基于μ综合的ICPT系统鲁棒控制研究
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摘要
感应耦合电能传输(ICPT)技术是一种基于高频电磁场近场耦合原理实现电能近距离无线传输的技术，涉及了电磁耦合、电力电子、自动控制等多个领域。由于谐振网络、高频变换以及磁路耦合等环节的存在，ICPT系统具有的自治振荡特性、高维非线性、不确定性等复杂的数学特性，显著增加了对系统建模及综合分析的难度。通过文献检索发现，目前尚无一种有效的方法可以解决ICPT系统的不确定非线性动力学行为建模及综合分析问题。
本文旨在针对ICPT系统的复杂动力学行为特性，提出一种可普遍适用于这类不确定非线性系统的建模与控制、稳定性与性能分析的鲁棒综合方法，并通过将这种方法应用到实际ICPT系统中以验证该方法的有效性。作者主要从以下几个方面展开研究工作：
1．提出一种改进型广义状态空间平均（GSSA）建模方法
针对ICPT系统的自治振荡特性、高维非线性、不确定性等复杂动力学行为的建模问题，文中综合考虑系统的动态不确定性（高频未建模部分）、参数不确定性及可能存在的外部扰动，在传统GSSA模型的基础上，通过应用线性分式变换方法分离系统不确定性，以及附加反映各类摄动频谱特性的性能加权函数，形成一种改进型GSSA建模方法。
2．研究并分析在结构化不确定性下ICPT系统的鲁棒综合控制问题
文中以系统的鲁棒稳定性和鲁棒性能为设计指标，将ICPT系统在各类摄动因素影响下的鲁棒综合问题转化为一个系统结构奇异值的最小化问题，并采用D-K迭代算法求解出一个高阶、连续的μ综合鲁棒控制器。基于最优Hankel范数逼近方法和离散相似法，文中还分别对高阶、连续的μ综合控制器进行了降阶及离散化处理，以使该复杂的控制律更加易于在实际工程中实现。
3．研究ICPT系统在各类摄动因素影响下的稳定性与性能分析问题，并提出一种电路参数鲁棒优化方法
文中分别从标称性能、鲁棒稳定性及鲁棒性能三个方面对闭环摄动系统进行了检验和分析，得出了结构化不确定性下系统维持鲁棒稳定性和鲁棒性能的不确定参数边界条件，并进一步提出了一种以提高系统鲁棒性为目标的电路参数优化方法，其核心思想就是通过增加闭环摄动系统的稳定裕值（结构奇异值的倒数）来降低系统对电路参数摄动的敏感程度。
4．通过实际的ICPT系统验证该鲁棒综合研究方法的有效性
以一个LCL型ICPT系统为研究实例，根据其改进型GSSA模型及鲁棒优化电路参数，设计出一个基于μ综合理论的鲁棒控制器，并通过建立该μ综合控制系统的仿真模型和实验平台，分别对系统存在外部扰动、负载摄动以及参考电压变化情况下的瞬态响应过程进行了分析和研究。仿真及实验结果不仅说明了μ综合控制作用的有效性，而且还验证了理论研究成果的正确性。
本文的创新性贡献在于：
1.针对ICPT系统这一类具有自治振荡特性、高维非线性及不确定性的系统建模问题，创新性地将各种不确定性和外部扰动因素考虑到GSSA建模及分析过程中，以实现对这类系统复杂动力学行为更加客观及精确的描述。
2.针对ICPT系统中各类摄动因素所带来的鲁棒综合问题，提出了一种基于结构奇异值的鲁棒控制策略。该控制策略以系统的鲁棒稳定性和鲁棒性能为设计指标，能保证所设计的闭环系统按照预设的性能指标稳定地运行。
3.针对ICPT系统在各类摄动因素影响下的稳定性及性能分析问题，推导出系统维持鲁棒稳定性和鲁棒性能的不确定参数边界条件，并基于此边界判断条件，提出了一种以提高整个系统鲁棒性为目标的电路参数优化方法。
Inductively coupled power transfer (ICPT) technology can be defined as atechnology where power is transferred in wireless way between two electrical isolationsides by a high-frequency alternating magnetic-field. This novel technology involveselectromagnetic coupling, power electronics, automatic control and other field. Due tothe vital components including resonant network, high-frequency converter and coupledmagnetic circuit, ICPT systems have represented some complicated mathematicalproperties such as autonomous oscillating property, high dimensional nonlinearity,uncertainty, etc. These system properties lead to a significant increase in the complexityand difficulty for system modeling and synthesis. From the literature review, it can befound that there isn’t such one effective method so far to solve the problems ofuncertain nonlinear behaviors modelling and robust synthesis for ICPT systems.
