Pub Date : 1989-06-21DOI: 10.23919/ACC.1989.4790265
T. Djaferis
Let ¿(s) = ¿0(s) = ¿0(s) + a1 ¿1(s) + a2¿2(s) +...+ ak¿k(s) be a polynomial with coefficients that depend linearly on real parameters ai, 1 ¿ i ¿ k. Let ¿0(s) be stable of degree n and ¿i, 1 ¿ i ¿ k, of degree less than n. Assume that the ai are allowed to take values in the k dimensional hypercube ¿¿a = {(a1,...,ak)¿Rk: a-i ¿ ai ¿ ¿ a+i}, where a-1i ≪ 0, a+i ≫ 0, 1 ¿ i ¿ k are fixed and ¿ ¿ 0. In this paper we consider the problem of how to compute the largest value ¿* such that the family is stable in ¿¿a for 0 ¿ ¿ ≪ ¿*. Considering the problem in the frequency domain, a function of frequency can be constructed whose infimum is ¿*. In this paper we show that to compute ¿* one need only consider the values of this function at a finite number of frequencies. The number of frequencies is polynomial in k, and the frequencies themselves are explicitly determined from the given data.
让他们害怕(s) = 0 (s)害怕= 0 (s) +害怕害怕a1 - 1 (s) + a2 2 (s) +…+害怕ak k (s)是一个多项式的系数线性依赖于实际参数ai, 1他们害怕我害怕k。0 (s)是稳定程度的n和害怕,我害怕我害怕k,程度小于n。假设允许人工智能在k值维超立方体害怕害怕a = {(a1,…,ak)害怕Rk:我害怕我害怕害怕ai +},在a-1i≪0,+我≫0,1害怕我害怕害怕害怕k是固定和0。在本文中，我们考虑了如何计算最大值的问题，使该族在0¿¿≪¿*时稳定。考虑到频域问题，可以构造一个频率函数，其最小值为¿*。在本文中，我们证明了计算¿*只需要考虑这个函数在有限个频率下的值。频率的数量是k的多项式，频率本身是根据给定的数据显式确定的。
{"title":"The Largest Stability Hypercube for Families of Polynomials with Linear Uncertainty","authors":"T. Djaferis","doi":"10.23919/ACC.1989.4790265","DOIUrl":"https://doi.org/10.23919/ACC.1989.4790265","url":null,"abstract":"Let ¿(s) = ¿<inf>0</inf>(s) = ¿<inf>0</inf>(s) + a<inf>1</inf> ¿<inf>1</inf>(s) + a<inf>2</inf>¿<inf>2</inf>(s) +...+ a<inf>k</inf>¿<inf>k</inf>(s) be a polynomial with coefficients that depend linearly on real parameters a<inf>i</inf>, 1 ¿ i ¿ k. Let ¿<inf>0</inf>(s) be stable of degree n and ¿<inf>i</inf>, 1 ¿ i ¿ k, of degree less than n. Assume that the a<inf>i</inf> are allowed to take values in the k dimensional hypercube ¿<inf>¿a</inf> = {(a<inf>1</inf>,...,a<inf>k</inf>)¿R<sup>k</sup>: a<sup>-</sup><inf>i</inf> ¿ a<inf>i</inf> ¿ ¿ a<sup>+</sup><inf>i</inf>}, where a<sup>-1</sup><inf>i</inf> ≪ 0, a<sup>+</sup><inf>i</inf> ≫ 0, 1 ¿ i ¿ k are fixed and ¿ ¿ 0. In this paper we consider the problem of how to compute the largest value ¿* such that the family is stable in ¿<inf>¿a</inf> for 0 ¿ ¿ ≪ ¿*. Considering the problem in the frequency domain, a function of frequency can be constructed whose infimum is ¿*. In this paper we show that to compute ¿* one need only consider the values of this function at a finite number of frequencies. The number of frequencies is polynomial in k, and the frequencies themselves are explicitly determined from the given data.","PeriodicalId":383719,"journal":{"name":"1989 American Control Conference","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1989-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129416155","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}
Pub Date : 1989-06-21DOI: 10.23919/ACC.1989.4790344
D. Cho, J. Hedrick
An alternative formulation of the sliding mode control method for dealing with the uncertainties in actuator or control dynamics is presented in this paper. The advantages of the formulation are in the reduced computational requirements and simplified procedures for meeting robustness and performance requirements. The method is then applied to control an automotive powertrain system, whose dynamics are highly nonlinear. In particular, coordinating engine and transmission control variables to perform clutch-to-clutch shifts is illustrated. The design objectives are to provide smooth transients for passenger comfort and to reduce clutch energy dissipation requirements for component longevity. The robustness and performance characteristics of the designed controller are demonstrated for a case that involves neglected actuator dynamics, whose bandwidth is very close to the frequency of the controlled system dynamics.
