Research on Real-time Control of a Continuous-time System by Discrete-time Variable Structure Control

1.对于参数未知的线性系统，即使已知系统的结构，也很难设计出稳定的滑动超平面。本研究提出了一种单输入输出系统稳定滑动超平面的自适应辨识方法。当线性系统的输入和输出均可测时，提出了一种滑模动态补偿器的设计方法，使系统的行为遵循最优控制。变结构系统的输入幅值实际上可以取一个极限值。在这种情况下，确定可以通过VSS控制律稳定的状态空间中的集合。研究表明，由状态变量的线性组合确定的常规滑模比由状态的非线性函数确定的滑模具有更小的可镇定集。特别是当适当选择非线性函数时，可以发现整个状态空间是可镇定的。对于…作为该方法的进一步应用，我们开发了计算机辅助软件包，并实现了新的算法。在此基础上，进行了大量的应用研究。设计了具有附加动力学的旋转式摆，并使其稳定在直立位置。实验结果表明，与传统的线性调节器相比，该控制系统具有较强的鲁棒性。代替滑动模式，将状态范数在其内部减小的集合定义为滑动扇区。这使得综合设计连续系统和离散系统的变结构控制成为可能。当采样时间变大时，该滑动扇区变得更窄。对于自适应离散时间VSS，采用扇区方法。基于二次判据函数设计了连续时间系统及其采样数据系统的变结构控制律。扇区由相应的Riccati方程确定。较少

1. For the linear system with unknown parameters, it is difficult to design a stable sliding hyper plane even if the structure of the system is known. This research presents an adaptive method to identify a stable sliding hyper plane for a single input and output system.2. When the input and output of the linear system are measurable, it is proposed to design a dynamic compensator for a sliding mode on which the system behaves following the optimal control.3. The input amplitude for the variable structure system can be practically taken a limited value. In this case the set in a state space which can be stabilized by the VSS control law is determined. This research tells that the conventional sliding mode determined by the linear combination of the state variable gives smaller stabilizable set comparing with the one given by the nonlinear function of the state. Especially when the proper choice of the nonlinear function it is found that the whole state space can be stabilizable.4. For … More the applications of the proposed approach, we have developed the computer aided software package and implemented the new algorithms. Using this, many researches on applications have been done.5. The rotating type pendulum with the additional dynamics has been designed and it is stabilized at the upright position. From the experiment it is found that the controlled system is robust in comparing to the conventional linear regulators.6. Instead of the sliding mode, the set inside which the norm of the state is decreasing is defined as the sliding sector. This makes possible to design a VSS control for both continuous and discrete-time systems comprehensively. This sliding sector becomes narrower when the sampling time becomes larger.7. It is employed sector approach for the adaptive discrete-time VSS.8. The VSS control law is designed for both continuous-time and its sampled-data systems based on the quadratic criterion function. The sector is determined by the corresponding Riccati equation. Less