estimate the lumped uncertainties and their first derivatives. The concepts of finite-time stability and a new proposition are utilized to prove the finite-time uniformly ultimately boundness of the proposed observer. Then, based on the disturbance estimation, an NFTSMC is developed for AUVs. The inverse tangent function and linear control term are used to provide robustness against estimation error and avoid chattering in the thrusters. The position and attitude trajectories are proved to be fast finite-time stable via the Lyapunov theorem. To verify the theoretical analysis, comparative numerical simulations are provided to demonstrate the effectiveness of the proposed control scheme.

Model-free controller with an observer applied in real-time to a 3-DOF helicopter

In this paper, a model-free controller with an observer is presented for a class of uncertain continuous-time multiinput-multioutput nonlinear dynamic systems. The proposed model-free control law consists of 2 parts: the first part is a linear control term used to specify the dynamics of the closed loop system, and the second part is a compensator of the effects of uncertainties and external disturbances. The compensator is synthesized from an estimator of the effects of uncertainties and disturbances based on the Lyapunov approach. In order to estimate the unavailable states of the controlled system, a linear state observer is designed. All of the signals in the closed-loop system are proved to be uniformly ultimately bounded using the Lyapunov stability theory. The effectiveness and feasibility of the proposed control strategy are examined in a real-time application for a helicopter with 3 degrees of freedom.

Bifurcation Control of in Morris-Lecar Neuron Model via Washout Filter with a Linear Term Based on Filter-Aided Dynamic Feedback

In this paper, based on Routh-Hurwitz stability criterion, the linear control term of washout filter-aided dynamic feedback controller is added to the Morris-Lecar (ML) system to stabilize the bifurcation. We deduce the linear control parameters according to the stability criterion, and the simulation results indicate that the controller is effective to stabilize ML model. In addition, electrical stimulation is selected as an output of the controller, thus it may provide theoretical guidance for clinical diagnosis and therapy of dynamical diseases.

Stabilizing control of Hopf bifurcation in the Hodgkin–Huxley model via washout filter with linear control term

It is a significant issue to control bifurcation because many neuronal diseases have close relevance to bifurcation of neuron system. Some studies have been done on bifurcation control in the Hodgkin–Huxley (HH) model, but there is no clear mathematical criterion for bifurcation stabilization. In this paper, according to Routh–Hurwitz stability criterion, we employ linear control term of washout filter-aided dynamic feedback controller to stabilize bifurcation of the HH model. As a result, we can deduce linear control gain based on the criterion, and simulation shows the method is effective for making the HH model stable. The controller designs described here are achieved by electrical stimulus, so it may have potential applications in the diagnosis and therapy of dynamical diseases.

DELAY FEEDBACK CONTROL FOR INTERACTION OF HOPF AND PERIOD DOUBLING BIFURCATIONS IN DISCRETE-TIME SYSTEMS

Interaction of Hopf and period doubling bifurcations, as a so-called codimension two singularity, may give rise to rich bifurcation outcomes depending on the two-parameter unfolding at the bifurcation point. In this paper, we develop a nonlinear delay control for interaction of Hopf and period doubling bifurcations at a desired parameter location with preferred bifurcation properties. For its linear control term, the gains are determined by the bifurcation critical conditions and are used to create this type of bifurcations at a desired parameter location. For its nonlinear control term, the gains are derived by the center manifold theorem and theory of normal form. They determine the type and stability of bifurcation solutions. The proposed control method is applicable to any uncontrolled system which can be stable, unstable or even chaotic. Numerical experiments verify the feasibility of the control methodology and clearly show easy manipulation of all kinds of possible solutions of the created bifurcation.