一种基于边界特征线且特征点可变的二阶非线性离散跟踪微分器及在测速定位系统中的应用

利用状态反推方法确定最速离散二阶系统的线性区域的边界特征线及控制特征线，以相平面上的点及边界曲线、控制线的相对位置按线性规则确定控制量的大小，区分可达区与线性区，并依此构造最速分段线性函数形式的跟踪微分器（Tracking-differentiator，TD），这种算法可以方便地修改特征点，适应能力强，而且运算中不包含任何根号运算，使得控制综合函数的形式极大简化，有利于工程实现.对正弦信号及方波信号的仿真结果表明了上述结论的合理性.验证了特征点分段线性算法在适当修改特征点后得到的TD，与经典TD以及它的线性近似进行比较，跟踪能力和微分提取能力都得到了较大的提高.应用移动平均算法构成的跟踪微分器组，具有相位补偿功能，适当选取TD参数后，得到了滤波能力强、相位特性良好的滤波器，并应用于基于长定子齿槽检测的永磁电动磁悬浮列车的测速定位系统中.实验结果表明，本文提出的简化TD按相位补偿确定的方案能有效滤除脉冲和扰动等噪声，对过轨道接缝时的畸变信号进行修复，边界容易修改，算法简单有效，实时性强，易于工程实现.

Discrete Second-order Nonlinear Tracking-differentiator Based on Boundary Characteristic Curves and Variable Characteristic Points and Its Application to Velocity and Position Detection System

The boundary characteristic curves of linear regions with the second-order discrete time optimal control are presented using the method of the state back step. The control variable is decided by the linearized criterion according to the relative position between phase plane point and switching curve, and the boundary characteristic curves. The reachable region and the boundary region are given. Then some sectionalized constructed linear synthetic functions are obtained. Based on this function, the discrete form of tracking-differentiator (TD) is constructed. This algorithm is able to amend its characteristic points and is flexible to applications. It does not contain the square roots algorithm, and its form is simple and its implement action is easy. Numerical simulation of sinusoidal wave and square wave shows that this discrete form of tracking-differentiator can quickly track an input signal without overshooting or chattering and can produce a good differential signal. Its effect is similar to one of the nonlinear boundary transformation. A kind of TD group with phase compensation and filter ability is acquired using the moving average algorithm. The excellent filter ability and phase compensation are obtained after a proper TD parameter choice. The velocity and position detection of a permanent magnet electro dynamic maglev train system based on long stator alveolus count employs the above scheme. The running experiment of the train shows that the above algorithm can effectively remove noise and lead to little phase delay, and amend distortion signals at the guide juncture. The algorithm is easy, effective and convenient to engineering implementation action.