Aiming at the complex dynamical behavior characteristics of ICPT systems, thispaper is devoted to proposing a robust synthesis method which can be universallyapplied to the modeling, control, analyses of stability and performance for this kind ofuncertain nonlinear systems, and further researching a practical ICPT system in order toverify the validity of the proposed method. The main works of this paper are listed asfollows:
1． Proposed an improved generalized state-space averaging (GSSA) modellingmethod
To model the complex dynamical behaviors such as autonomous oscillatingproperty, high dimensional nonlinearity and uncertainty for ICPT systems, an improvedGSSA method is proposed by taking into account the system dynamic uncertainty(high-frequency unmodeled part), parameter uncertainty and external disturbances.Based on the system model described by traditional GSSA method, the system uncertainpart is first separated from the nominal part by means of the linear fractionaltransformation, and then the performance weighting functions are attached to the systemmodel for reflecting the spectrum characteristics of all the perturbations, and theimproved GSSA model is finally established to describe this augmented object.
2. Studied and analyzed the robust synthesis control problem for ICPT system withstructured uncertainty
Based on the design indexes of system robust stability and robust performance, the robust synthesis problem caused by all the perturbations in ICPT system is firsttransformed into a minimization problem of the structured singular values so that ahigh-order and continuous μ synthesis robust controller can be solved by D-K Iterativealgorithm. In order to make μ synthesis robust controller easy in implementation ofpractical engineering, the optimal Hankel-norm approximation and discrete similarmethod are given in the paper which are respectively used to reduce the order anddiscrete the algorithm for μ synthesis robust controller.
3．Studied the stability and performance analysis problems for the perturbed ICPTsystem, and proposed a robust optimization method for circuit parameters
To investigate the performance of closed-loop perturbed system, the nominalperformance, robust stability and robust performance are all tested and analyzed. Thenthe boundary condition of uncertain parameters to maintain the system robust stabilityand robust performance is further derived. On this basis, a robust optimization strategyof circuit parameters for the purpose of improving the system robustness is proposed.The core idea of robust optimization strategy is to reduce the system sensitivity tocircuit parameter perturbations by increasing the stability margin of closed-loop system,i.e. the reciprocal of structured singular value.
4．Verified the validity of the proposed synthesis method via a practical ICPTsystem
According to the improved GSSA model and circuit parameters obtained from therobust optimization for LCL type ICPT system, a robust controller is designed on thebasis of μ synthesis theory, and further the simulation model and experimental platformfor the μ synthesis control system are respectively established. From analyzing thesystem transient responses to external disturbances, load perturbations and referencevoltage changes, the simulation and experimental results can not only illustrate thevalidity of μ synthesis control, but also can verify the correctness of theoreticalresearch.
The main contributions of the paper are as follows:
1. Aiming at the modeling problem for a class of systems with autonomous oscillatingproperty, high dimensional nonlinearity and uncertainty such as ICPT systems, thevarious uncertainties and external disturbances have been innovatively taken intoaccount in the process of GSSA modeling and analysis, so that the complexdynamical behaviors of such systems can be described more objectively andaccurately.
2. Aiming at the robust synthesis problem of ICPT systems caused by all theperturbations, a robust control strategy based on the structured singular values hasbeen proposed. This control strategy that uses the system robust stability and robustperformance as the design indexes can guarantee the closed-loop system operationaccording to the predetermined performance.
