Pub Date : 1989-06-21DOI: 10.1109/ACC.1989.4173445
Wei Li, L. Biegler
For linear processes, QDMC has proven to be an effective way of systematically handling both input and output process constraints. This note describes an analogous extension of QDMC for nonlinear, constrained Processes. Based on Newton-type methods implemented in a moving horizon framework, a multi-step algorithm is derived that solves a single quadratic program (QP) over each time horizon. Sufficient stability properties can be invoked through the concept of descent directions, and these conditions can also be checked on-line. Finally, the method is illustrated on a small reactor example with state and input time delays.
{"title":"A Multistep, Newton-Type Control Strategy for Constrained, Nonlinear Processes","authors":"Wei Li, L. Biegler","doi":"10.1109/ACC.1989.4173445","DOIUrl":"https://doi.org/10.1109/ACC.1989.4173445","url":null,"abstract":"For linear processes, QDMC has proven to be an effective way of systematically handling both input and output process constraints. This note describes an analogous extension of QDMC for nonlinear, constrained Processes. Based on Newton-type methods implemented in a moving horizon framework, a multi-step algorithm is derived that solves a single quadratic program (QP) over each time horizon. Sufficient stability properties can be invoked through the concept of descent directions, and these conditions can also be checked on-line. Finally, the method is illustrated on a small reactor example with state and input time delays.","PeriodicalId":383719,"journal":{"name":"1989 American Control Conference","volume":"273 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":"132797636","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.1989.4790262
S. Javid, R. Hammond, B. R. Ummel, J. Chow, M. .. Kale
This paper describes a lateral axis control problem for a transport aircraft. The application of a multivariable control design method to solve this problem is then presented. Simulation results show the performance of the control system.
{"title":"A Multivariable Control Design for the Lateral Axis Autopilot of a Transport Aircraft","authors":"S. Javid, R. Hammond, B. R. Ummel, J. Chow, M. .. Kale","doi":"10.23919/ACC.1989.4790262","DOIUrl":"https://doi.org/10.23919/ACC.1989.4790262","url":null,"abstract":"This paper describes a lateral axis control problem for a transport aircraft. The application of a multivariable control design method to solve this problem is then presented. Simulation results show the performance of the control system.","PeriodicalId":383719,"journal":{"name":"1989 American Control Conference","volume":"14 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":"132903157","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.1989.4790283
A. Saberi, P. Sannuti
In this paper we study global stabilization of a class of nonlinear uncertain systems while decoupling the output from external disturbances to any specified degree of accuracy. The nominal systems are assumed to be smooth, have a certain strong relative degree and are of minimum phase. Model uncertainties are dealt with either by restricting them to be structured or/and by treating a family of plants P. Both state and output feedback control laws are developed.
{"title":"Global Stabilization with Almost Disturbance Decoupling of a Class of Nonlinear Uncertain Systems using Output Feedback","authors":"A. Saberi, P. Sannuti","doi":"10.23919/ACC.1989.4790283","DOIUrl":"https://doi.org/10.23919/ACC.1989.4790283","url":null,"abstract":"In this paper we study global stabilization of a class of nonlinear uncertain systems while decoupling the output from external disturbances to any specified degree of accuracy. The nominal systems are assumed to be smooth, have a certain strong relative degree and are of minimum phase. Model uncertainties are dealt with either by restricting them to be structured or/and by treating a family of plants P. Both state and output feedback control laws are developed.","PeriodicalId":383719,"journal":{"name":"1989 American Control Conference","volume":"43 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":"133027003","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.1989.4790389
A. Yousuff, Ian Dias, B. Chang
This paper deals with the reduction of the order of controllers. The approach suggested herein is to introduce a static feed-through between the measurement residual and the control signals, in order to render any preselected eigenvalues of the given controller unobservable. and/or uncontrollable. The resulting reduced controllers preserve the stability of the closed loop system. Such order-reducing feed-through loops are parametrized.
{"title":"Controller Reduction by Direct Feed-Through","authors":"A. Yousuff, Ian Dias, B. Chang","doi":"10.23919/ACC.1989.4790389","DOIUrl":"https://doi.org/10.23919/ACC.1989.4790389","url":null,"abstract":"This paper deals with the reduction of the order of controllers. The approach suggested herein is to introduce a static feed-through between the measurement residual and the control signals, in order to render any preselected eigenvalues of the given controller unobservable. and/or uncontrollable. The resulting reduced controllers preserve the stability of the closed loop system. Such order-reducing feed-through loops are parametrized.","PeriodicalId":383719,"journal":{"name":"1989 American Control Conference","volume":"252 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":"133039778","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.1989.4790349
A. K. Adebekun, F. Schork
The paper focusses on reference model control of a continuous stirred tank reactor for solution polymerization of methylmethacrylate. The reactor is a nonsquare plant with more outputs than inputs. Two schemes are employed both of which under certain conditions, ensure global stabilization of the reactor.