{"title":"Sliding Mode Control of Automotive Powertrains with Uncertain Actuator Models","authors":"D. Cho, J. Hedrick","doi":"10.23919/ACC.1989.4790344","DOIUrl":"https://doi.org/10.23919/ACC.1989.4790344","url":null,"abstract":"An alternative formulation of the sliding mode control method for dealing with the uncertainties in actuator or control dynamics is presented in this paper. The advantages of the formulation are in the reduced computational requirements and simplified procedures for meeting robustness and performance requirements. The method is then applied to control an automotive powertrain system, whose dynamics are highly nonlinear. In particular, coordinating engine and transmission control variables to perform clutch-to-clutch shifts is illustrated. The design objectives are to provide smooth transients for passenger comfort and to reduce clutch energy dissipation requirements for component longevity. The robustness and performance characteristics of the designed controller are demonstrated for a case that involves neglected actuator dynamics, whose bandwidth is very close to the frequency of the controlled system dynamics.","PeriodicalId":383719,"journal":{"name":"1989 American Control Conference","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1989-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129603499","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}
Pub Date : 1989-06-21DOI: 10.1109/ACC.1989.4173213
A. Georgiou, C. Floudas
The role of the structural properties of large scale systems for the synthesis of feasible control schemes is investigated in this paper. The feasibility of considering a state variable as an output (control objective) of a system is expressed via the concepts of multi-input connectability and structural functional controllability. It is shown, that these concepts can be formulated as mixed-integer linear programming (MILP) problems and efficient algorithms are presented for the determination of the above notions as well as for accessability and structural controllability. Two examples illustrate the concepts and the proposed approach.
{"title":"Optimization Models for Structural Analysis and Control Synthesis of Large Scale Systems","authors":"A. Georgiou, C. Floudas","doi":"10.1109/ACC.1989.4173213","DOIUrl":"https://doi.org/10.1109/ACC.1989.4173213","url":null,"abstract":"The role of the structural properties of large scale systems for the synthesis of feasible control schemes is investigated in this paper. The feasibility of considering a state variable as an output (control objective) of a system is expressed via the concepts of multi-input connectability and structural functional controllability. It is shown, that these concepts can be formulated as mixed-integer linear programming (MILP) problems and efficient algorithms are presented for the determination of the above notions as well as for accessability and structural controllability. Two examples illustrate the concepts and the proposed approach.","PeriodicalId":383719,"journal":{"name":"1989 American Control Conference","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1989-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129853416","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}
Pub Date : 1989-06-21DOI: 10.23919/ACC.1989.4790417
C. Kang, G. Leitmann, R. Horowitz
A robust deterministic control for a class of singularly perturbed uncertain systems, where uncertainties are characterized deterministically rather than stochastically, is developed based mainly on information available on an uncertain reduced-order system. The deterministic control scheme is applied to the motion control of a two degree of freedom, direct drive robotic SCARA manipulator. The manipulator has significant parasitic actuator and sensor dynamics. The parasitic dynamics are explicitly considered in the stability analysis of the deterministic controller using a singular perturbation model. Simulation studies are conducted to evaluate the effectiveness of the derived control scheme.
