时滞最优控制及其在轮式倒立摆中的应用

发布时间：2018-05-04 05:30

本文选题：最优控制 + 输入时滞　；参考：《南京航空航天大学》2016年博士论文

【摘要】：最优控制就是要在容许的控制方案中找到一个符合要求的最佳控制方案,这是一个经典的优化问题。由于最优控制具有广泛的应用背景,这使得最优控制理论的研究经久不衰,尤其是线性二次型最优控制问题,它的解是一个简单的状态反馈形式,在实际工程应用中非常容易实现。然而,最优控制对系统的精确性要求比较高,时滞因素和系统的不确定性因素又是实际系统中普遍存在的,完全忽略这些因素的影响设计和使用最优控制器往往得不到好的控制效果,甚至会导致系统不稳定。从信号测量到控制器作用于系统会有一个时间差,这个时间差就是输入时滞,这是不可避免的存在因素。由于输入时滞的存在会导致控制器的设计难度大大增加,所以在设计控制器时,经常会把小量的输入时滞忽略掉。但是对于最优控制来说,其性能指标值对时滞是很敏感的,一个非常小的输入时滞也会大大增加实际的性能指标值。因此考虑输入时滞影响下的最优控制器设计是本文的研究课题。全文共七章。第一章分别介绍了时滞系统最优控制、时滞系统鲁棒最优控制、两轮式倒立摆机器人的研究现状等背景知识。第二章详细阐述了输入时滞对控制系统的影响,以及输入时滞研究的必要性。第三章研究了线性输入时滞系统的最优状态反馈控制,通过引入积分状态变换将输入时滞系统转化为无时滞系统,得到两个系统之间的关系式。通过该关系式,可以利用无时滞系统求解原输入时滞系统的最优控制。最终结果揭示了输入时滞在线性系统的最优控制设计中所起的作用:输入时滞的存在并不改变当前时刻所需要的最优控制量,只是延后了最优控制的作用时间。基于这个认识,我们可以求出时滞最优控制的时滞反馈增益公式。另外,对于多输入时滞系统,可利用动态规划的思想,并结合单输入时滞系统的结果,同样可以得到各输入的时滞最优反馈增益表达式。第四章研究具有外部扰动的输入时滞系统的最优轨迹跟踪控制问题。先通过一个简单的变换将轨迹跟踪目标转化为一个已知扰动,再引入一个改进的积分状态变换,将输入时滞误差系统转化为无时滞系统,并得到两个系统之间的关系式。这样原问题就被转化为无时滞系统的最优扰动抑制问题。为了补偿掉不确定因素的影响,在标称误差系统最优控制的基础上引入扰动观测器,最终设计的控制器包含两部分:一部分是标称系统的时滞最优轨迹跟踪控制,主要作用是用来实现给定的控制任务;另一部分是由扰动观测器所得到的,主要用来补偿掉不确定性因素的影响。由于输入时滞的影响,不能利用当前误差状态来设计控制器,所以引入预测状态代替当前状态,得到最终的时滞最优轨迹跟踪控制器。仿真结果显示,所设计的控制器不但能保持最优控制的性能,还大大提高了最优控制的鲁棒性。在第五章和第六章,我们将理论结果应用于两轮式倒立摆的“往返运动”控制和“低头抬头运动”控制。在两轮式倒立摆的“往返运动”控制设计中,通过引入特殊的线性二次型性能指标,将摆角的误差权重取得尽量大,这样就将“往返运动”控制问题转化为输入时滞线性系统的最优轨迹跟踪控制问题。由于输入时滞的影响,最终设计的控制器中的当前状态用预测状态代替。考虑到实际问题中具有不确定性因素的影响,我们将标称系统的最优状态选取为积分滑模面,设计积分滑模控制器补偿掉不确定因素的影响。仿真结果显示,系统的位移状态几乎没有振动,高频振动都出现在速度变量中,这说明所设计的控制器不但能够很好地实现“往返运动”控制,还对不确定性具有很强的鲁棒性。对于“低头抬头运动”控制设计,由于避障需要的摆角运动范围比较大,所以直接应用线性化模型是不可行的。在不考虑转向运动的情形下,由于系统具有一定的解耦性,可以采用反馈线性化的方法,将关于摆角的子系统转化为简单的线性系统来考虑。根据实际任务设计合适的轨迹跟踪目标,最后设计时滞最优轨迹跟踪控制器来实现运动任务。仿真结果显示,所设计的控制器能够很好地完成“低头抬头运动”任务。最后,在第七章,我们对本文做了一个总结。
[Abstract]:The optimal control is to find an optimal control scheme in the admissible control scheme. This is a classic optimization problem. Because the optimal control has a wide application background, the optimal control theory has been studied for a long time, especially the linear two order optimal control problem, and its solution is a simple state. The feedback form is very easy to be realized in practical engineering applications. However, the accuracy of the optimal control system is higher, the time delay factor and the uncertainty factor of the system are common in the actual system. The system is unstable. From the signal measurement to the controller, there is a time difference between the system and the system. This time difference is the input time delay. This is an inevitable existence factor. Because of the existence of the input delay, the design difficulty of the controller is greatly increased, so the small amount of input time delay is often ignored in the design of the controller. But for optimal control, its performance index value is very sensitive to time delay, and a very small input time delay will also greatly increase the actual performance index. Therefore, considering the effect of input delay, the optimal controller design is a research topic in this paper. The full text is seven chapters. The first chapter introduces the optimal control of time delay systems respectively. In the second chapter, the influence of input time delay on the control system and the necessity of input time-delay research are described in detail. In the third chapter, the optimal state feedback control system for linear input time-delay systems is studied, and the input time delay is introduced by introducing integral state transformation. The system is transformed into a time delay system, and the relationship between the two systems is obtained. Through this relation, the optimal control of the original input delay system can be solved by the time delay system. The final result reveals the function of the input delay in the optimal control design of the linear system. The existence of the input delay does not change