连续时间广义预测控制及其实现方法研究
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摘要
预测控制是直接从工业过程控制中产生的一类基于模型的先进控制算法,它最大限度地结合了工业实际的要求,综合控制质量高,一直是工业控制界以及理论界的研究热点。控制技术通常都有离散时间版本和连续时间版本,控制工程师可以根据具体的情况选择需要的形式,预测控制也不例外。连续时间广义预测控制(CGPC)提出后,得到了很多学者的关注,它具有与离散时间广义预测控制类似的性能,而且在采样时间的选择上比较灵活,对非最小相位系统也无需控制加权。但是,对它的研究远不如离散时间广义预测控制成熟,仍然存在很多有待解决的问题。本文正是从这一观点出发,在前人研究的基础上,对在连续时间框架下设计的广义预测控制算法及其实现方法进行了研究。本文的主要研究内容有:
第一,为消除余差,推导了带积分作用的CGPC控制律,在此基础上分析了CGPC闭环设定值响应和干扰响应性能,导出其内模结构,并与具有观测器的CGPC结构比较,说明观测多项式的存在增加了设计自由度,它的调节对系统鲁棒性能和抗干扰性能起着重要作用。为得到预测输出而引入的多项式恒等式方程,需要大量的多项式长除运算,为此提出了一种多项式参数的递推计算方法,简化计算,以利于在线实施。根据CGPC的设计参数对系统性能的影响,以带积分作用的设计模型为基础,提出新的参数整定规则,简化CGPC算法的设计和实现。
第二,针对传统串级控制结构内外环性能互相耦合的问题,提出一种特殊的具有解耦内外环鲁棒性能的预测控制器。控制算法基于连续时间广义预测控制,将原来的预测输出用带有内环输出信息的预测输出代替,利用类似的性能指标求解控制律。使用一个控制器实现传统的串级控制功能,简化计算和实施。通过分析观测多项式对系统性能的影响,说明观测多项式的设计不影响系统的设定值响应,而且系统内外环的鲁棒性能可以通过各自的设计多项式独立调节。与几种串级控制器的比较仿真结果验证了所提出控制器的有效性能。
第三,针对时滞对象推导了一种显式处理时滞的方法,通过恒等式运算将时滞补偿引入到控制律中,简化设计,减小计算量。分析了观测多项式对系统抗干扰性能和鲁棒性能的影响,提出在系统存在较大模型误差,尤其是时滞误差时,通过添加失配滤波器提高鲁棒性能的方案(F-SDCGPC)。该滤波器比观测多项式结构简单,同时具有观测多项式不影响系统标称设定值响应的类似性能,因此可以只针对模型失配进行设计,提高CGPC系统对模型失配的主动抑制能力。而且,滤波器的加入简化了参数整定,可以先根据无时滞模型设计参数得到标称设定值跟踪性能,然后再根据可能的模型误差设置滤波器参数。该方法适于控制高阶系统、尤其是有较大的时滞误差的系统。理论分析和数值仿真证明所提出控制结构的有效性。
第四,针对多变量连续时间广义预测控制提出了一种新的时滞解决方案(MDCGPC)。对于物理可实现的多变量系统,将模型的与多项式矩阵构造成对角形式,将一个多输入多输出模型分解成多个多输入单输出模型进行考虑,在算法的推导过程中,显式考虑纯滞后项,通过参数恒等式的变换将时滞补偿项引入到控制律中,加入一个结构简单的反馈滤波器,调节剩余时滞误差的影响,简化控制器的设计。通过对预测时域和参考轨迹的调节,减小变量间的耦合作用,使系统具有一定的解耦能力。提出了一种恒等式多项式参数的递推计算方法,避免复杂的多项式矩阵除法运算,简化计算,利于在线实施。对Wood-berry模型和Shell模型的仿真验证了所提出方案的有效性。
第五,使用基于随机数直接搜索的优化方法,辨识过程的连续时间传递函数模型,在此基础上设计连续时间广义预测控制器。基于通常使用的PC机平台,用VC开发了CGPC仿真软件,为推广其实际应用奠定基础。仿真过程中将CGPC控制律视为多个传递函数输出信号的组合,分成单个模块进行计算,为添加新的模块、修改控制律结构和参数提供方便。
Predictive control is a model based advanced control method which is originated directly from the industry process control.It combines the requirement of the practical industry processes and has good control performance.Generally the control techniques have both continuous-and discrete-time versions,and the control engineer,however,is free to choose the design approach according to the practical condition-either continuous or discrete.And predictive control is no exception.Since the continuous-time generalized predictive control(CGPC)is proposed it has attracted many attentions in control fields.It has properties similar to those of the discrete-time generalized predictive control.In addition the choice of sample interval is flexible and the control weighting is not essential for the control of non-minimum phase systems.However,there are still many open problems to be solved.Just from this view,the continuous-time generalized predictive control and its implementation methods are studied.
