Robust Nonlinear Control: Feedback Passivation and Input Saturation Techniques

9972045Lin非线性反馈设计提供了利用真正的非线性效应的可能性，例如，使用小的控制来诱导大的效应。该方案的目的是发展理论上合理的、实用的基于无源性的低增益和低高增益控制方法，用于设计反馈控制器，对于现有方法不能充分控制的一大类非线性系统实现全局渐近稳定性、对建模不确定性的性能鲁棒性和干扰抑制。在我们的理论发展中，一条独特的主线将是系统地使用小控制和反馈无源，其重点是如何在反馈设计中利用动态系统固有的主导非线性，而不是通过反馈线性化来消除非线性来设计控制器。反馈控制的目的是全局稳定或调节系统，并以一种稳健的方式做到这一点，即以一种对系统中的各种扰动和结构不确定性不敏感的方式。一个统一的、基于无源性的鲁棒非线性控制理论将有助于我们设计高性能的非线性控制器，能够抑制干扰并跟踪期望的轨迹，而不像传统的现代控制理论那样依赖于对系统模型或模型参数的准确描述以及对干扰信号的明确描述。许多具有实际意义的动态系统(如机器人、电刺激肌肉、旋转机械、感应电机、电力系统、航空航天飞行器、飞机、导弹等)本质上具有在反馈设计中不可忽视的固有非线性特征。更重要的是，利用其真正的非线性的控制系统可能比那些没有利用的控制系统获得更好的性能。由于大多数工程系统涉及高度非线性的执行器、传感器和过程元件，主动研究的一个目标是将一个非线性系统转换为一个线性系统，这样定义良好的线性控制技术就可以很容易地应用于这个系统。这种方法具有严重的局限性，例如对高能执行器的要求以及此类方案对参数变化和扰动缺乏鲁棒性。因此，这些技术在解决现实世界问题方面的成功相对较少。这份提案中的研究计划解决了反馈设计中的需求，并提出了一些方法来解决一些最重要的问题，我们认为这些问题对非线性控制理论的进步和应用至关重要。这项研究的主要成果将是用于控制非线性动态系统的新的、系统的设计方法，这在现有的文献中是不存在的。这一建议的意义在于，它找出了阻碍非线性控制理论发展和应用的主要障碍，也勾勒出了固有非线性系统控制的具体问题，并提出了理论创新和实践可行的解决方法。将解决一些重要的、具有挑战性的开放问题。从长远来看，这将为今后对几个理论和实践问题的研究提供洞察力和推动力。人们相信，使用低能量控制的系统化方法的好处将得到越来越广泛的认识，特别是在工业(如制造业、航空航天、电力和生物医学工程)中，可以找到许多具有执行器饱和的非线性控制的应用。由于非线性控制方案的显著特点和包含的现实假设，本程序中开发的非线性控制方案将在其他工程分支中得到比传统控制理论更广泛的应用。

9972045LinNonlinear feedback designs offer the potential to take advantage of genuinely nonlinear effects, for instance, to induce large effects using small controls. The objective of this proposal is to develop theoretically-sound, practically-useful passivity-based low-gain and low-and-high gain control methods for designing feedback controllers that achieve global asymptotic stability, performance robustness against modeling uncertainty, and disturbance attenuation, for a large class of nonlinear systems which cannot be adequately controlled by existing methods. A unique thread in our theoretical development would be the systematic use of small controls and feedback passivation, which focus on ways to exploit the inherently dominant nonlinearities of the dynamic system in the feedback design, rather than to design controllers by canceling the nonlinearities via feedback linearization. The purpose of a feedback control is to stabilize or regulate the system globally and do so in a robust fashion, that is, in a manner that is not sensitive to various perturbations and structural uncertainties in the system. A unified, passivity-based theory of robust nonlinear control would contribute to our ability to design high performance nonlinear controllers capable of attenuating disturbances and tracking desired trajectories, without relying as much on an accurate description of the system model or model parameters and on explicit descriptions of the disturbance signals as does conventional modern control theory.Many dynamic systems of practical importance (e.g. robotics, electrically stimulated muscles, rotating machines, induction motors, power systems, aerospace vehicles, aircraft, missiles and so on) have essentially inherent nonlinear characteristics that cannot be ignored in feedback design. More importantly, control systems that exploit their genuine nonlinearities are likely to achieve better performance than those that do not. Because most engineering systems involve highly nonlinear actuators, sensors and process elements, a goal of active research is to transform a nonlinear system into a linear system for which well-defined linear control techniques are readily applicable. This approach has serious limitations, e.g. the requirement of high energy actuators and the lack of robustness of such schemes to parameter variations and disturbances. Consequently, these techniques have had relatively little successful in solving real-world problems. The research plan in this proposal addresses the needs called for in feedback design, and it proposes approaches to tackle some of the most important issues that we believe are critical to the advancement and application of nonlinear control theory. The main outcome of the proposed research will be new, systematic design methodologies for the control of nonlinear dynamic systems, which are not available in the existing literature. The significance of this proposal is that it identifies the main barriers that hamper the advance and application of nonlinear control theory, but also delineates concrete problems for the control of inherently nonlinear systems, and suggests theoretically innovative and practically feasible methods to resolve them. A number of important and challenging open problems will be solved. In the long term, it will provide insight and thrust for future investigations into several theoretical and practical issues. It is believed that the benefits to a systematic approach towards using low energy control will be becoming more widely appreciated, particularly in industries (e.g. manufacturing, aerospace, power and biomedical engineering) where many applications of nonlinear control with actuator saturation can be found. It is also expected that the nonlinear control schemes to be developed in this program will find much broader applications in other branches of engineering than traditional control theory, due to their significant features and the inclusion of realistic assumptions.