{"title":"Robust Deterministic Controller Design of a Two Degree of Freedom SCARA Manipulator","authors":"C. Kang, G. Leitmann, R. Horowitz","doi":"10.23919/ACC.1989.4790417","DOIUrl":"https://doi.org/10.23919/ACC.1989.4790417","url":null,"abstract":"A robust deterministic control for a class of singularly perturbed uncertain systems, where uncertainties are characterized deterministically rather than stochastically, is developed based mainly on information available on an uncertain reduced-order system. The deterministic control scheme is applied to the motion control of a two degree of freedom, direct drive robotic SCARA manipulator. The manipulator has significant parasitic actuator and sensor dynamics. The parasitic dynamics are explicitly considered in the stability analysis of the deterministic controller using a singular perturbation model. Simulation studies are conducted to evaluate the effectiveness of the derived control scheme.","PeriodicalId":383719,"journal":{"name":"1989 American Control Conference","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1989-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128454934","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}
Pub Date : 1989-06-21DOI: 10.23919/ACC.1989.4790331
K. Sobel, S. Banda, H. Yeh
A recent sufficient condition for the stability robustness of linear systems with time-varying norm bounded state space uncertainty is extended to include the structure of the uncertainty. Our new result requires that the nominal eigenvalues lie to the left of a vertical line in the complex plane which is determined by a norm involving the structure of the uncertainty and the nominal closed loop eigenvector matrix. Therefore, this robustness result is especially well suited to the design of control systems using eigenstructure assignment. When the uncertainty is time-invariant, our norm is also an upper bound on the incremental eigenvalue perturbations. We also consider the use of Perron weightings to reduce conservatism and the extension of the results to discrete time systems.
{"title":"Structured State Space Robustness with Connection to Eigenstructure Assignment","authors":"K. Sobel, S. Banda, H. Yeh","doi":"10.23919/ACC.1989.4790331","DOIUrl":"https://doi.org/10.23919/ACC.1989.4790331","url":null,"abstract":"A recent sufficient condition for the stability robustness of linear systems with time-varying norm bounded state space uncertainty is extended to include the structure of the uncertainty. Our new result requires that the nominal eigenvalues lie to the left of a vertical line in the complex plane which is determined by a norm involving the structure of the uncertainty and the nominal closed loop eigenvector matrix. Therefore, this robustness result is especially well suited to the design of control systems using eigenstructure assignment. When the uncertainty is time-invariant, our norm is also an upper bound on the incremental eigenvalue perturbations. We also consider the use of Perron weightings to reduce conservatism and the extension of the results to discrete time systems.","PeriodicalId":383719,"journal":{"name":"1989 American Control Conference","volume":"71 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1989-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128804439","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}
Pub Date : 1989-06-21DOI: 10.23919/ACC.1989.4790544
E. Y. Ibrahim, V. Lovass-Nagy, R. Mukundan, D. L. Powers, R. Schilling
Linear time-invariant time-delay control systems are approximated by time-invariant descriptor-variable systems. The approximating descriptor-variable systems do not contain any time-delay but they are controlled by a linear combination of the input vector and some of its derivatives. Necessary conditions are derived for existence of optimal controls; a "minimum energy" optimal control problem is investigated in some detail.
{"title":"On Application of Descriptor-Variable Theory to the Investigation of Optimal Control Problems of Linear Time-Delay Systems","authors":"E. Y. Ibrahim, V. Lovass-Nagy, R. Mukundan, D. L. Powers, R. Schilling","doi":"10.23919/ACC.1989.4790544","DOIUrl":"https://doi.org/10.23919/ACC.1989.4790544","url":null,"abstract":"Linear time-invariant time-delay control systems are approximated by time-invariant descriptor-variable systems. The approximating descriptor-variable systems do not contain any time-delay but they are controlled by a linear combination of the input vector and some of its derivatives. Necessary conditions are derived for existence of optimal controls; a \"minimum energy\" optimal control problem is investigated in some detail.","PeriodicalId":383719,"journal":{"name":"1989 American Control Conference","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1989-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128568670","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}
Pub Date : 1989-06-21DOI: 10.23919/ACC.1989.4790593
S. Foda, P. Agathoklis
The metal-rotting process is modelled as a delay differential system with noncommensurate delays. Stability conditions for delay differential systems have been recently developed using asymptotic stability tests and the Lyapunov approach. These results are applied to the stability analysis and stabilization of the metal rolling process. Conditions on the gains of finite dimensional controllers such as proportional plus derivative controllers are developed to ensure the stability of the controlled process against delay variations.