3. Aiming at the stability and performance analysis problem for ICPT systems withthe perturbations, the boundary condition of uncertain parameters to maintain thesystem robust stability and robust performance is derived. According to theboundary condition, a robust optimization method of circuit parameters has beenproposed for the sake of improving the system robustness.
本文旨在针对ICPT系统的复杂动力学行为特性，提出一种可普遍适用于这类不确定非线性系统的建模与控制、稳定性与性能分析的鲁棒综合方法，并通过将这种方法应用到实际ICPT系统中以验证该方法的有效性。作者主要从以下几个方面展开研究工作：
1．提出一种改进型广义状态空间平均（GSSA）建模方法
针对ICPT系统的自治振荡特性、高维非线性、不确定性等复杂动力学行为的建模问题，文中综合考虑系统的动态不确定性（高频未建模部分）、参数不确定性及可能存在的外部扰动，在传统GSSA模型的基础上，通过应用线性分式变换方法分离系统不确定性，以及附加反映各类摄动频谱特性的性能加权函数，形成一种改进型GSSA建模方法。
2．研究并分析在结构化不确定性下ICPT系统的鲁棒综合控制问题
文中以系统的鲁棒稳定性和鲁棒性能为设计指标，将ICPT系统在各类摄动因素影响下的鲁棒综合问题转化为一个系统结构奇异值的最小化问题，并采用D-K迭代算法求解出一个高阶、连续的μ综合鲁棒控制器。基于最优Hankel范数逼近方法和离散相似法，文中还分别对高阶、连续的μ综合控制器进行了降阶及离散化处理，以使该复杂的控制律更加易于在实际工程中实现。
3．研究ICPT系统在各类摄动因素影响下的稳定性与性能分析问题，并提出一种电路参数鲁棒优化方法
文中分别从标称性能、鲁棒稳定性及鲁棒性能三个方面对闭环摄动系统进行了检验和分析，得出了结构化不确定性下系统维持鲁棒稳定性和鲁棒性能的不确定参数边界条件，并进一步提出了一种以提高系统鲁棒性为目标的电路参数优化方法，其核心思想就是通过增加闭环摄动系统的稳定裕值（结构奇异值的倒数）来降低系统对电路参数摄动的敏感程度。
4．通过实际的ICPT系统验证该鲁棒综合研究方法的有效性
以一个LCL型ICPT系统为研究实例，根据其改进型GSSA模型及鲁棒优化电路参数，设计出一个基于μ综合理论的鲁棒控制器，并通过建立该μ综合控制系统的仿真模型和实验平台，分别对系统存在外部扰动、负载摄动以及参考电压变化情况下的瞬态响应过程进行了分析和研究。仿真及实验结果不仅说明了μ综合控制作用的有效性，而且还验证了理论研究成果的正确性。
本文的创新性贡献在于：
1.针对ICPT系统这一类具有自治振荡特性、高维非线性及不确定性的系统建模问题，创新性地将各种不确定性和外部扰动因素考虑到GSSA建模及分析过程中，以实现对这类系统复杂动力学行为更加客观及精确的描述。
2.针对ICPT系统中各类摄动因素所带来的鲁棒综合问题，提出了一种基于结构奇异值的鲁棒控制策略。该控制策略以系统的鲁棒稳定性和鲁棒性能为设计指标，能保证所设计的闭环系统按照预设的性能指标稳定地运行。
3.针对ICPT系统在各类摄动因素影响下的稳定性及性能分析问题，推导出系统维持鲁棒稳定性和鲁棒性能的不确定参数边界条件，并基于此边界判断条件，提出了一种以提高整个系统鲁棒性为目标的电路参数优化方法。
Inductively coupled power transfer (ICPT) technology can be defined as atechnology where power is transferred in wireless way between two electrical isolationsides by a high-frequency alternating magnetic-field. This novel technology involveselectromagnetic coupling, power electronics, automatic control and other field. Due tothe vital components including resonant network, high-frequency converter and coupledmagnetic circuit, ICPT systems have represented some complicated mathematicalproperties such as autonomous oscillating property, high dimensional nonlinearity,uncertainty, etc. These system properties lead to a significant increase in the complexityand difficulty for system modeling and synthesis. From the literature review, it can befound that there isn’t such one effective method so far to solve the problems ofuncertain nonlinear behaviors modelling and robust synthesis for ICPT systems.
