受扰时滞系统的控制方法研究及应用
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摘要
在化工、炼油、冶金和造纸等一些复杂的工业过程中,广泛地存在干扰和时滞现象。干扰是影响系统综合性能的重要因素,干扰的消除或抑制是设计高性能鲁棒控制器的关键环节。由于时滞的存在,使得被控变量不能及时地反映系统输入变量的影响,从而使控制系统产生明显的超调,系统的稳定性变差,调节时间加长,这些因素都导致了时滞系统难于控制,时滞的存在常常是系统不稳定或产生不良性能的原因。因此,研究受扰时滞系统的控制具有重要的理论和实际价值,它们越来越成为过程控制界深入研究的热点。
在实际工程应用中通常很难得到被控对象的精确数学模型,在控制系统设计过程中所采用的模型常常是在一定程度上经过近似化处理的数学模型,数学模型的这种不确定性必须在控制系统设计时予以考虑。因此,如何切实有效地处理不确定性的影响已经越来越成为工程应用中刻不容缓的迫切要求,对其进行研究具有重大的理论意义和实际意义。本文针对受扰时滞系统控制中的几个重要问题及应用进行了研究,对传统控制方法做了不同程度的改进,并提出了一些新的控制算法。
本文的主要工作和贡献有以下几个方面:
(1)研究了复合有色噪声的特性,针对状态空间模型具有非线性、非高斯特点的、并且未知量有可能是高维的复合有色噪声的干扰,提出了采用粒子滤波对其进行状态估计。研究了随机扰动序列功率谱特性,提出了一种统计自相关函数,使得功率谱估计的系数矩阵正定,解决了传统Levinsion算法系数矩阵非正定问题。
(2)在基本前馈-反馈控制结构的基础上,提出了基于粒子滤波前馈-反馈控制系统整套设计和整定方法。首先基于闭环系统的稳态增益指标设计给定值状态目标跟踪控制器,利用粒子滤波的方法消除非高斯噪声对控制系统的影响。然后根据系统稳态运行时的抗扰动要求,基于鲁棒最优性能指标,通过提出期望的闭环灵敏度函数的方法来反向确定控制器的设计,从而实现闭环控制系统的输出响应平稳且无振荡。本文提出的控制方法对给定值响应和负载干扰响应分别进行优化调节,调节的灵活性显著得到提高。
(3)针对受扰时滞不确定非线性连续系统的鲁棒控制问题,对其进行了时域特性的研究,研究了受扰时滞不确定非线性系统的控制问题,且不确定性不要求满足匹配条件。提出了具有范数有界参数不确定性受扰时滞非线性连续系统的鲁棒H∞控制问题,分别推导出通过状态反馈控制器和通过动态输出反馈控制器,不仅确保闭环系统二次稳定而且确保闭环系统满足H∞范数界约束的充分条件。本文设计的鲁棒H∞控制器使得闭环系统最终有界。
(4)研究了受扰时滞时变不确定离散系统的鲁棒H∞控制问题。针对受扰时滞时变不确定线性离散系统,基于线性矩阵不等式(LMI)方法,推导出存在无记忆状态反馈控制律使闭环系统镇定及具有H∞性能指标的充分条件;另外,以具有时变状态时滞和输入时滞的不确定受扰非线性离散系统为研究对象,基于适当的Lyapunov函数,给出了时滞相关型状态反馈控制器设计方案,使得闭环系统一致最终有界。
(5)为了验证控制方法的有效性,本文将基于粒子滤波前馈控制器和扰动观测器的二自由度控制系统实施于永磁同步电机速度控制上,具有很强的抗扰动性能,能更精确地实现对控制对象的速度控制。另外,提出了一种改进型重复控制系统来对伺服电机的位置系统进行控制,以进一步改善系统的稳定性和跟踪精度。通过仿真,实现了控制系统算法和设计验证。
Disturbances and time-delay are common phenomenon in the complex process industry, such as Chemical Engineering, Oil refining, Metallurgy, and Paper-making industry. Disturbance has important effect for system performance. Removing and controlling disturbance is key for design robust controller of high performance. Since the controlled variable in time-delayed system can not reflect the manipulate variable in time, it causes high overshoot and long settling time. The stability of closed-loop system will be degraded. It is difficult to control time-delayed system. Hence, there are much important theory and practical value on the study of control on disturbances and time-delay system. More and more researchers devote to research on control method for controlling disturbances and time-delayed processes.
