线性系统实时辨识在微型计算机上的实现

实现最优控制必须研究控制对象的数学模型.对于定常系统,可以用离线系统辨识方法.如果对象数学模型为时变,就需要实时系统辨识.本文假定对象数学模型的微分方程形式已知,需要通过系统辨识确定其方程的系数,并能追踪参数的变化.这类问题称为灰箱问题.实际遇到的大多数工程系统及工业过程都属于此类问题.系统辨识的理论已相当成熟.本文着重讨论如何在微型计算机有限的资源条件下实现.选择的辨识对象为本校研制的碳纤维热分析仪试样加热电炉及其功率放大器(作为一个系统来进行辨识). 问题之关键在于系统辨识算法的选择.算法决定了系统辨识实现的开销以及辨识的可靠性.经过仿真与系统辨识实验比较,并验证了系统辨识的算法以及起步方式、参数选择、激励信号之产生等实际问题.结论为:对于线性系统实时辨识应用递归算法的最小二乘法比较简易可靠.可以在微型机或单板机上实现.

MICROCOMPUTER IMPLEMENTATION OF REAL TIME SYSTEM IDENTIFICATION FOR LINEAR SYSTEMS

This paper focuses emphasis on the implementation of real time system identification on a microcomputer with limited resources. The recursive least squares parameter estimation method recommended not only gives more precise estimated value of system parameters within a resonably short period, but also requires very little memory overhead. This algorithm holds good for single variable or multivariable Nth order linear system, and can also be applied to linear system with pure time delay. For the purpose of tracing time varing system parameters an exponential weighting factor 'L' may be Introduced into the recursive equation to place heavier emphasis on the more recent data. For slowly varing system parameters, 'L' should be set above 0.95.In case the signal to noise ratio of the data acquisition system is not good enough, digital filtering technique such as data bunching and moving average is demanded. The flow chart of the system parameter identification program is finally given, the object code of the above program linked with data acquisition module occupies 8K bytes of memory.Some pratical problems in the implementation of system parameter identification are also discussed.