{"title":"Control of the Metal Rolling Process: A Multidimensional System Approach","authors":"S. Foda, P. Agathoklis","doi":"10.23919/ACC.1989.4790593","DOIUrl":"https://doi.org/10.23919/ACC.1989.4790593","url":null,"abstract":"The metal-rotting process is modelled as a delay differential system with noncommensurate delays. Stability conditions for delay differential systems have been recently developed using asymptotic stability tests and the Lyapunov approach. These results are applied to the stability analysis and stabilization of the metal rolling process. Conditions on the gains of finite dimensional controllers such as proportional plus derivative controllers are developed to ensure the stability of the controlled process against delay variations.","PeriodicalId":383719,"journal":{"name":"1989 American Control Conference","volume":"92 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1989-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128622154","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}
Pub Date : 1989-06-21DOI: 10.23919/ACC.1989.4790472
A. Nassirharand, A. Patwardhan
In this paper we present a new procedure for synthesis of dual-range linear controllers for use with nonlinear systems as well as linear systems with integrity. The procedure uses a factorization approach coupled with nonlinear optimization. The procedure is demonstrated by solving an example problem.
{"title":"Time-Domain Synthesis of Dual-Range Controller For Use With Nonlinear Systems","authors":"A. Nassirharand, A. Patwardhan","doi":"10.23919/ACC.1989.4790472","DOIUrl":"https://doi.org/10.23919/ACC.1989.4790472","url":null,"abstract":"In this paper we present a new procedure for synthesis of dual-range linear controllers for use with nonlinear systems as well as linear systems with integrity. The procedure uses a factorization approach coupled with nonlinear optimization. The procedure is demonstrated by solving an example problem.","PeriodicalId":383719,"journal":{"name":"1989 American Control Conference","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1989-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123978825","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}
Pub Date : 1989-06-21DOI: 10.23919/ACC.1989.4790536
Xunguo Lin, M. Tadé, R. B. Newell
Structural controllability is an important consideration in the synthesis of control systems. In this paper, the concept of output structural controllability is introduced and the condition for output structural controllability is proposed. Based on this condition, a new approach to the synthesis of control structures is described. The ease and flexibility of the output structural controllability condition in the synthesis of control systems for chemical plants is demonstrated.
{"title":"Synthesis of Control Systems : A New Approach to Output Structural Controllability","authors":"Xunguo Lin, M. Tadé, R. B. Newell","doi":"10.23919/ACC.1989.4790536","DOIUrl":"https://doi.org/10.23919/ACC.1989.4790536","url":null,"abstract":"Structural controllability is an important consideration in the synthesis of control systems. In this paper, the concept of output structural controllability is introduced and the condition for output structural controllability is proposed. Based on this condition, a new approach to the synthesis of control structures is described. The ease and flexibility of the output structural controllability condition in the synthesis of control systems for chemical plants is demonstrated.","PeriodicalId":383719,"journal":{"name":"1989 American Control Conference","volume":"18 9","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1989-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120862875","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}
Pub Date : 1989-06-21DOI: 10.23919/ACC.1989.4790614
M. Safonov, H. Flashner
Recent flexible space structure control design studies have identified several important and to some extent surprising features of this class of problem suggesting that much simpler models than those obtained by traditional modal truncation methods may suffice for even very high bandwidth control systems. Implications regarding how one should do modeling and model order reduction for control and regarding how one may want to improve control design methods will be discussed.
{"title":"Modeling and Robustness Issues in Control Design for Flexible Structures","authors":"M. Safonov, H. Flashner","doi":"10.23919/ACC.1989.4790614","DOIUrl":"https://doi.org/10.23919/ACC.1989.4790614","url":null,"abstract":"Recent flexible space structure control design studies have identified several important and to some extent surprising features of this class of problem suggesting that much simpler models than those obtained by traditional modal truncation methods may suffice for even very high bandwidth control systems. Implications regarding how one should do modeling and model order reduction for control and regarding how one may want to improve control design methods will be discussed.","PeriodicalId":383719,"journal":{"name":"1989 American Control Conference","volume":"67 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1989-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121156929","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}
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