A new Lyapunov design approach for nonlinear systems based on Zubov's method

The present research work proposes a new nonlinear controller synthesis approach that is based on the methodological principles of Lyapunov design. In particular, it relies on a short-horizon model-based prediction and optimization of the rate of “energy dissipation” of the system, as it is realized through the time derivative of an appropriately selected Lyapunov function. The latter is computed by solving Zubov's partial differential equation based on the system's drift vector field. A nonlinear state feedback control law with two adjustable parameters is derived as the solution of an optimization problem that is formulated on the basis of the aforementioned Lyapunov function and closed-loop performance characteristics. A set of system-theoretic properties of the proposed control law are examined as well. Finally, the proposed Lyapunov design method is evaluated in a chemical reactor example which exhibits nonminimum-phase behaviour.     

Strategie for adjustment of the complete boiler control system in power units

A method for obtaining optimal controller parameters for complex designed control systems is described and applied to the parameter setting-up in a power control system of a fossil fuel fired power unit. The plant model consists of nonlinear ordinary differential equations and as performance index to be minimized a generalized quadratic index is used. The nonlinear model is linearized for each combination of search parameters for which the performance index is determined by solving a Lyapunov equation. The search is carried out in discrete parameter space axis parallel. The computed optimal values were tested by simulation runs and were verified by application to the power unit.     

Genetic algorithm-based optimal fuzzy controller design in the linguistic space

In this paper, a genetic algorithm (GA) based optimal fuzzy controller design is proposed. The design procedure is accomplished by establishing an index function as the consequent part of the fuzzy control rule. The inputs of the controller, after scaling, are utilized by the index function for computing the output linguistic value. This linguistic value can then be used to map the suitable fuzzy control actions. This proposed novel fuzzy control rule has crisp input and fuzzified output characteristics. The index function plays a role in mapping the desired fuzzy sets for defuzzification resulting in a controlled hypersurface in the linguistic space formed by the input fuzzy variables. Two types of index functions, both linear and nonlinear, are introduced for controlling systems with different degrees of nonlinearity. The parameters of the index function are obtained by applying a simple GA with a suitable fitness function. Various controlled systems result in various parameter sets depending on their dynamics. Under the acquired optimal parameter set the optimal index function can be used to generate the desired control actions. Several simulation examples are given to verify the performance of the proposed GA-based fuzzy controller.     

基于线性二次型高斯基准的多变量预测控制技术经济性能评估

由于受控过程参数的漂移及缺乏维护,令采用的控制器性能逐渐降低,需要做经济性能评估,以确保其最佳运行状态.因为目前最小方差评估算法没有考虑控制器的约束条件,对此我们采用线性二次型高斯(linearquadratic Gaussian,LQG)基准的模型预测控制(model predictive control,MPC)双层优化控制结构,将控制和输出的加权值引入上层经济性能指标,通过求解LQG问题获取控制与输出方差关系的离散点集,进一步拟合Pareto最优曲面方程,建立优化命题并求解最优经济指标及设定值.对延迟焦化加热炉的多变量MPC控制进行了性能评估及分析,证明该方法可以改进控制器设计,提高经济效益.     

A Numerical Approximation‐Based Controller for Mobile Robots with Velocity Limitation

In this paper the problem of trajectory tracking considers that the values of the control actions do not exceed a maximum allowable value and the zero convergence of tracking errors is demonstrated. The control law is based on a linear algebra approach. First, the desired trajectories of some state variables are determined by analyzing the conditions for a system of linear equations to have an exact solution. Therefore, the control signals are obtained by solving the system of linear equations. The optimal controller parameters are selected through nonlinear programming so as to prevent the saturation of the control actions. Experimental results are presented and discussed, demonstrating the controller's good performance. Finally, the performance of the proposed controller is compared with a fuzzy controller, and all the results are validated through experimental laboratory tests.     

一种自抗扰控制器参数的学习算法

针对自抗扰控制器（Automatic disturbance rejection controller,ADRC）参数多且耦合性强,参数难于被确定的问题,提出了一种ADRC参数的自动调整算法. 该算法以构造的控制性能函数为学习目标,根据参数对性能指标的影响,通过惩罚函数在线不断更新参数在有界区间内的概率密度分布,使得控制参数最优值的概率密度值最大. 通过开环不稳定系统算例和对工业机电驱动器单元（Industrial mechatronic drives unit,IMDU）的控制实验,仿真和实验结果证明了该算法的有效性.     

基于支持向量机的一类非线性系统预测控制

针对一类具有输出反馈耦合的离散非线性系统,将过程的非线性部分通过支持向量机转化为全局线性状态空间模型,并在目标函数中引入系统状态的变化,给出一种类似于离散PI最优调节器的新型预测控制器.该方法不需要在线辨识系统参数,因为系统的内模已转换成全局离线模型.由于引入了新的优化目标函数,该控制器的控制效果和鲁棒性优于仅考虑预测输出误差的传统预测控制器.仿真结果表明,它也优于经典离散PI最优调节器.     