First,the CGPC law with integration is derived to eliminate the offset.The closed-loop set-point tracking performance and disturbance-rejection performance are analyzed.The internal model structure of CGPC with integration is derived,and compared with the observer structure of CGPC the important role of observer polynomial is analyzed.A recursive computation method of polynomial parameters which can avoid the complex division computation of polynomial is proposed.According to the effects of tuning parameters to the system performance,some tuning rules are given based on the design model with integration,and they can simplify the design and implementation of CGPC.
Second,for the coupling performance of the traditional cascade control structure,a special controller with decoupling robustness is proposed.Based on the CGPC algorithm,the original output predictor is replaced by a special predictor with cascade function by using the parameters identities.Thus only one predictive controller can perform the cascade control task.The effects of observer polynomial to the system performance are analyzed.The results show that the robust performance of the inner loop and the outer loop can be tuned separately by the corresponding observer polynomial while the set-point tracking performance is not affected.The compared simulations with the traditional cascade structure verify the performance of the proposed controller.
Third,a CGPC method explicitly considering time delay (F-SDCGPC)is proposed.By using modified predictive output signal the delay compensator is incorporated in the control law with observer structure.The effects of observer polynomial to the disturbance-rejection performance and robustness are analyzed.A filter is added to enhance the robustness when considering large model error especially time delay error. The tuning of filter can enhance the initiative tuning ability of robustness. The design of filter does not affect the nominal set-point response,and it is more flexible than the design of observer polynomial.This property allows the design of the controller in two steps:firstly the controller parameters are chosen to attempt the nominal set-point performance specifications and then the filter is tuned to increase the robustness.The analysis and simulation results show that the F-SDCGPC has better robustness than the observer structure without filter when large time-delay error is considered.
Forth,a new delay predictive solution is proposed for the multivariable continuous-time generalized predictive control(MDCGPC). For most of the physical realizable processes,the model parameter matrices can always be diagonally constructed,so that we can transform the multiple inputs and multiple outputs system into a set of multiple inputs single output model.By using the computation of the identities,the delay compensator is introduced in the control law.A filter is added to adapt delay error.Moreover the decoupling performance can be obtained by tuning the predictive horizon and the reference trajectory.The recursive computation method of polynomial parameters reduces the computation load and complexity.Simulations of Wood-berry and Shell models verify the performance.
Fifth,the continuous-time model is identified by the NLJ method, and then based on this model the continuous-time predictive controller is designed.The CGPC simulation software is developed using VC which is the base to practical application.The CGPC law is considered as combination with the outputs of multiple transfer function blocks,and then the output of the block can be computed separately.This method provides some conveniences to add new blocks.
第一,为消除余差,推导了带积分作用的CGPC控制律,在此基础上分析了CGPC闭环设定值响应和干扰响应性能,导出其内模结构,并与具有观测器的CGPC结构比较,说明观测多项式的存在增加了设计自由度,它的调节对系统鲁棒性能和抗干扰性能起着重要作用。为得到预测输出而引入的多项式恒等式方程,需要大量的多项式长除运算,为此提出了一种多项式参数的递推计算方法,简化计算,以利于在线实施。根据CGPC的设计参数对系统性能的影响,以带积分作用的设计模型为基础,提出新的参数整定规则,简化CGPC算法的设计和实现。
第二,针对传统串级控制结构内外环性能互相耦合的问题,提出一种特殊的具有解耦内外环鲁棒性能的预测控制器。控制算法基于连续时间广义预测控制,将原来的预测输出用带有内环输出信息的预测输出代替,利用类似的性能指标求解控制律。使用一个控制器实现传统的串级控制功能,简化计算和实施。通过分析观测多项式对系统性能的影响,说明观测多项式的设计不影响系统的设定值响应,而且系统内外环的鲁棒性能可以通过各自的设计多项式独立调节。与几种串级控制器的比较仿真结果验证了所提出控制器的有效性能。
第三,针对时滞对象推导了一种显式处理时滞的方法,通过恒等式运算将时滞补偿引入到控制律中,简化设计,减小计算量。分析了观测多项式对系统抗干扰性能和鲁棒性能的影响,提出在系统存在较大模型误差,尤其是时滞误差时,通过添加失配滤波器提高鲁棒性能的方案(F-SDCGPC)。该滤波器比观测多项式结构简单,同时具有观测多项式不影响系统标称设定值响应的类似性能,因此可以只针对模型失配进行设计,提高CGPC系统对模型失配的主动抑制能力。而且,滤波器的加入简化了参数整定,可以先根据无时滞模型设计参数得到标称设定值跟踪性能,然后再根据可能的模型误差设置滤波器参数。该方法适于控制高阶系统、尤其是有较大的时滞误差的系统。理论分析和数值仿真证明所提出控制结构的有效性。
第四,针对多变量连续时间广义预测控制提出了一种新的时滞解决方案(MDCGPC)。对于物理可实现的多变量系统,将模型的与多项式矩阵构造成对角形式,将一个多输入多输出模型分解成多个多输入单输出模型进行考虑,在算法的推导过程中,显式考虑纯滞后项,通过参数恒等式的变换将时滞补偿项引入到控制律中,加入一个结构简单的反馈滤波器,调节剩余时滞误差的影响,简化控制器的设计。通过对预测时域和参考轨迹的调节,减小变量间的耦合作用,使系统具有一定的解耦能力。提出了一种恒等式多项式参数的递推计算方法,避免复杂的多项式矩阵除法运算,简化计算,利于在线实施。对Wood-berry模型和Shell模型的仿真验证了所提出方案的有效性。
