Generally, in real life, most of systems are expressed in the form of nonlinear system. It is a well-known fact that nonlinear systems usually have very rich and sometimes even unexpected behaviors such that classical linear system theories and techniques have severe limitations if we try to apply them to control nonlinear systems. So, many serious and meaningful researches have been conducted by many scientists and engineers to develop new theories over the linear system theories to mainly targeted for nonlinear systems such as backstepping control, variable structure control, gain scheduling control and feedback linearization control. Among the methods, the main idea of feedback linearization is that a vontroller is developed in a way that it cancels any nonlinear terms in a system to transform the original system models into the equivalent models of simpler form. However, there are also a number of shortcomings and limitations associated with the feedback linearization approach. They are (1) the exact cancelation of nonlinearity is impossible for the uncertain nonlinear system, (2) the class of feedback linearizable system is limited. Recently, some results have been appeared to make feedback linearization robust. The rigorous conditions for feedback linearization are summarized as controllability and involutivity, which are somewhat restrictive - in particular, the involutivity condition. Thus, to overcome this problem, many efforts have been made during the last decade. Among them, the approxi-mate linearization method has been one of the dominant approaches. In practical systems, there are always some parameter uncertainty, model uncertainty, noise exogenous signals, etc. Thus, we propose a feedback linearizing controller with a dynamic diffeomorphism to treat a class of uncertain nonlinear systems that have unknown constant parameters and some model uncertainty. With the proposed method, we analytically show that some of uncertain systems which possess the geometrically challenging structure (e.g. systems with perturbations which do not satisfy the triangularity condition) can be stabilized.
There are several results on the stabilization or regulation of a class of nonlinear systems with either triangular or feedforward nonlinearity. However, the existing results are applicable to their considered systems when the nonlinearity structure is known a priori. We propose an adaptive switching controller for a class of uncertain nonlinear systems. Specifically, the adaptive switching scheme can tune the dynamic gain depending on the nonlinearity structure. The nonlinear systems whose linear growth rate and nonlinearity structure are unknown are regulated by our bi-directional switching controller.
We consider a class of nonlinear high-order systems and propose a new high-order condition on the nonlinearity and suggest a global stabilizing controller. The proposed condition is quite °exible due to the freedom of choosing a positive function in the inequality. It is shown that a general high-order triangular forms can be contained. Moreover, due to the flexibility, some high-order nonlinearities which do not belong to existing conditions can be contained. For global regulation, the suggested controller employs a dynamic gain to accommodate the nonlinearity. The new controller is continuous and time varying in nature such that it is easy to implement. Also, we propose a new state feedback controller using a dynamic gain for input-delayed systems with high-order nonlinearity containing feedforward and non-feedforward forms.The controller design is based on the reduction method to remove the input delay and the gain scaling technique involving appropriate powers of high-order nonlinearity. As a result, more generalized systems containing feedforward and nonfeedforward terms with an input delay are regulated when the proposed ratio condition of the nonlinear function is satisfied. Lastly, we show that the problem generating by the centrifugal force of the ball and beam system is solved by a regulating state feedback controller with an adaptive dynamic gain and the proposed controller improves performance by showing experiment results.
궤환 선형화 기법은 비선형 시스템을 선형화 시켜서 비선형성을 없애는 기법이다. 하지만, 실제 시스템에서는 불확실성이 존재하게되어 정확한 선형궤환화 기법을 적용할수 없어서 approximate 선형궤환화 기법을 적용하여 선형화 하게되고 이러한 시스템에서도 여전히 불확실성은 존재하게 된다. 이러한 현상에 의해서 나타나는 시스템의 불확실성 문제로써 시스템의 불확실한 구조, 고차 비선형성, 시간지연성 문제가 있다. 본 논문에서는 표준 형태의 궤환 선형화 기법이 가지고 있는 여러가지 문제점들을 다루고 각각의 문제에 대한 분석적인 방법에 입각한 해결책을 제시하였다. 우선 triangular condition을 만족하거나 feedforward condition을 만족하지만 어떠헌 구조인지에 대한 불확실성을 가지는 비선형 시스템에 적용될 수 있는 스위칭 형태의 제어기를 제시하였다. 이것은 각 condition에 대해서 적용 가능한 dynamic gain을 각각 제안한 후 시스템의 구조를 모르므로 두가지의 dynamic gain을 적절히 스위칭 할 수 있도록 설계하였다. 그리고 같은 현상에서 output feedback 문제를 가질 때에도 역시 스위칭 형태의 제어기를 제시하였다. 다음으로 고차 비선형성을 가지는 비선형 시스템의 regulation에 대해서 연구하였다. 고차 비성형성의 구조를 high-order triangular condition과 high-order feedforward condition으로 나누었고 각 경우에 적합한 dynamic gain을 설계하였다. 처음에는 제어기에 고차항이 gain scaling 된 스위칭 형태의 제어기를 제시하였고, 확장하여 적절한 initial condition에 따라서 각 경우에 적합한 미분가능한 dynamic gain을 각각 제시하였다. 아울러 입력에 시간지연이 있는 고차 비선형 시스템의 문제를 연구하였다. 입력과 불확실한 텀에 시간지연이 있을 때 gain scaling sliding surface를 이용한 제어기와 adaptive law를 설계하여 local regulation을 보였다. 입력에 시간지연이 있고 비성형텀의 구조가 non-feedforward 형태 일 때 고차항의 영향을 줄일 수 있는 dynamic gain을 제안하였다. 시간 지연을 가지는 시스템을 효과적으로 제어할 수 있는 제어 기법을 제시하였으며 시스템의 안정성 분석은 새로운 Lyapunov 안정성 기법과 Razumikhin의 이론을 접목하여 하였다. 마지막으로, 고차항을 고려하여 설계된 dynamic gain을 이용한 제어기를 원심력, 즉 고차항을 고려하여 모델링 된 ball and beam 시스템에 적용하여 그 유용성을 검증하였다.