the need for the current time. The optimal control amount is only delayed the optimal control time. Based on this understanding, we can find the time delay feedback gain formula for time delay optimal control. In addition, for multi input time-delay systems, the idea of dynamic programming and the results of single input time-delay systems can be combined with the results of single input time-delay systems, and the optimal feedback of each input time delay can be obtained. The fourth chapter studies the optimal trajectory tracking control problem of an input time-delay system with external disturbances. First, a simple transformation is used to transform the trajectory tracking target into a known disturbance, and then an improved integral state transformation is introduced to transform the input delay error system into a time delay system and two systems are obtained. In order to compensate for the influence of the uncertain factors, the disturbance observer is introduced on the basis of the optimal control of the nominal error system, and the final designed controller consists of two parts: one part is the optimal time delay trajectory tracking control of the nominal system, The main function is to realize the given control task; the other is obtained by the disturbance observer, which is mainly used to compensate for the influence of the uncertain factors. Due to the influence of the input delay, the controller can not be designed by the current error state, so the predictive state is introduced to replace the current state and the final time delay optimal trajectory is obtained. The simulation results show that the designed controller can not only maintain the performance of the optimal control, but also greatly improve the robustness of the optimal control. In the fifth and sixth chapters, we apply the theoretical results to the "round trip" control and "low head lift" control of the two wheeled inverted pendulum. "Two wheel inverted pendulum". In the control design of round and round motion, by introducing a special linear two type performance index, the error weight of the swing angle is obtained as large as possible. Thus the "round trip" control problem is transformed into the optimal trajectory tracking control problem of linear system with input delay. The current state of the final design of the controller due to the influence of input delay. Using the predictive state instead. Considering the influence of the uncertain factors in the actual problem, we select the optimal state of the nominal system as the integral sliding surface, and design the integral sliding mode controller to compensate the influence of the uncertain factors. The simulation results show that the displacement state of the system is almost no vibration, and the high frequency vibration appears in the velocity variable. This shows that the designed controller not only can realize the "round trip" control well, but also has strong robustness to the uncertainty. For the control design of "low head lift", it is not feasible to apply the linearized model directly because of the large range of swing angle required by the obstacle avoidance. In the case of a certain decoupling of the system, the feedback linearization method can be used to convert the pendulum angle subsystem into a simple linear system. The appropriate trajectory tracking target is designed according to the actual task, and the time delay optimal trajectory tracking controller is designed to realize the motion task. The simulation results show that the design is designed. The controller can perform the task of "low head lift" very well. Finally, in the seventh chapter, we make a summary of this article.

【学位授予单位】：南京航空航天大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O232

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