非线性系统迭代学习控制算法研究

发布时间：2018-09-09 12:33

【摘要】：理论上迭代学习控制能够完全消除被控系统的可重复误差,实现对理想输出轨迹的完美跟踪,但迭代学习控制算法在应用过程中却存在一些问题。首先在应用实践中,系统的非重复误差不可避免地存在着,例如测量误差、随机扰动等等。然而迭代学习控制对存在的这些非重复误差却无能为力。所以随着迭代次数的增加,非重复误差会不断叠加,当非重复误差的累计达到一定程度的时候,被控系统的瞬时响应波动会变得很大,甚至超出了被控系统的范围,这种现象极大地增加了系统安全运行的风险,也严重的恶化了控制系统的性能。其次,迭代学习控制算法要实现对被控系统重复误差的完全消除需要满足一定的条件。例如初值问题,即要求被控系统的初始状态位于期望轨迹上,初始误差为零。还有收敛性问题,对于非线性被控系统,为了保证控制系统控制输入收敛到理想控制输入,总是提前假设理想控制输入是存在的,而且要求被控系统满足Lipschiz连续条件。这些假设条件大大地限制了迭代学习控制算法的应用范围。所以针对以上迭代学习控制中存在的这些问题,本文研究将预测控制技术与迭代学习控制技术结合起来构造出新的控制策略来处理非线性系统中出现的这些非重复误差。利用预测技术来构造学习律中的误差信号或者学习增益,提高控制系统的性能。针对不满足Lipschiz连续条件的非线性系统,在内积空间运用算子理论构造新的迭代学习控制方案,实现这些非线性系统学习控制的收敛性。主要的研究内容和创新点如下：针对非线性系统的迭代学习控制中非重复误差存在的问题,应用学习控制技术和预测控制技术相结合的策略来实现对系统重复误差和非重复误差的补偿。因为连续的非线性系统可以离散化,所以文中的控制策略是针对离散系统来设计的。因为迭代学习控制律是离线设计的,文中主要考虑预测控制方案。假设被控系统在每次地重复运行过程中有若干个采样点,在每个采样点,都要实施不同的学习控制律,这些控制律的不同在于输出误差的不同,而这些不同的输出误差是通过在每个采样点实施预测控制得到的。文中还给出这种迭代预测控制算法的收敛性和稳定性证明。针对古典的非线性迭代学习控制要求被控系统满足Lipschiz连续的条件约束这一问题,提出了一种新的迭代学习控制律,也可称之为两步迭代学习控制,所提出的学习控制律在被控系统不能满足Lipschiz连续的条件下实现了收敛。这大大扩展了迭代学习控制的应用范围。在迭代学习控制中,需要对系统输出进行测量,通过与理想输出做差得到被控系统输出误差,来更新过控制输入,这就不可避免地出现测量误差,从而影响控制系统的性能。针对测量误差,本文提出基于预测的可变增益的迭代学习控制策略,通过可变预测增益消除由测量误差的存在引起的消极影响,并将这种方法应用到永磁同步电机系统来消除转矩脉动。在已经发表的文献中,大多数迭代学习控制策略都是在有限维空间提出的,针对无限维空间提出的迭代学习控制很少。而且,迭代学习控制算法的提出,都提前假设理想控制输入是存在的,但在实际应用中,我们并不知道理想控制输入是否存在。为此,本文在无限维空间提出了迭代学习控制方法,并给出了判断被控系统是否存在理想控制输入的方法,大大地降低了控制输入存在的主观性,丰富和发展了迭代学习控制理论。针对VSC-HVDC环流抑制控制中解耦不彻底,非线性不能完全补偿等问题,提出了基于误差模型的预测控制方法,首先根据欧拉公式得到被控系统离散化模型,然后推导建立跟踪误差的离散化模型,通过误差模型消除可重复性扰动,利用卡尔曼滤波估计当前状态值,利用预测消除随机误差,实现对理想目标地完全跟踪。针对预测控制方法本身计算量大,结合模块化多电平换流器使得在线运算量更大的问题,根据均值不等式,推导出了最优分组方法来求解预测控制中的目标函数的最优值,并推广最优分组方法到多层最优方法来解预测控制的最值问题,大大的减少了预测控制在线运算的运算量,提高了系统的控制性能。
[Abstract]:In theory, iterative learning control can completely eliminate the repeatable error of the controlled system and achieve perfect tracking of the ideal output trajectory, but there are some problems in the application process of iterative learning control algorithm. However, iterative learning control can't do anything about these non-repetitive errors. As the number of iterations increases, the non-repetitive errors will continue to superimpose. When the accumulation of non-repetitive errors reaches a certain degree, the transient response fluctuation of the controlled system will become very large, even beyond the scope of the controlled system. This phenomenon is very great. Secondly, Iterative Learning Control (ILC) algorithm needs to satisfy certain conditions to completely eliminate the repetitive error of the controlled system. For example, the initial value problem requires the initial state of the controlled system to be on the desired trajectory, and the initial error to be zero. Convergence problem. For a nonlinear controlled system, in order to ensure that the control input of the control system converges to the ideal control input, the existence of the ideal control input is always assumed in advance, and the Lipschiz continuous condition is required for the controlled system. These assumptions greatly limit the application scope of the iterative learning control algorithm. In this paper, predictive control technology and iterative learning control technology are combined to construct a new control strategy to deal with these non-repetitive errors in nonlinear systems. The main research contents and innovations are as follows: Aiming at the problem of non-repetitive error in iterative learning control for nonlinear systems which do not satisfy Lipschiz continuous conditions, a new iterative learning control