Aiming at the complex dynamical behavior characteristics of ICPT systems, thispaper is devoted to proposing a robust synthesis method which can be universallyapplied to the modeling, control, analyses of stability and performance for this kind ofuncertain nonlinear systems, and further researching a practical ICPT system in order toverify the validity of the proposed method. The main works of this paper are listed asfollows:
1． Proposed an improved generalized state-space averaging (GSSA) modellingmethod
To model the complex dynamical behaviors such as autonomous oscillatingproperty, high dimensional nonlinearity and uncertainty for ICPT systems, an improvedGSSA method is proposed by taking into account the system dynamic uncertainty(high-frequency unmodeled part), parameter uncertainty and external disturbances.Based on the system model described by traditional GSSA method, the system uncertainpart is first separated from the nominal part by means of the linear fractionaltransformation, and then the performance weighting functions are attached to the systemmodel for reflecting the spectrum characteristics of all the perturbations, and theimproved GSSA model is finally established to describe this augmented object.
2. Studied and analyzed the robust synthesis control problem for ICPT system withstructured uncertainty
Based on the design indexes of system robust stability and robust performance, the robust synthesis problem caused by all the perturbations in ICPT system is firsttransformed into a minimization problem of the structured singular values so that ahigh-order and continuous μ synthesis robust controller can be solved by D-K Iterativealgorithm. In order to make μ synthesis robust controller easy in implementation ofpractical engineering, the optimal Hankel-norm approximation and discrete similarmethod are given in the paper which are respectively used to reduce the order anddiscrete the algorithm for μ synthesis robust controller.
3．Studied the stability and performance analysis problems for the perturbed ICPTsystem, and proposed a robust optimization method for circuit parameters
To investigate the performance of closed-loop perturbed system, the nominalperformance, robust stability and robust performance are all tested and analyzed. Thenthe boundary condition of uncertain parameters to maintain the system robust stabilityand robust performance is further derived. On this basis, a robust optimization strategyof circuit parameters for the purpose of improving the system robustness is proposed.The core idea of robust optimization strategy is to reduce the system sensitivity tocircuit parameter perturbations by increasing the stability margin of closed-loop system,i.e. the reciprocal of structured singular value.
4．Verified the validity of the proposed synthesis method via a practical ICPTsystem
According to the improved GSSA model and circuit parameters obtained from therobust optimization for LCL type ICPT system, a robust controller is designed on thebasis of μ synthesis theory, and further the simulation model and experimental platformfor the μ synthesis control system are respectively established. From analyzing thesystem transient responses to external disturbances, load perturbations and referencevoltage changes, the simulation and experimental results can not only illustrate thevalidity of μ synthesis control, but also can verify the correctness of theoreticalresearch.
The main contributions of the paper are as follows:
1. Aiming at the modeling problem for a class of systems with autonomous oscillatingproperty, high dimensional nonlinearity and uncertainty such as ICPT systems, thevarious uncertainties and external disturbances have been innovatively taken intoaccount in the process of GSSA modeling and analysis, so that the complexdynamical behaviors of such systems can be described more objectively andaccurately.
2. Aiming at the robust synthesis problem of ICPT systems caused by all theperturbations, a robust control strategy based on the structured singular values hasbeen proposed. This control strategy that uses the system robust stability and robustperformance as the design indexes can guarantee the closed-loop system operationaccording to the predetermined performance.
3. Aiming at the stability and performance analysis problem for ICPT systems withthe perturbations, the boundary condition of uncertain parameters to maintain thesystem robust stability and robust performance is derived. According to theboundary condition, a robust optimization method of circuit parameters has beenproposed for the sake of improving the system robustness.
引文
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