It is very difficult to get exact mathematical models of industrial processes, models used in design procedure of control systems are commonly mathematical models through approximation. Uncertainties of mathematical models must be considered in control systems design procedure. Hence, how to deal with effects of uncertainties is becoming urgent requirement, and it is also a big challenge facing control theory and application recently. Some problems in disturbance and time-delayed system control techniques and applications are researched in this thesis. Some improvements of tradition control methods have been made at different degree, and some new control algorithms are also proposed in this thesis.
The main working results and contribution of this dissertation are stated as follows:
Researched the character of coloured disturbance. A particle filter is proposed for the nonlinear non-Guassian filter problem in the state tracking process of coloured disturbance. A statistical autocorrelation function is proposed for power spectral character of random orders. So, using biased estimator, which produces a stable system with a matrix that numerically is positive definite.
Based on the feedforward-feedback control structure, a set of design method and tuning rule of feedforward-feedback control system is proposed based on particle filter. The particle filter is utilized for rejecting the non-Guassian disturbance. Firstly the setpoint tracking controller is designed in terms of the robust optimal performance objective. Then according to the load disturbance rejection requirement during the system steady operation, based on robust optimal performance index, the design of controller is proposed based on the expected sensitivity function. The setpoint response and the load disturbance response are decoupled from each other so that both of them can be separately regulated and optimized on line. The performance is improved.
For robust control of time-varying uncertain time-delay disturbance non-linear continuous systems, the characters are researched in time domain. It need not matched uncertainties. The robust control problems and related problems are presented for uncertain time-delay disturbance non-linear continuous systems. The design algorithms are given about robust state feedback controller and robust dynamic output feedback controller. The asymptotic stability of robust controller is guaranteed.
The problem of robust control for time-varying disturbance discrete linear system with uncertain time-delay is investigated. Based on LMI method, design algorithms are presented about memoryless robust state feedback controller for system stability and performance index. On the other hand, based on new Lyapunov function, the design method of state feedback controller is presented for time-varying disturbance discrete non-linear systems with uncertain time-delay. The asymptotic stability of robust controller is guaranteed.
To demonstrate the validity and superiority of the proposed control structure, a two-degree-of-freedom control structure with particle filter feedforward controller and disturbance observer is designed for PMSM speed control. It has strong rejecting the disturbance. The speed precision of motor can be effectively improved by the scheme. On the other hand, a new repeat control system is proposed for PMSM position control. The tracking precision and system stability of motor can be effectively improved by the scheme. The results of simulation examples show that the proposed control method is satisfied.
在实际工程应用中通常很难得到被控对象的精确数学模型,在控制系统设计过程中所采用的模型常常是在一定程度上经过近似化处理的数学模型,数学模型的这种不确定性必须在控制系统设计时予以考虑。因此,如何切实有效地处理不确定性的影响已经越来越成为工程应用中刻不容缓的迫切要求,对其进行研究具有重大的理论意义和实际意义。本文针对受扰时滞系统控制中的几个重要问题及应用进行了研究,对传统控制方法做了不同程度的改进,并提出了一些新的控制算法。
本文的主要工作和贡献有以下几个方面:
(1)研究了复合有色噪声的特性,针对状态空间模型具有非线性、非高斯特点的、并且未知量有可能是高维的复合有色噪声的干扰,提出了采用粒子滤波对其进行状态估计。研究了随机扰动序列功率谱特性,提出了一种统计自相关函数,使得功率谱估计的系数矩阵正定,解决了传统Levinsion算法系数矩阵非正定问题。
(2)在基本前馈-反馈控制结构的基础上,提出了基于粒子滤波前馈-反馈控制系统整套设计和整定方法。首先基于闭环系统的稳态增益指标设计给定值状态目标跟踪控制器,利用粒子滤波的方法消除非高斯噪声对控制系统的影响。然后根据系统稳态运行时的抗扰动要求,基于鲁棒最优性能指标,通过提出期望的闭环灵敏度函数的方法来反向确定控制器的设计,从而实现闭环控制系统的输出响应平稳且无振荡。本文提出的控制方法对给定值响应和负载干扰响应分别进行优化调节,调节的灵活性显著得到提高。
(3)针对受扰时滞不确定非线性连续系统的鲁棒控制问题,对其进行了时域特性的研究,研究了受扰时滞不确定非线性系统的控制问题,且不确定性不要求满足匹配条件。提出了具有范数有界参数不确定性受扰时滞非线性连续系统的鲁棒H∞控制问题,分别推导出通过状态反馈控制器和通过动态输出反馈控制器,不仅确保闭环系统二次稳定而且确保闭环系统满足H∞范数界约束的充分条件。本文设计的鲁棒H∞控制器使得闭环系统最终有界。
(4)研究了受扰时滞时变不确定离散系统的鲁棒H∞控制问题。针对受扰时滞时变不确定线性离散系统,基于线性矩阵不等式(LMI)方法,推导出存在无记忆状态反馈控制律使闭环系统镇定及具有H∞性能指标的充分条件;另外,以具有时变状态时滞和输入时滞的不确定受扰非线性离散系统为研究对象,基于适当的Lyapunov函数,给出了时滞相关型状态反馈控制器设计方案,使得闭环系统一致最终有界。