scheme is constructed by using operator theory in inner product space to realize the convergence of learning control for these nonlinear systems. The strategy of combining learning control technique with predictive control technique is applied to compensate the repetitive error and non-repetitive error of the system.Because the continuous nonlinear system can be discretized,the control strategy in this paper is designed for the discrete system.Because the iterative learning control law is designed offline,the prediction is mainly considered in this paper. Suppose that the controlled system has several sampling points in each repetitive operation, and different learning control laws are implemented at each sampling point. The difference of these control laws lies in the difference of output errors, which are obtained by implementing predictive control at each sampling point. The convergence and stability of an iterative predictive control algorithm are proved. To solve the problem that the classical nonlinear iterative learning control requires the controlled system to satisfy Lipschiz continuous conditions, a new iterative learning control law, also called two-step iterative learning control, is proposed. The convergence is achieved under the condition of Lipschiz continuity, which greatly expands the application scope of iterative learning control. In iterative learning control, the output of the system needs to be measured, and the output error of the controlled system is obtained by making a difference with the ideal output to update the control input. In this paper, a predictive variable gain iterative learning control strategy is proposed to eliminate the negative effects caused by measurement errors. This method is applied to permanent magnet synchronous motor (PMSM) systems to eliminate torque ripple. Learning control strategies are proposed in finite-dimensional space, and few iterative learning control methods are proposed for infinite-dimensional space. Moreover, the proposed iterative learning control algorithm assumes that the ideal control input exists in advance, but in practice, we do not know whether the ideal control input exists. Iterative learning control method is put forward, and the method of judging the existence of ideal control input is given, which greatly reduces the subjectivity of control input and enriches and develops the theory of iterative learning control. First, the discretization model of the controlled system is obtained according to the Euler formula, then the discretization model of the tracking error is deduced. The repeatable disturbance is eliminated by the error model, the current state value is estimated by Kalman filter, the random error is eliminated by prediction, and the ideal target is completely tracked. The predictive control method has a large amount of calculation. Combining with the problem that modular multilevel converter makes the on-line computation more difficult, the optimal grouping method is deduced to solve the optimal value of the objective function in predictive control according to the mean inequality, and the optimal grouping method is extended to the multi-level optimal method to solve the optimal value problem of predictive control. It reduces the operation of predictive control online operation and improves the control performance of the system.
【学位授予单位】：华北电力大学(北京)
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TP13

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