Approximate Controllability for Degenerate Heat Equation with Bilinear Control

This paper investigates the nonnegative approximate controllability for the one-dimensional degenerate heat equation governed by bilinear control.Both non-controllability and approximate controllability are studied for the system.If the control is restricted to act on a fixed domain,it is not controllable.If the control is allowed to mobile,it is approximately controllable.

Non-fragile guaranteed cost control of discrete-time fuzzy bilinear system

This paper focuses on the problem of non-fragile guaranteed cost control for a class of T-S discrete-time fuzzy bilinear systems（DFBS）.Based on the parallel distributed compensation（PDC） approach,the sufficient conditions are derived such that the closed-loop system is asymptotically stable and the cost function value is no more than a certain upper bound in the presence of the additive controller gain perturbations.The non-fragile guaranteed cost controller can be obtained by solving a set of bilinear matrix inequalities（BMIs）.The Van de Vusse model is utilized to demonstrate the validity and effectiveness of the proposed approach.

BILINEAR PREDICTIVE CONTROL USING HIERARCHICAL OPTIMIZATION

Based on the Decomposition-Coordination principle, a hierarchical optimization algorithm is put forward for predictive control of bilinear systems. Time consuming is an usual problem of hierarchieal optimization algorithms, this paper tries to improve the online computational efficiency by taking the advantage of the characteristics of bilinear system itself. The effectiveness is shown by the simulation results.

Design of switched controllers for discrete singular bilinear systems

In this paper, switched controllers are designed for a class of nonlinear discrete singular systems and a class of discrete singular bilinear systems. An invariant principle is presented for such switched nonlinear singular systems. The invariant principle and the switched controllers are used to globally stabilize a class of singular bilinear systems that are not open-loop stable.

Static output feedback control for discrete-time fuzzy bilinear system

The problem of designing fuzzy static output feedback controller for T-S discrete-time fuzzy bilinear system （DFBS） is presented. Based on parallel distribution compensation method, some sufficient conditions are derived to guarantee the stability of the overall fuzzy system. The stabilization conditions are further formulated into linear matrix inequality （LMI） so that the desired controller can be easily obtained by using the Matlab LMI toolbox. In comparison with the existing results, the drawbacks, such as coordinate transformation, same output matrices, have been elim- inated. Finally, a simulation example shows that the approach is effective.

Feedback Linearization Optimal Control Approach for Bilinear Systems in CSTR Chemical Reactor

This paper considers the optimal control problem for the bilinear system based on state feedback. Based on the concept of relative order of the output with respect to the input, first we change a bilinear system to a pseudo linear system model through the coordinate transformation. Then based on the theory of linear quadratic optimal control, the optimal controller is designed by solving the Riccati equation and introducing state feedback with state prediction. At last, the simulation results in CSTR Chemical reactor show the effectiveness of the method.

Optimal Control for Time-Delay Bilinear Systems with Sinusoidal Disturbances

This paper considers the optimal control problem for time-delay bilinear systems affected by sinusoidal disturbances with known frequency and measurable amplitude and phase. Firstly, using the differential homeomorphism, a time-delay bilinear system affected by sinusoidal disturbances is changed to a time-delay pseudo linear system through the coordinate transformation. Then the system with time-delay in control variable is transformed to a linear controllable system without delay using model transformation. At last based on the theory of linear quadratic optimal control, an optimal control law which is used to eliminate the influence of the disturbances is derived from a Riccati equation and Matrix equations. The simulation results show the effectiveness of the method.

三相电压型PWM整流器控制技术分析

阐述三相电压型PWM整流器的工作原理、拓扑结构及控制策略,分析三相电压型PWM整流器的控制结构、双闭环整流系统的控制方法。通过仿真和实验验证控制策略的正确性和有效性。

H_∞ Control of Bio-dissimilation Process of Glycerol to 1,3-Propanediol

A robust controller is designed by using the bilinear transformation and H∞ mixed sensitivity method for bio-dissimilation process of glycerol to 1,3-propanediol. Under the controller the system works near an optimal steady-state for the volumetric productivity of 1,3-propanediol attaining its maximization. The design procedure is carried out by tuning the transformation parameter and DC gain of the performance weighted function, which is an iterative and optimal search process. Simulation results are presented which show that the designed robust controller not only ensures the robust stability of the system in face of the parametric variations in the model, but also makes the system have a favourable robust tracking performance. The validity of the proposed H∞ controller has been tested.

BMI Approach to the Interconnected Stability and Cooperative Control of Linear Systems

这份报纸学习互连的稳定性和大规模线性系统的合作控制。用双线性的矩阵不平等(BMI ) 的技术，必要、足够的条件为互连的稳定性和二个分系统的合作稳定被给。就算分系统不是稳定的，系统能合作地被稳定，这被显示出就算分系统不是稳定的。我们假定分系统的稳定性不是必要的。而且，设计的问题相连，合作控制器用 BMI 限制被变换成优化问题。解决这些问题，某些最佳的交替的算法被建议，并且为算法的集中的证明被介绍。最后，几个例子被给说明优化结果。

Robust H_∞ control for neutral stochastic uncertain systems with time-varying delay

The problem of robust H_∞ control for uncertain neutral stochastic systems with time-varying delay is discussed.The parameter uncertaintie is assumed to be time varying norm-bounded.First,the stochastic robust stabilization of the stochastic system without disturbance input is investigated by nonlinear matrix inequality method.Then,a full-order stochastic dynamic output feedback controller is designed by solving a bilinear matrix inequality（BMI）,which ensures a prescribed stochastic robust H_∞ performance level for the resulting closed-loop system with nonzero disturbance input and for all admissible uncertainties.An illustrative example is provided to show the feasibility of the controller and the potential of the proposed technique.