(5)为了验证控制方法的有效性,本文将基于粒子滤波前馈控制器和扰动观测器的二自由度控制系统实施于永磁同步电机速度控制上,具有很强的抗扰动性能,能更精确地实现对控制对象的速度控制。另外,提出了一种改进型重复控制系统来对伺服电机的位置系统进行控制,以进一步改善系统的稳定性和跟踪精度。通过仿真,实现了控制系统算法和设计验证。
Disturbances and time-delay are common phenomenon in the complex process industry, such as Chemical Engineering, Oil refining, Metallurgy, and Paper-making industry. Disturbance has important effect for system performance. Removing and controlling disturbance is key for design robust controller of high performance. Since the controlled variable in time-delayed system can not reflect the manipulate variable in time, it causes high overshoot and long settling time. The stability of closed-loop system will be degraded. It is difficult to control time-delayed system. Hence, there are much important theory and practical value on the study of control on disturbances and time-delay system. More and more researchers devote to research on control method for controlling disturbances and time-delayed processes.
It is very difficult to get exact mathematical models of industrial processes, models used in design procedure of control systems are commonly mathematical models through approximation. Uncertainties of mathematical models must be considered in control systems design procedure. Hence, how to deal with effects of uncertainties is becoming urgent requirement, and it is also a big challenge facing control theory and application recently. Some problems in disturbance and time-delayed system control techniques and applications are researched in this thesis. Some improvements of tradition control methods have been made at different degree, and some new control algorithms are also proposed in this thesis.
The main working results and contribution of this dissertation are stated as follows:
Researched the character of coloured disturbance. A particle filter is proposed for the nonlinear non-Guassian filter problem in the state tracking process of coloured disturbance. A statistical autocorrelation function is proposed for power spectral character of random orders. So, using biased estimator, which produces a stable system with a matrix that numerically is positive definite.
Based on the feedforward-feedback control structure, a set of design method and tuning rule of feedforward-feedback control system is proposed based on particle filter. The particle filter is utilized for rejecting the non-Guassian disturbance. Firstly the setpoint tracking controller is designed in terms of the robust optimal performance objective. Then according to the load disturbance rejection requirement during the system steady operation, based on robust optimal performance index, the design of controller is proposed based on the expected sensitivity function. The setpoint response and the load disturbance response are decoupled from each other so that both of them can be separately regulated and optimized on line. The performance is improved.
For robust control of time-varying uncertain time-delay disturbance non-linear continuous systems, the characters are researched in time domain. It need not matched uncertainties. The robust control problems and related problems are presented for uncertain time-delay disturbance non-linear continuous systems. The design algorithms are given about robust state feedback controller and robust dynamic output feedback controller. The asymptotic stability of robust controller is guaranteed.
The problem of robust control for time-varying disturbance discrete linear system with uncertain time-delay is investigated. Based on LMI method, design algorithms are presented about memoryless robust state feedback controller for system stability and performance index. On the other hand, based on new Lyapunov function, the design method of state feedback controller is presented for time-varying disturbance discrete non-linear systems with uncertain time-delay. The asymptotic stability of robust controller is guaranteed.
To demonstrate the validity and superiority of the proposed control structure, a two-degree-of-freedom control structure with particle filter feedforward controller and disturbance observer is designed for PMSM speed control. It has strong rejecting the disturbance. The speed precision of motor can be effectively improved by the scheme. On the other hand, a new repeat control system is proposed for PMSM position control. The tracking precision and system stability of motor can be effectively improved by the scheme. The results of simulation examples show that the proposed control method is satisfied.
引文
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