混杂系统建模与控制方法研究
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摘要
随着工业控制对象的规模日益复杂以及对控制精度的要求日益提高,工业控制过程中的连续过程动态系统(CVDS)和离散事件动态系统(DEDS)的耦合关系越来越明显,着眼于连续和离散过程之间的耦合作用及其所表现出来的特殊动力学特性,混杂系统(Hybrid System)理论的研究引起了国际控制界的广泛关注。
所谓混杂系统,是指系统内存在相互作用的连续时间动态子系统和离散事件动态子系统,其中离散部分在控制中常以调度程序或监控管理者的形式出现,譬如ON/OFF切换开关、阀门、传动装置、限幅器或者选择器,而连续部分则随着时间的发展不断演化,二者相互作用,使系统的运动轨迹在整体上呈现出离散位置的迁移,局部上呈现连续状态的渐进演化。混杂系统狭义上是指一个既包含离散变量,又包含连续变量的系统;广义上是指一个包括相互作用的连续过程和离散过程的系统。
本文围绕混杂系统的建模和控制器优化设计展开研究,从混杂系统本身的特点出发,以混杂系统分类模型的建立和相应模型控制方法的实现为研究目标,综合运用自动机、Petri网、并行投影结构(Projection Construct)等离散事件系统分析方法以及广义预测控制算法(GPC)、多模型控制、模糊监督等连续时间系统分析方法,从系统模型的建立、控制器的优化设计和简化方面进行了深入探讨和分析,在混杂系统的离散建模方面、混合逻辑动态(MLD)模型的控制、切换模型混杂系统控制、混杂系统控制方法的推广方面提出了一些新的思路和方法。
1.针对一类从整体上更能体现出离散事件系统特点的混杂系统,以混杂系统自动机建模理论为基础,结合一种特殊的并行投影结构,提出了针对这类混杂系统的推广自动机模型。该模型着眼于连续状态空间的划分。并行投影结构有效的处理了离散事件动态子系统和连续变量动态子系统之间的接口问题。该方法获得的混杂系统模型用图形的方式表示,简单直观,容易理解。并借助于Matlab环境中的Stateflow,给出了该类模型的仿真方法。
2.针对混合逻辑动态模型的特点,将经典广义预测控制算法的被控对象进行了扩展,引入了代表离散事件行为的开关量,用混合整数二次规划算法对该控制方法进行求解,并且在此基础上,对于带约束条件的混杂系统的控制问题也进行了研究。
3.根据混杂系统的切换系统模型,提出了应用多模型控制的方法实现混杂系统控制的思想,借助于基于隶属度加权的模糊监督控制思想,设计了适用于混杂系统的监督控制器,在该监督器的作用下,实现了控制系统中局部控制器之间的切换,并且使扰动达到最小,之后采用Lyapunov稳定性定理及推论,求解矩阵不等式组,对其全局稳定性提出了判定方法。
4.将前面提到的MLD模型和GPC相结合的控制方法,应用到多模型系统的控制当中,将多模型控制系统等效为混杂系统的切换模型,根据工况点引入相应的逻辑量,用带有线性不等式约束的统一表达式代替多模型系统中的典型工况点模型。这样做的最大好处是降低了模型切换时的扰动,减少了控制器的数量。通过对典型多模型对象的仿真验证了该方法控制效果很好。
5.结合风力发电系统中风力机的特点,针对其混杂特性,将前面提到的控制方法应用到风力机的全工况控制当中。
While the industrial objects become more complex and the precision control becomes higher and higher, the coupled relation between the continuous variables dynamic systems (CVDS) and the discrete event dynamic systems(DEDS) which are in the process of industrial control is increasing obviously. Focusing on the coupled relation and the exceptive dynamics, the research of hybrid system attracted the attention of the international control sector.
The hybrid system means that the system contains both continuous subsystem and discrete subsystem. The discrete part often acts as the scheduler or monitor managers in the control system, such as the ON/OFF switches, valves, gearings, limiters or selectors, and the continuous part is evolved with the elapse of time. The interaction of the two parts makes the trajectory of the system presents a transition of discrete position on the whole and a gradual evolution of continuous states in local. The hybrid system, narrowly, refers to a system which contains both discrete variables and continuous variables; while broadly it means a system which contains two interactional processes, continuous process and discrete process.