Implementing Broadcast Encryption Scheme Using Bilinear Map and Group Characteristic

This paper introduced a novel method for implementing broadcast encryption. Our scheme takes advantages of bilinear map and group characteristic, and shifts most of the storage overhead to the public device instead of storing in the tamper-proof device which is a major problem on current implementation. Furthermore, the broadcast keys in our scheme could be reused periodically resulting in more operational efficiency.

Output feedback controller design for uncertain piecewise linear systems

This paper proposes output feedback controller design methods for uncertain piecewise linear systems based on piecewise quadratic Lyapunov function. The α-stability of closed-loop systems is also considered. It is shown that the output feedback controller design procedure of uncertain piecewise linear systems with α-stability constraint can be cast as solving a set of bilinear matrix inequalities （BMIs）. The BMIs problem in this paper can be solved iteratively as a set of two convex optimization problems involving linear matrix inequalities （LMIs） which can be solved numerically efficiently. A numerical example shows the effectiveness of the proposed methods.

Room temperature and humidity decoupling control of common variable air volume air-conditioning system based on bilinear characteristics

Variable air volume(VAV)air-conditioning(AC)systems are widely employed to achieve a comfortable room thermal and humid environment depending on its better regulation performance and energy efficiency.In the single coil VAV AC system,conventional proportional-integral(PI)control algorithm is usually adopted to track the set-points of the room temperature and humidity by regulating the supply air flow rate and the chilled water flow rate,respectively.However,the control performance is usually not good due to the high coupling of the heat and mass transfer in the air-handling unit(AHU).A model-based control method is developed to realize the decoupling control of the room temperature and humidity according to the bilinear characteristics of the temperature and humidity variation.In this control method,a bilinear room temperature controller is used to track the room temperature set-point based on the real-time cooling load,while a room humidity controller is used to track the room humidity set-point depending on the real-time humidity load.The control performance was validated in a simulated VAV AC system.The test results show that comparing with the conventional PI control,the room temperature and humidity are controlled much more robustly and accurately by using the proposed model-based control method.

H_∞ controller synthesis of piecewise discrete time linear systems

This paper presents an H∞ controller design method for piecewise discrete time linear systems based on a piecewise quadratic Lyapunov function. It is shown that the resulting closed loop system is globally stable with guaranteed H∞ performance and the controller can be obtained by solving a set of bilinear matrix inequalities. It has been shown that piecewise quadratic Lyapunov functions are less conservative than the global quadratic Lyapunov functions. A simulation example is also given to illustrate the advantage of the proposed approach.

Implementation of Control Algorithms in Small Embedded Systems

This work describes how a control algorithm can be implemented in a small (8-bit) microcontroller for the main purpose of merging embedded systems and control theory in electrical engineering undergraduate classes. Two different methods for discretizing the control expression are compared: Euler transformation and bilinear transformation. The sampling rate’s impact on the algorithm is discussed and theoretical results are verified by an application to a temperature control system in a heating plant. Four control algorithms are compared: PID and PI algorithms discretized with Euler and bilinear transformation, respectively. It is shown that for the heating plant used in this work, a bilinear PI algorithm implemented in a small 8-bit microcontroller outperforms a commercial controller from Panasonic. It is also demonstrated that all the derived algorithms can be implemented using integer calculations only, obviating the need for expensive and time-consuming floating-point calculations. This work bridges the gap between control theory equations and the implementation of control systems in small embedded systems with no inherent floating-point processing power.

双线性奇异摄动系统的无源控制器设计

研究了1类不确定变时滞双线性奇异摄动系统的无源控制。通过构造依赖于奇异摄动参数ε的Lyapunov函数,采取线性矩阵不等式和范数有界的方法,获得了使系统渐近稳定和严格无源的时滞依赖的充分条件,进而利用线性矩阵不等式的解给出了无源控制器的设计方法。考虑到系统模型的复杂性,给出了时滞独立的充分条件,从而降低了线性矩阵不等式的阶数。提出了一种奇异摄动参数ε允许上界的估计方法。通过数值仿真验证了以上方法的有效性。

桥臂不对称情形下MMC无源性PI控制方法

考虑模块化多电平变换器(modular multilevel converter,MMC)桥臂不对称情形,针对环流基频分量不对称引起的dq解耦变换误差问题,提出基于双线性模型的无源性PI控制方法,实现故障相电容电压保持稳定、不对称环流分量的准确抑制、三相并网电流的平衡输出。在abc坐标系下,建立桥臂不对称情形下MMC双线性模型,完成非线性系统控制变量随状态变量同步变化的线性化转换,简化控制器设计,避免dq解耦变换引入的控制误差。从系统全局能量耗散特性出发,设计形式简单的无源性PI控制器,实现子模块电容电压纹波快速抑制,消除桥臂电流不对称性,同时确保闭环控制系统全局渐近稳定运行。基于Matlab的仿真结果验证了所提控制策略能够有效抑制MMC桥臂不对称的不利影响,具有响应快速、稳定性好、鲁棒性强的特点。