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Fractional Order Robust Control For Uncertain Systems

Posted on:2018-12-25Degree:DoctorType:Dissertation
Country:ChinaCandidate:X ZhouFull Text:PDF
GTID:1318330512982676Subject:Control Science and Engineering
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As a generalization from traditional calculus,fractional order calculus enjoys both conciseness and veracity in complex system modeling and control.Fractional order system(FOS)theory,as well as fractional order controller design,has attracted lots attention in recent years.It is shown that fractional order control(FOC)owns a higher degree of freedom than integer ones in controller parameters' selection,and therefore owns a greater potential in system performance improvement.However,due to the environmental change,components ageing and other unavoidable reasons,parameter-s' uncertainties and disturbances always exist in systems.Thus,uncertainties should be taken into consideration in the controller design in order to ensure a desired per-formance under all those disturbances.Hence,it is a meaningful task to study the fractional order robust control problem for those disturbed systems.Frequency analysis is widely used in the robust analysis and controller parameter tuning.A number of relative conclusions have been achieved as for today.However,difficulties and challenges still exist in the robust controller designing in FOSs,espe-cially when facing complicated systems with multi uncertain parameters.Influence of the fractional order has made it much more difficult to analyze FOSs' frequency and time domain performances.On one hand,parts of the existing results in integer or-der systems(IOSs)have not yet been generalized into fractional order domain as the imperfection of FOC theory.On the other hand,stability and robust specifications for FOSs are always manifested as a set of nonlinear equations involving massive calcula-tion,which is difficult to be solved by traditional methods.At the same time,inherence conflicting between engineering indices under conventional controllers has restricted further improvement of system performances.Therefore,this dissertation concerns fractional order robust control scheme in a more comprehensive version.Based on the frequency analysis and estimation methods,fractional order robust controller design-ing and performance improving for complicated systems is studied,and the nonlinear robust FOC and disturbance compensation scheme is involved.Firstly,robustPI?D? controller parameters tuning methods are proposed for com-plicated linear systems with both gain and multi time constants variations.Normaliza-tion of FOS's frequency domain expression is introduced in the beginning.For those systems with gain and a single time constant uncertainties,the robustness specifics-tions in frequency domain are proposed and then simplified.When dealing with those systems under multi time constants variations,a decoupling method is used to decrease the number of nonlinear equations and avoid overdetermined equations.Meanwhile,basing on the great robustness of Bode's ideal transfer function,a nonlinear optimiza-tion problem is raised for controller parameters' tuning.Secondly,a promotion in both the system's overshoot and rise time is achieved un-der system gain variations by introducing a novel nonlinear FOS scheme,that is called fractional order signed power feedback control.Even though the CRONE approach de-veloping from the Bode's ideal transfer function owns a great robustness property,the amount of tuning parameters has limited a further performance improvement in control systems.Utilizing the 'smaller error larger gain,larger error smaller gain' property of the nonlinear feedback function,as well as the CRONE approach,the robustness and re-sponse speed of disturbed systems are guaranteed and improved in this dissertation.In order to analyze and estimate time responses of nonlinear FOSs,comparison theorems for FOSs are proposed and proved.Hereafter,the rise time(or fall time)comparison and estimation for both tracking and regulation problems are given.For the sake of chattering elimination,a framework for robust and fast FOC schemes are proposed in terms of convex or concave functions.Finally,a deep research and further promotion for fractional order active distur-bance rejection control(FO-ADRC)is studied.ADRC is a promotion of traditional PID control.On one hand the transient process has ensures a balance between over-shoot and response speed.On the other hand,the idea of disturbance compensation has greatly promoted the system's robustness.However,present researches on FO-ADRC only focus on those SISO systems or decoupled MIMO systems,which has limited the practicability.In this dissertation a flatness based FO-ADRC is proposed for commen-surate controllable FOSs.The flat outputs for both single and multiple input systems are given in a concise form.From further discussion on stability region of controller parameters,it is shown that existence of stable controller depends on the commensurate order as well as the system's dimension.On the other hand,a FO-ADRC framework is also proposed for parallel FOSs with commensurate order by choosing suitable state variables and the desired system dynamic behaviors.
Keywords/Search Tags:fractional order system, robust control, frequency analysis, PI~?D~? control, parameter tuning, nonlinear fractional order system analysis, robust fast control, FO-ADRC
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