{"title":"A synthesized integral sliding mode controller for an underactuated unicycle","authors":"Jian-xin Xu, Zhao-Qin Guo, Tong-heng Lee","doi":"10.1109/VSS.2010.5545132","DOIUrl":"https://doi.org/10.1109/VSS.2010.5545132","url":null,"abstract":"In this paper we present a synthesized integral sliding mode controller (ISMC) that can stabilize an underactuated unicycle system. The unicycle consists of a wheel and a saddle that is modeled as an inverse pendulum. The only driving force is the torque applied to the shaft of the wheel, hence it is underactuated. Based on a linear approximation model, a linear controller using LQR method is designed. The control error bound achieved by the linear controller is derived for the unicycle. Next, the matched system nonlinearity of the unicycle is compensated, hence the error bound is reduced. The proposed synthesized ISMC consists of the linear controller, nonlinear compensation, a switching term, and an integral sliding surface. The synthesized ISMC can effectively reject the matched disturbance, and minimize the influence from unmatched disturbances, thus yielding a further reduced error bound.","PeriodicalId":407705,"journal":{"name":"2010 11th International Workshop on Variable Structure Systems (VSS)","volume":"24 13","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131506267","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Sensorless high order sliding mode control of permanent magnet synchronous motor","authors":"M. Ezzat, A. Glumineau, F. Plestan","doi":"10.1109/VSS.2010.5544687","DOIUrl":"https://doi.org/10.1109/VSS.2010.5544687","url":null,"abstract":"In this paper, a robust sensorless speed observer-controller scheme for a permanent magnet synchronous motor (PMSM) is proposed. To estimate both position and speed, without any mechanical sensors and only from the electrical measurements, a back-EMF-based sliding mode is designed. The convergence of this observer is proved. Then a high order sliding mode controller is developed. By using this technique, the drawback of the sliding mode technique called “chattering phenomenon” is strongly attenuated. After that, the convergence of the overall system is analyzed. Moreover, the robustness of this method with respect to the parameters uncertainties is verified by significant simulation results in the framework of an industrial benchmark.","PeriodicalId":407705,"journal":{"name":"2010 11th International Workshop on Variable Structure Systems (VSS)","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124278143","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Multi-input sliding mode control of nonlinear systems with uncertain affine dependence on the control","authors":"G. Bartolini, Elisabetta Punta, T. Zolezzi","doi":"10.1109/VSS.2010.5544729","DOIUrl":"https://doi.org/10.1109/VSS.2010.5544729","url":null,"abstract":"In the extension to multi-input non linear uncertain systems of the sliding mode methodology a crucial role is played by the matrix pre multiplying the control in the dynamic equation of the sliding output. If this matrix is perfectly known and invertible it is possible to transform a multi-input sliding mode control problem in an almost decoupled set of single input problems. If this matrix is uncertain nothing can be done in general, and the investigation is oriented to find condition ensuring the feasibility of control strategies in a progressively increasing set of uncertain matrices. In the case of uncertain but constant matrices it is possible, in principle, to manage the case in which the matrix in question is invertible. The corresponding adaptive or switching strategy suffer of the curse of dimensionality of the so called Unmixing Set. In this paper the case of time and state varying uncertain matrix is dealt with. The more general class of such a matrices for which there is, at least locally, a solution of the problem is found. The introduction of artificial integrators in the output channel (the integral sliding mode control methodology) allows the practical implementation of the control law without requiring the a priori knowledge of parameters featured by the solution of a relevant nonlinear Lyapunov equation.","PeriodicalId":407705,"journal":{"name":"2010 11th International Workshop on Variable Structure Systems (VSS)","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114685087","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
H. Sira-Ramírez, J. Cortés-Romero, A. Luviano‐Juárez
{"title":"A GPI sliding mode control approach for linear controllable switched systems","authors":"H. Sira-Ramírez, J. Cortés-Romero, A. Luviano‐Juárez","doi":"10.1109/VSS.2010.5544665","DOIUrl":"https://doi.org/10.1109/VSS.2010.5544665","url":null,"abstract":"In this article, we propose a state-free discontinuous feedback controller design approach for the asymptotic sliding mode control of a large class of linear switched systems. The method is devoid of state measurements and efficiently extends the sliding mode control methodology to traditional input-output descriptions of the plant. The approach is based on regarding the average Generalized Proportional Integral (GPI) controller design as a guide for inducing the sliding mode features through the switching controller. Throughout, it is assumed that the available output signal coincides with the system's flat output, an output capable of completely differentially parameterizing all the variables in the system (inputs, original outputs and state variables) and exhibits no zero dynamics. Encouraging simulation results are presented in connection with the tutorial example. Experimental results are also presented for the trajectory tracking problem on a popular DC-to-DC switched power converter of the “buck” type.","PeriodicalId":407705,"journal":{"name":"2010 11th International Workshop on Variable Structure Systems (VSS)","volume":"53 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117153430","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Observation for non-linear uncertain systems with multiple outputs via non-homogeneous high-order sliding modes","authors":"H. Ríos, J. Dávila, L. Fridman","doi":"10.1109/VSS.2010.5544715","DOIUrl":"https://doi.org/10.1109/VSS.2010.5544715","url":null,"abstract":"This article presents the problem of finite time state observation for a class of non-linear systems with multiple outputs affected by modeling uncertainties and unknown inputs. The proposed