摘要
本文以板球控制系统为工程背景,研究一类非线性系统的解耦与控制算法。首先应用拉格朗日功能平衡法,推导建立了板球系统的复杂及简化数学模型;其次,针对板球系统的大范围镇定问题,提出了基于反馈线性化的智能切换控制算法。用模糊动态模型替代原非线性系统,按奇异点将状态空间分为三个区域,仿真实验验证了算法的可行性;然后,提出了基于单一输入规则(SIRM,Single Input Rule Module)模糊推理模型的输出解耦滑模(SMC,Sliding Mode Control)控制方法,通过4个滑模函数和2个SIRM模糊控制器,解决了8阶板球系统模型的两个方向输出耦合问题。仿真实验表明除了能有效解耦外,算法还具有很强的鲁棒性;最后,针对实际平台的数学模型未知,提出了一种具有两层结构的监督模糊控制系统的设计方法,研究了实现问题。下层控制器采用三维输入结构的SIRMs模糊推理模型作为基本控制器,上层为监督保稳控制器,随时监控Lyapunov能量函数的变化及系统状态轨迹的有界性,确保闭环系统的稳定控制。上下两层控制各司其职,下层SIRMs模型很好的解决“维数灾”问题且控制性能指标优良,而上层监督控制器则确实起到了监督保稳作用。实验结果表明:该方案能有效的解决一类基于位置的视觉伺服非线性系统的运动控制问题。
本论文研究得到2006年高等学校博士学科点专项科研基金项目(20060183006)资助。
The problems with decoupling and control for the nonlinear ball and plate system are very representative. It belongs to that one type movement control problem based on position visual servo system. Because ball and plate system is nature nonlinear, with strong coupling when the ball move on high velocity and multi-uncertainty of fact platform, there is is important significance that the study of the ball and plate system for nonlinear control theory and real engineering application. Ball and plate system is an exemplification of nonlinear dynamics system, it has been received more and more attentions. Now, it has been used to study various control method as experimental device in some overseas university. Many scholars investigate the dynamics and control problems of it. Therefore it can be used as exploiting flat for control theory and control engineering.
Many scholars have designed control algorithm only based on simplification model of ball and plate system, but they thought little of ill-defined relative degree, strong coupling and uncertainty. However, theory isn't suitable to the ill-defined relative degree nonlinear system which thus is the important difficulty in nonlinear control. The problem of coupling hasn’t been proposed in relative research paper so far. When the ball move on high speed, the coupling of two directions is one mostly factor that impact to control precision and dynamic performance. Third, the model for real ball and plate system is unknown because to vision lag, drive machine interspace, no flat on the surface of plate, variable friction coefficient and so on. But there are language knowledge with expert to provide the controlled plant and fuzzy controller. All of these factors make trajectory tracking of the ball and plate system difficult.
The problems with decoupling and control algorithm of nonlinear system are investigated on the ball and plate equipment BPVS-JLUⅠwhich is independently developed by our laboratory. The work is supported by College Doctor Special Scientific Research Fund of China under Grant 20060183006. The tasks of study are included: Firstly, building the system’s mathematic model by its dynamics and kinematics analysis. Secondly, making the ball is stabilizated at a set point. According to simulation experiment, we study the ball’s regulation problem in long distance. Thirdly, the decoupling control is investigated on two directions. Lastly, putting forward some control schemes to make the ball track given trajectory and searching an optimization path for the ball in complex environment, for example, some obstacles put on the plate, and control the ball track the path. The paper focuses on problems that decoupling and control algorithm for the ball and plate system via the experimental platform BPVS-JLUⅠ.The innovation include four parts that are shown as following.
1. The models are obtained under different conditions with Lagrange methods. We have established the mathematical model of the ball and plate system with complex and simply condition that include friction,coupling and approximate linearization on the equilibrium points.We analyze and discuss some nonlinear character items that are included in model. 2. We study the regulation problem for the ball and plate system on large bound, give and realize an approximate input-output linearization and a nonlinear switch control method with the singularities system. Intelligent switching control that is regard as new idea is also proposed to solve the singular problem. We analyze and investigate the zero dynamics of system and switch rules with stability, play to simulate experiment for the proposed controller. Results indicate the intelligent switching control is proposed to solve the singular problem and increase the area of stability. Advantage of the method is definite contrast approximate linearization.
3. FSMC(Fuzzy Sliding Mode Control) decoupling method can partly solve dimension disaster problem. However, it is very difficult when applied to the high order system for example the ball and plate system. Therefore we propose the output decoupling control methods that SMC(Sliding Mode Control) theory based on SIRM(Single Input Rule Module) fuzzy reasoning model, apply to four sliding surface and two fuzzy controllers. It is effective to settle coupling problem with two output orientations for the ball and plate system. The decoupling will not work until the system enters into the sliding mode surface.It is different than the ordinary decoupling method.The method is not influenced by uncertain disturbances. Thus its anti-disturbance performance is sound.
4. The discussed the design and realization methods of the fuzzy control system. The system model is unknown, but there is some knowledge with plant and language controller. The supervisory fuzzy controller under hierarchical fuzzy control scheme that has the characteristics of adaptive control is proposed. The controller is divided into two layers. The controller of the lower layer is built with single input rule module fuzzy inference logic. Number of the input is 3. The above layer is the stabilization controller for supervision. It is monitoring Lyapunov energy function transformation and system state bound. The hierarchical fuzzy controller is effect respectively. The controller of the lower layer has solved the problems of too many rules and control capability target, and the controller for supervision does stabilize the system. This control method has been tested on the experiment platforms. The results have shown that the method is able to solve the motion control problem of a class of visual servo system without system mathematical models.
Summarily, this paper accomplishes a lot of academic and experimental research on decoupling and control algorithm for ball and plate system, and basically achieves its given goals. The main respect of this dissertation is innovation and feasibility of some key technique constituting the ball and plate system. With respect to long distance regulation and decoupling problem, intelligent switching control and fuzzy sliding decoupling algorithms are verified in the simulation system developed by this paper. The hierarchical supervisory fuzzy control algorithm is verified in the real system.
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