A computational technique for the design of a specific optimal controller

For a linear plant, the optimization of a performance index of integral type, which is quadratic in states and control, results in a control law. This ideal controller, however, must often be replaced by an approximate controller; e.g., due to inaccessible state variables. The input-output relation of such a controller may be specified within some parameters in advance. A specific optimal controller (SOC) is obtained when the parameters are chosen in an optimal manner so as to minimize a performance criterion; for example, the degradation of a performance index. Since these parameters depend on the initial state, the SOC is designed in regard to the worst initial state resulting in the maximum deterioration, which is then minimized by the best parameters. A computational procedure for this design is proposed. An algorithm is constructed and applied to this min-max problem.     

Application of game theory to the sensitivity design of optimal systems

The theory of games is applied to the design of systems with unknown plant parameters. It is assumed that a controller structure is known and furthermore that this controller is optimal when the controller parameters are equal to the plant parameters. The performance index then becomes a function of plant and controller parameters. This function is treated as a pay-off function with the antagonists represented by the controller and plant parameters. The theory is illustrated with some simple samples.     

Suppression of nonlinear regenerative chatter in milling process via robust optimal control

During the milling process, self-excited vibration or chatter adversely affects tool life, surface quality and productivity rate. In this paper, nonlinear cutting forces of milling process are considered as a function of chip thickness with a complete third order polynomial (instead of the common linear dependency). An optimal control strategy is developed for chatter suppression of the system described through nonlinear delay differential equations. Counterbalance forces exerted by actuators in x and y directions are the control inputs. For optimal control problem, an appropriate performance index is defined such that the regenerative chatter is suppressed while control efforts are minimized. Optimal control law is determined based on variation of extremals algorithm. Results show that under unstable machining conditions, regenerative chatter is suppressed effectively after applying the optimal control strategy. In addition, optimal controller guarantees robust performance of the process in the presence of model parametric uncertainties.     

Optimal control of LQG problem with an explicit trade-off between mean and variance

For discrete-time linear-quadratic Gaussian (LQG) control problems, a utility function on the expectation and the variance of the conventional performance index is considered. The utility function is viewed as an overall objective of the system and can perform the optimal trade-off between the mean and the variance of performance index. The nonlinear utility function is first converted into an auxiliary parameters optimisation problem about the expectation and the variance. Then an optimal closed-loop feedback controller for the nonseparable mean–variance minimisation problem is designed by nonlinear mathematical programming. Finally, simulation results are given to verify the algorithm's effectiveness obtained in this article.     

Design of an optimal fuzzy logic controller using response surfacemethodology

When the fuzzy logic controller (FLC)-designed based on the plant model-is applied to the real control system, satisfactory control performance may not be attained due to modeling errors from the plant model. Also, a controller that is designed under specific circumstances may not show satisfactory control performance when applied to other circumstances. In such cases, the control parameters of the controller must be adjusted to enhance control performance. Until now, the trial and error method has been used, consuming much time and effort. Also, the set of adjusted values is not guaranteed to be optimal. To resolve such problems, response surface methodology (RSM), a method of adjusting the control parameters of the controller, is suggested. This method is more systematic than the previous trial and error method, thus, optimal solutions can be provided with less tuning. First, the initial values of the control parameters are determined through the plant model and the optimization algorithm. Then designed experiments are performed in the region around the initial values, determining the optimal values of the control parameters that satisfy both the rise time and overshoot simultaneously     

Stable LPV realisation of the Smith predictor

The paper is concerned with the control of a linear plant with an output delay. As is known, when the plant parameters do not vary in time, the transfer function approach can be used to find a high-performing controller with the Smith-predictor structure. Such an approach in the domain of the Laplace transform is not directly applicable in the time-variant case. Nevertheless, it is shown that the transfer function of the Smith controller valid for constant values of the parameters can be realised in such a way that closed-loop stability, as well as point-wise optimal performance, is ensured also when the parameters vary with time. The suggested technique is applied to the control of a heat exchanger whose varying parameters include a measurement delay.     