adaptable method is based on the non-homogeneous high-order sliding mode control approach. The observability is derived in terms of certain geometric restrictions on the vector fields of the system. A method for the exact reconstruction of the unknown inputs is stated. The method does not require the system to be transformed to any normal form. Simulation results support the proposed method.","PeriodicalId":407705,"journal":{"name":"2010 11th International Workshop on Variable Structure Systems (VSS)","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125657365","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Time-varying parameter estimation in continuous-time under colored perturbations using “equivalent control concept” and LSM with forgetting factor","authors":"J. Escobar, A. Poznyak","doi":"10.1109/VSS.2010.5544662","DOIUrl":"https://doi.org/10.1109/VSS.2010.5544662","url":null,"abstract":"This paper deals with time problem of time-varying parameters estimation of stochastic systems under colored noise perturbations. A two step method is proposed. First, it is designed a tracking process, based in the “equivalent control” technique, providing the finite-time equivalence of the original stochastic process with unknown parameters to an auxiliary one. This equivalence does not cancel the noise effects, but allows to estimate the model in a “regression form” for a sufficient short time. In the second step, the Least Squares Method with a scalar forgetting factor is applied to estimate the time-varying parameters of the given model. Two examples illustrate the effectiveness of the proposed approach, the first shows an application in a system of location and motion, and the second an estimation of a growth rate of a population dynamic.","PeriodicalId":407705,"journal":{"name":"2010 11th International Workshop on Variable Structure Systems (VSS)","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127946578","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Solving the unknown control direction problem for strongly nonlinear systems by means of periodic switching function and norm observers","authors":"T. R. Oliveira, A. J. Peixoto, L. Hsu","doi":"10.1109/VSS.2010.5545135","DOIUrl":"https://doi.org/10.1109/VSS.2010.5545135","url":null,"abstract":"This paper addresses the design of a sliding mode tracking controller for single-input-single-output (SISO) uncertain strongly nonlinear plants with relative degree one and unknown sign of the high frequency gain, i.e., with unknown control direction. We demonstrate that it is possible to achieve global exact tracking using only output-feedback by combining a recently introduced periodic switching function with a novel norm state observer framework. One significant advantage of the new scheme is its robustness to time-varying control direction which has been theoretically justified for jump variations and successfully tested by simulation.","PeriodicalId":407705,"journal":{"name":"2010 11th International Workshop on Variable Structure Systems (VSS)","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131305830","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Periodic switching function based sliding mode control applied to output-feedback extremum-seeking problem","authors":"A. J. Peixoto, T. R. Oliveira, L. Hsu","doi":"10.1109/VSS.2010.5545136","DOIUrl":"https://doi.org/10.1109/VSS.2010.5545136","url":null,"abstract":"In a companion paper submitted to VSS 2010, we have addressed the design of sliding mode tracking control for single-input-single-output (SISO) uncertain nonlinear plants with unknown sign of the high frequency gain, that is, with unknown control direction. We have demonstrated that it is possible to achieve global exact tracking using only output-feedback by combining a periodic switching function with a norm state observer framework. One significant advantage of this scheme was its robustness to time-varying control direction. In the present paper, we show that this property makes it adequate for solving extremum-seeking problems using only output-feedback for relative degree one strongly nonlinear systems. Applications to a nonderivative optimizer and to the wheel slip control in Antilock Braking Systems (ABS) illustrate the viability of the proposed control scheme.","PeriodicalId":407705,"journal":{"name":"2010 11th International Workshop on Variable Structure Systems (VSS)","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121289091","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Sliding mode observer for systems with mismatched parametric uncertainties","authors":"J. A. Silva, C. Edwards","doi":"10.1109/VSS.2010.5544727","DOIUrl":"https://doi.org/10.1109/VSS.2010.5544727","url":null,"abstract":"A sliding mode observer (SMO) analysis and synthesis framework for systems with mismatched parametric uncertainties is proposed. Stability of the uncertain state estimation error system is addressed using the concept of uniform ultimate bounded stability, also known as practical stability. The design methodology involves linear matrix inequality methods and employs a polytopic description for designing the gain matrices of the SMO. A numerical example illustrates the design methodology and its effectiveness.","PeriodicalId":407705,"journal":{"name":"2010 11th International Workshop on Variable Structure Systems (VSS)","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121723716","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
M. Rubagotti, A. Estrada, F. Castaños, A. Ferrara, L. Fridman
{"title":"Optimal disturbance rejection via integral sliding mode control for uncertain systems in regular form","authors":"M. Rubagotti, A. Estrada, F. Castaños, A. Ferrara, L. Fridman","doi":"10.1109/VSS.2010.5544698","DOIUrl":"https://doi.org/10.1109/VSS.2010.5544698","url":null,"abstract":"This paper considers the problem of using an integral sliding mode strategy to reduce the disturbance terms acting on nonlinear systems in regular form. It is proved that the definition of a suitable sliding manifold and the generation of sliding modes upon it can guarantee the minimization of the disturbance terms. Simulation examples shows the effectiveness of the proposal.","PeriodicalId":407705,"journal":{"name":"2010 11th International Workshop on Variable Structure Systems (VSS)","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121792379","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}