{"title":"Nonlinear Control of a Solution Polymerization Reactor","authors":"A. K. Adebekun, F. Schork","doi":"10.23919/ACC.1989.4790349","DOIUrl":"https://doi.org/10.23919/ACC.1989.4790349","url":null,"abstract":"The paper focusses on reference model control of a continuous stirred tank reactor for solution polymerization of methylmethacrylate. The reactor is a nonsquare plant with more outputs than inputs. Two schemes are employed both of which under certain conditions, ensure global stabilization of the reactor.","PeriodicalId":383719,"journal":{"name":"1989 American Control Conference","volume":"82 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":"133067788","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.1989.4173222
H. Kazerooni, K. Narayanan
The work presented here is a simple feedback controller methodology that allows for exact tracking of the sinusoidal input signals and rejection of the sinusoidal disturbances in a closed loop control system. The control method is motivated by a mathematical inequality that expresses the tracking and disturbance rejection requirements for a closed loop system. The exact tracking of the input command at a particular frequency requires an infinite loop gain for the system at the frequency of the input command. A second order undamped transfer function is cascaded to teach input channel to increase the loop transfer function gain at the frequency of the input command. A feedback controller is then designed via the LQG/LTR method to stabilize the system while the loop gain remains large at the frequency of the input. The method is experimentally verified on a single axis servo system and extended to multivariable systems.
{"title":"Theory and Experiments on Tracking of the Repetitive Signals","authors":"H. Kazerooni, K. Narayanan","doi":"10.1109/ACC.1989.4173222","DOIUrl":"https://doi.org/10.1109/ACC.1989.4173222","url":null,"abstract":"The work presented here is a simple feedback controller methodology that allows for exact tracking of the sinusoidal input signals and rejection of the sinusoidal disturbances in a closed loop control system. The control method is motivated by a mathematical inequality that expresses the tracking and disturbance rejection requirements for a closed loop system. The exact tracking of the input command at a particular frequency requires an infinite loop gain for the system at the frequency of the input command. A second order undamped transfer function is cascaded to teach input channel to increase the loop transfer function gain at the frequency of the input command. A feedback controller is then designed via the LQG/LTR method to stabilize the system while the loop gain remains large at the frequency of the input. The method is experimentally verified on a single axis servo system and extended to multivariable systems.","PeriodicalId":383719,"journal":{"name":"1989 American Control Conference","volume":"60 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":"133545757","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.1989.4790286
D. Garg, Z. G. Shanidze, Ewald G. Rondeli
This paper deals with the stability of solutions of nonlinear control systems in the entire phase space. It is shown that for determining the global stability of motion, it is necessary to first obtain a single scalar equation from the specified system, and only then apply the Hurwitz conditions. In the derived scalar equations corresponding to the initial system, both nonlinear functions and their derivatives appear. Therefore, not only do the nonlinear functions, but also their derivatives enter in the conditions for ensuring stability of the solutions in the entire phase space. Examples are given to illustrate the procedure.
{"title":"Global Stability of the Solutions of Nonlinear Control Systems","authors":"D. Garg, Z. G. Shanidze, Ewald G. Rondeli","doi":"10.23919/ACC.1989.4790286","DOIUrl":"https://doi.org/10.23919/ACC.1989.4790286","url":null,"abstract":"This paper deals with the stability of solutions of nonlinear control systems in the entire phase space. It is shown that for determining the global stability of motion, it is necessary to first obtain a single scalar equation from the specified system, and only then apply the Hurwitz conditions. In the derived scalar equations corresponding to the initial system, both nonlinear functions and their derivatives appear. Therefore, not only do the nonlinear functions, but also their derivatives enter in the conditions for ensuring stability of the solutions in the entire phase space. Examples are given to illustrate the procedure.","PeriodicalId":383719,"journal":{"name":"1989 American Control Conference","volume":"13 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":"132566255","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.1989.4173500
Jianxin Tang, P. Luh, T. Chang
In this paper, we present a new approach for solving long horizon, discrete-time optimal control problems by using the mixed coordination method. The idea is to decompose a long horizon problem into subproblems along the time axis. The requirement that the initial state of a subproblem equals the terminal state of the preceding subproblem is relaxed by using Lagrange multipliers. The Lagrange multipliers and the initial state of each subproblem are then selected as high level variables. The equivalence of the two-level formulation and the original problem is proved for both the convex and nonconvex cases. Under the two-level formulation, the low level subproblems are optimal control problems with a shorter time horizon, and are solved in parallel by using the extended Differential Dynamic Programming (DDP). An efficient way for finding the gradient and Hessian of a low level objective function with respect to high level variables is developed. The high level problem, on the other hand, is solved by using the Modified Newton's Method. An effective procedure is developed to select initial values of multipliers based on the given initial trajectory. Since both the DDP and the Modified Newton's Method have fast convergence rate and are compatible with each other, the method is very efficient. Furthermore, because of the specific way in selecting high level variables, the method can convexify the high level problem while maintain the separability of an originally nonconvex problem.