Around of the modeling of the hybrid system and the design of optimization controller, from the characteristics of the hybrid system, some new methods from discrete modeling and continuous control on the traditional system are shown in this article. Many methods for discrete event system like as Automata, Petri net, Projection Construct and many methods for continuous time system like as Generalized Predictive Control algorithm (GPC), Multi-Model Control and Fuzzy Supervisory are discussed and analyzed deeply from the construct of a system model and designing of optimal controller.
1. Aimed at the hybrid system which can incarnate the characters of the discrete event system and based on the automata modeling theory, an extended automata model for the hybrid system is developed. The projection construct is used to solve the interface problem between the discrete event dynamic subsystems and the continuous variable dynamic subsystems. The model obtained by this way is described by graphs, so it is easy to understand. And the modeling process is illustrated by two examples and the stateflow toolbox in matlab is introduced for simulation. The simulation results show the extended automata model is good at solving the synchronous problem between the two subsystems of hybrid systems.
2. Aiming at the object’s properties of the hybrid system, digital variables which represents the discrete event is imported to enlarge the classical GPC’s object. Using mixed integer quadratic programming algorithm to solve this control system, and on this basis, the solution of control the hybrid systems which contain constrained conditions is studied.
3. Based on switching system model of hybrid system, the idea of hybrid system control by using Multi-Model Control is developed. In virtue of the design rule of the fuzzy monitor in the fuzzy supervisory control, a monitor which can be used in the hybrid system control has been designed, and on the function of the monitor, the transitions of local controllers and the minimum disturbance have been achieved. And then using the Lyapunov stability theory and its reasoning to solve the matrix inequalities and developed the decision method of its global stability.
4. The control method which combined with MLD model and GPC is applied in the multi-model control systems. In this theoretic, multi-model control systems are equivalent to switch model in the hybrid system, importing corresponding logic variable, using a uniform expression with a linear inequality which contains constraints to replace models in representative conditions. In this way, we can get the biggest advantage that the disturbance which is produced in switching models is debased and the amount of controllers is reduced too. It shows that the effect of this control method is very good through the simulation.
5. Combined with the characteristic of wind turbine, aiming at its characteristic of hybrid, the control methods are shown above are used in the control of the wind turbine in all condition.
所谓混杂系统,是指系统内存在相互作用的连续时间动态子系统和离散事件动态子系统,其中离散部分在控制中常以调度程序或监控管理者的形式出现,譬如ON/OFF切换开关、阀门、传动装置、限幅器或者选择器,而连续部分则随着时间的发展不断演化,二者相互作用,使系统的运动轨迹在整体上呈现出离散位置的迁移,局部上呈现连续状态的渐进演化。混杂系统狭义上是指一个既包含离散变量,又包含连续变量的系统;广义上是指一个包括相互作用的连续过程和离散过程的系统。
本文围绕混杂系统的建模和控制器优化设计展开研究,从混杂系统本身的特点出发,以混杂系统分类模型的建立和相应模型控制方法的实现为研究目标,综合运用自动机、Petri网、并行投影结构(Projection Construct)等离散事件系统分析方法以及广义预测控制算法(GPC)、多模型控制、模糊监督等连续时间系统分析方法,从系统模型的建立、控制器的优化设计和简化方面进行了深入探讨和分析,在混杂系统的离散建模方面、混合逻辑动态(MLD)模型的控制、切换模型混杂系统控制、混杂系统控制方法的推广方面提出了一些新的思路和方法。
1.针对一类从整体上更能体现出离散事件系统特点的混杂系统,以混杂系统自动机建模理论为基础,结合一种特殊的并行投影结构,提出了针对这类混杂系统的推广自动机模型。该模型着眼于连续状态空间的划分。并行投影结构有效的处理了离散事件动态子系统和连续变量动态子系统之间的接口问题。该方法获得的混杂系统模型用图形的方式表示,简单直观,容易理解。并借助于Matlab环境中的Stateflow,给出了该类模型的仿真方法。
2.针对混合逻辑动态模型的特点,将经典广义预测控制算法的被控对象进行了扩展,引入了代表离散事件行为的开关量,用混合整数二次规划算法对该控制方法进行求解,并且在此基础上,对于带约束条件的混杂系统的控制问题也进行了研究。
3.根据混杂系统的切换系统模型,提出了应用多模型控制的方法实现混杂系统控制的思想,借助于基于隶属度加权的模糊监督控制思想,设计了适用于混杂系统的监督控制器,在该监督器的作用下,实现了控制系统中局部控制器之间的切换,并且使扰动达到最小,之后采用Lyapunov稳定性定理及推论,求解矩阵不等式组,对其全局稳定性提出了判定方法。
4.将前面提到的MLD模型和GPC相结合的控制方法,应用到多模型系统的控制当中,将多模型控制系统等效为混杂系统的切换模型,根据工况点引入相应的逻辑量,用带有线性不等式约束的统一表达式代替多模型系统中的典型工况点模型。这样做的最大好处是降低了模型切换时的扰动,减少了控制器的数量。通过对典型多模型对象的仿真验证了该方法控制效果很好。
5.结合风力发电系统中风力机的特点,针对其混杂特性,将前面提到的控制方法应用到风力机的全工况控制当中。
