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本文针对多变量自校正控制在实际应用中存在的问题,提出了基于输出预报的多变量极点配置自校正控制算法。该算法是算法[2,3,5,6]的进一步发展,而这些算法可视为该算法的特例。该算法较好地解决了线性多变量自校正控制中的稳定性、非最小相位、稳态偏差和B_0阵非行满秩等问题。通过适当选取一个列满秩矩阵多项式P(z~(-)),控制器能够控制输入和输出维数不同的多变量系统。整个控制算法由三部分组成;K步超前输出预报、闭环极点配置和控制信号计算。由递推最小二乘(RLS)算法在线辨识预报器参数,并由此计算K步超前输出预报y~*(t+k|t)。极点配置问题归结为求解一个多变量Diophantine方程,而Diopha-ntine方程有解的充分和必要条件是矩阵多项式A(z~(-1))和S(z~(-1))右互质(证明见附录)。给定一个矩阵多项式T(z~(-1))并在系统中包含一个积分器,可以得到具有指定闭环极点和零稳态偏差的自校正控制器。本文最后给出计算机仿真结果,验证算法的有效性和实用性。
In this paper, aiming at the problems of multivariable self-tuning control in practical application, a multivariable pole placement self-tuning control algorithm based on output forecast is proposed. The algorithm is a further development of algorithms [2, 3, 5, 6], and these algorithms can be considered as special cases of the algorithm. This algorithm solves the problems of stability, non-minimum phase, steady-state deviation and non-full rank of B_0 array in the linear multivariable self-tuning control. By properly choosing a column full rank matrix polynomial P (z ~ (-)), the controller can control multivariable systems with different input and output dimensions. The whole control algorithm consists of three parts; K step ahead of the output forecast, closed-loop pole configuration and control signal calculation. Predictor parameters are identified online by Recursive Least Squares (RLS) algorithm, and the forecast of K-step ahead output is calculated as y ~ * (t + k | t). The pole assignment problem comes down to the solution of a multivariate Diophantine equation. The necessary and sufficient conditions for the Diophantine equation to be solved are the matrix polynomials A (z -1) and S (z -1) Proof see appendix). Given a matrix polynomial T (z ~ (-1)) and including an integrator in the system, a self-tuning controller with specified closed-loop poles and zero steady-state deviations can be obtained. At the end of this paper, computer simulation results are given to verify the effectiveness and practicability of the algorithm.