第五,使用基于随机数直接搜索的优化方法,辨识过程的连续时间传递函数模型,在此基础上设计连续时间广义预测控制器。基于通常使用的PC机平台,用VC开发了CGPC仿真软件,为推广其实际应用奠定基础。仿真过程中将CGPC控制律视为多个传递函数输出信号的组合,分成单个模块进行计算,为添加新的模块、修改控制律结构和参数提供方便。
Predictive control is a model based advanced control method which is originated directly from the industry process control.It combines the requirement of the practical industry processes and has good control performance.Generally the control techniques have both continuous-and discrete-time versions,and the control engineer,however,is free to choose the design approach according to the practical condition-either continuous or discrete.And predictive control is no exception.Since the continuous-time generalized predictive control(CGPC)is proposed it has attracted many attentions in control fields.It has properties similar to those of the discrete-time generalized predictive control.In addition the choice of sample interval is flexible and the control weighting is not essential for the control of non-minimum phase systems.However,there are still many open problems to be solved.Just from this view,the continuous-time generalized predictive control and its implementation methods are studied.
First,the CGPC law with integration is derived to eliminate the offset.The closed-loop set-point tracking performance and disturbance-rejection performance are analyzed.The internal model structure of CGPC with integration is derived,and compared with the observer structure of CGPC the important role of observer polynomial is analyzed.A recursive computation method of polynomial parameters which can avoid the complex division computation of polynomial is proposed.According to the effects of tuning parameters to the system performance,some tuning rules are given based on the design model with integration,and they can simplify the design and implementation of CGPC.
Second,for the coupling performance of the traditional cascade control structure,a special controller with decoupling robustness is proposed.Based on the CGPC algorithm,the original output predictor is replaced by a special predictor with cascade function by using the parameters identities.Thus only one predictive controller can perform the cascade control task.The effects of observer polynomial to the system performance are analyzed.The results show that the robust performance of the inner loop and the outer loop can be tuned separately by the corresponding observer polynomial while the set-point tracking performance is not affected.The compared simulations with the traditional cascade structure verify the performance of the proposed controller.
Third,a CGPC method explicitly considering time delay (F-SDCGPC)is proposed.By using modified predictive output signal the delay compensator is incorporated in the control law with observer structure.The effects of observer polynomial to the disturbance-rejection performance and robustness are analyzed.A filter is added to enhance the robustness when considering large model error especially time delay error. The tuning of filter can enhance the initiative tuning ability of robustness. The design of filter does not affect the nominal set-point response,and it is more flexible than the design of observer polynomial.This property allows the design of the controller in two steps:firstly the controller parameters are chosen to attempt the nominal set-point performance specifications and then the filter is tuned to increase the robustness.The analysis and simulation results show that the F-SDCGPC has better robustness than the observer structure without filter when large time-delay error is considered.
Forth,a new delay predictive solution is proposed for the multivariable continuous-time generalized predictive control(MDCGPC). For most of the physical realizable processes,the model parameter matrices can always be diagonally constructed,so that we can transform the multiple inputs and multiple outputs system into a set of multiple inputs single output model.By using the computation of the identities,the delay compensator is introduced in the control law.A filter is added to adapt delay error.Moreover the decoupling performance can be obtained by tuning the predictive horizon and the reference trajectory.The recursive computation method of polynomial parameters reduces the computation load and complexity.Simulations of Wood-berry and Shell models verify the performance.
Fifth,the continuous-time model is identified by the NLJ method, and then based on this model the continuous-time predictive controller is designed.The CGPC simulation software is developed using VC which is the base to practical application.The CGPC law is considered as combination with the outputs of multiple transfer function blocks,and then the output of the block can be computed separately.This method provides some conveniences to add new blocks.
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