Wind turbine integrated structural and LPV control design for improved closed-loop performance

An iterative redesign algorithm is proposed to integrate the design of the structural parameters and a linear parameter-varying (LPV) controller for a three-bladed horizontal-axis wind turbine. The LPV controller is designed for an eighth-order lumped model of the wind turbine consisting of blades, drive-train and the tower. The lumped model response is matched with detailed open-loop numerical simulations using the Fatigue, Aerodynamics, Structures and Turbulence (FAST) code. The controller is scheduled in real-time based on the mean wind speed to account for the varying system dynamics. The objective is to track the operating trajectory meanwhile minimise the H _∞ performance index from the wind turbulence to the controlled output vector consisting of pitch angle, blade tip deflection, and the generator speed and torque. Sensitivity analysis of the closed-loop performance index with respect to the structural parameters of the system is examined. The integrated design problem is formulated as an iterative sequential controller/structure redesign to obtain the structural parameters and controller matrices corresponding to a local optimal performance index. Each step of the iterative procedure is formulated as a linear matrix inequality (LMI) optimisation problem that can be solved efficiently using available LMI solvers. The evolution of the structural parameters and performance index through the integrated design is illustrated. The FAST closed-loop simulations for two selected designs with the smallest values of the performance index demonstrate the improved performance of the overall system through the integrated structure/control redesign in both minimising the effect of the wind disturbance on the generator output power, and reducing the structural loads on the wind turbine.     

基于神经网络的迭代优化预测控制

针对时变的非线性系统,提出一种基于神经网络的迭代优化预测控制。它将传统的预测控制策略与神经网络逼近任息非线性函数的能力结合,预测系统未来输出,然后用迭代学习方法优化预测控制器,即通过一阶泰勒展开的方法,把非线性优化问题转化为线性优化问题。不仅简化计算,同时避免用神经网络优化控制器时,由于调节参数过多、涮前速度慢而导致系统闭环稳定性和鲁棒性差的问题。仿真结果表明,该控制方案具有良好的控制品质,并适应对象参数的变化,具有较强的鲁棒性和自适应性。     

控制能量约束条件下时滞系统最优控制与仿真

文中对时滞系统在控制能量存在约束时的最优控制问题进行了探讨.由控制器Youla参数化得到控制系统的敏感度函数和控制敏感度函数用来表示一个包含跟踪误差和控制能量在内的积分平方性能指标,针对不同类型的时滞过程运用谱分解的方法最小化该性能指标,从而导出相应控制器的设计方法,可使系统在控制能量约束条件下具有最优的控制性能.仿真研究进一步说明了所给设计方法的有效性.     

改进QPSO算法的移动机器人轨迹跟踪控制方法

分析了智能群体的决策机制,发现在智能群体决策过程中,个体粒子参与决策的权利根据个体的优劣程度是不同的,提出了在量子粒子群优化（QPSO）算法中引入线性权重算子进一步提高QPSO算法的搜索效率及优化性能。分析了移动机器人轨迹跟踪控制的滑模变结构控制器设计方法,并采用指数趋近律和幂次趋近律相结合的方法,设计了新的滑模跟踪控制律,使用PSO算法、QPSO算法和改进算法优化了滑模跟踪控制器中的参数,通过两个实例验证了优化后的跟踪控制器的设计效果;设计效果的分析和比较表明了设计的跟踪控制器能够控制机器人实现对既定轨迹的跟踪,仿真结果显示改进QPSO算法能够在轨迹跟踪控制器的参数优化中取得更好的优化效果。     

在连续过程的离散最优控制中采样周期和加权系数的选择

本文提出了在连续过程的离散最优控制中选择采样周期和加权系数的一个方法。这个选择基于:1)线性的时间离散控制器;2)控制变量的范围受到限制;3)根据对系统的实际要求给定输出量的初始偏移。系统的性能则采用时间连续的二次型输出偏移损失函数以及类似的控制损失函数来表示。对不同的采样周期,利用标准的LQ方法来计算控制器,并通过选择控制损失项的加权系数,以使得对于给定的初始偏移,允许的控制范围得到充分利用。最后的采样周期则是权衡了偏移损失和控制损失的一个折衷选择。本文介绍的方法尤其适用于需要尽可能长的采样周期的情况。     

A method for auto-tuning of PID control parameters

A method for automatic tuning of the PID process control parameters, usually called ‘auto-tuning’, is developed. The procedure of applying the method consists of (1) sampling a process response to a test input signal, (2) processing the sampled data for estimating characteristic values of the process, and (3) calculating the optimal values of the PID control parameters. For the optimization, a new type of performance index, i.e. a weighted integral of squared error is introduced. The procedure is implemented on a digital controller using microprocessors and applied to some real processes, yielding satisfactory results.     

自寻优自适应动态面控制

针对一类不确定非线性系统的跟踪问题,利用神经网络和动态面技术设计控制器,提出一种控制器参数自寻优策略.在每个子系统中,应用径向基函数(RBF)神经网络逼近该子系统中的不确定项;在每一步递推中,引入一个滤波器以克服反推技术中控制项爆炸的缺点.通过定义一个优化目标函数,应用梯度法在控制器参数可行解中寻找一组最优的控制器参数.数值仿真表明该方案是可行的.