While the industrial objects become more complex and the precision control becomes higher and higher, the coupled relation between the continuous variables dynamic systems (CVDS) and the discrete event dynamic systems(DEDS) which are in the process of industrial control is increasing obviously. Focusing on the coupled relation and the exceptive dynamics, the research of hybrid system attracted the attention of the international control sector.
The hybrid system means that the system contains both continuous subsystem and discrete subsystem. The discrete part often acts as the scheduler or monitor managers in the control system, such as the ON/OFF switches, valves, gearings, limiters or selectors, and the continuous part is evolved with the elapse of time. The interaction of the two parts makes the trajectory of the system presents a transition of discrete position on the whole and a gradual evolution of continuous states in local. The hybrid system, narrowly, refers to a system which contains both discrete variables and continuous variables; while broadly it means a system which contains two interactional processes, continuous process and discrete process.
Around of the modeling of the hybrid system and the design of optimization controller, from the characteristics of the hybrid system, some new methods from discrete modeling and continuous control on the traditional system are shown in this article. Many methods for discrete event system like as Automata, Petri net, Projection Construct and many methods for continuous time system like as Generalized Predictive Control algorithm (GPC), Multi-Model Control and Fuzzy Supervisory are discussed and analyzed deeply from the construct of a system model and designing of optimal controller.
1. Aimed at the hybrid system which can incarnate the characters of the discrete event system and based on the automata modeling theory, an extended automata model for the hybrid system is developed. The projection construct is used to solve the interface problem between the discrete event dynamic subsystems and the continuous variable dynamic subsystems. The model obtained by this way is described by graphs, so it is easy to understand. And the modeling process is illustrated by two examples and the stateflow toolbox in matlab is introduced for simulation. The simulation results show the extended automata model is good at solving the synchronous problem between the two subsystems of hybrid systems.
2. Aiming at the object’s properties of the hybrid system, digital variables which represents the discrete event is imported to enlarge the classical GPC’s object. Using mixed integer quadratic programming algorithm to solve this control system, and on this basis, the solution of control the hybrid systems which contain constrained conditions is studied.
3. Based on switching system model of hybrid system, the idea of hybrid system control by using Multi-Model Control is developed. In virtue of the design rule of the fuzzy monitor in the fuzzy supervisory control, a monitor which can be used in the hybrid system control has been designed, and on the function of the monitor, the transitions of local controllers and the minimum disturbance have been achieved. And then using the Lyapunov stability theory and its reasoning to solve the matrix inequalities and developed the decision method of its global stability.
4. The control method which combined with MLD model and GPC is applied in the multi-model control systems. In this theoretic, multi-model control systems are equivalent to switch model in the hybrid system, importing corresponding logic variable, using a uniform expression with a linear inequality which contains constraints to replace models in representative conditions. In this way, we can get the biggest advantage that the disturbance which is produced in switching models is debased and the amount of controllers is reduced too. It shows that the effect of this control method is very good through the simulation.
5. Combined with the characteristic of wind turbine, aiming at its characteristic of hybrid, the control methods are shown above are used in the control of the wind turbine in all condition.
引文
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