{"title":"A Parallel Algorithm for Long Horizon Optimal Control Problems Using the Mixed Coordination Method","authors":"Jianxin Tang, P. Luh, T. Chang","doi":"10.1109/ACC.1989.4173500","DOIUrl":"https://doi.org/10.1109/ACC.1989.4173500","url":null,"abstract":"In this paper, we present a new approach for solving long horizon, discrete-time optimal control problems by using the mixed coordination method. The idea is to decompose a long horizon problem into subproblems along the time axis. The requirement that the initial state of a subproblem equals the terminal state of the preceding subproblem is relaxed by using Lagrange multipliers. The Lagrange multipliers and the initial state of each subproblem are then selected as high level variables. The equivalence of the two-level formulation and the original problem is proved for both the convex and nonconvex cases. Under the two-level formulation, the low level subproblems are optimal control problems with a shorter time horizon, and are solved in parallel by using the extended Differential Dynamic Programming (DDP). An efficient way for finding the gradient and Hessian of a low level objective function with respect to high level variables is developed. The high level problem, on the other hand, is solved by using the Modified Newton's Method. An effective procedure is developed to select initial values of multipliers based on the given initial trajectory. Since both the DDP and the Modified Newton's Method have fast convergence rate and are compatible with each other, the method is very efficient. Furthermore, because of the specific way in selecting high level variables, the method can convexify the high level problem while maintain the separability of an originally nonconvex problem.","PeriodicalId":383719,"journal":{"name":"1989 American Control Conference","volume":"12 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":"133853839","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.1989.4790527
A. Madiwale
The objective of this paper is to present a synthesis method for dynamic compensators for multivariable time varying non-linear feedback systems. The design equations are developed for LQG and/or H∞ dynamic compensators. The same method can be used for linear time invariant systems to design dynamic compensators with guaranteed gain and phase margins. The conservativeness of the design is reduced by computing an optimal diagonal scaling matrix and represents a new time domain solution to a sub-problem in mu-synthesis.
{"title":"Design of LQG/H∞ dynamic compensators for time varying non-linear feedback systems: circle criterion and guaranteed gain and phase margins","authors":"A. Madiwale","doi":"10.23919/ACC.1989.4790527","DOIUrl":"https://doi.org/10.23919/ACC.1989.4790527","url":null,"abstract":"The objective of this paper is to present a synthesis method for dynamic compensators for multivariable time varying non-linear feedback systems. The design equations are developed for LQG and/or H∞ dynamic compensators. The same method can be used for linear time invariant systems to design dynamic compensators with guaranteed gain and phase margins. The conservativeness of the design is reduced by computing an optimal diagonal scaling matrix and represents a new time domain solution to a sub-problem in mu-synthesis.","PeriodicalId":383719,"journal":{"name":"1989 American Control Conference","volume":"3 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":"115205453","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.1989.4173454
S. Katzir, E. Cliff, F. Lutze
Midcourse guidance is examined for an air-to-air missile featuring boost-coast-sustain propulsion. A vertical-plane, point-mass model is studied with load factor as a control variable and coasting time as a parameter. Time-range-energy optimal trajectories are computed, open-loop, via the usual necessary conditions and a multiple-shooting algorithm. A requirement on terminal velocity magnitude is examined for its effect on firing range. One of the major results for the missile studied is that, it is not optimal to add a coasting phase between the boost and the sustain phases.
{"title":"Best-Range Study for a Boost-Coast-Sustain Missile","authors":"S. Katzir, E. Cliff, F. Lutze","doi":"10.1109/ACC.1989.4173454","DOIUrl":"https://doi.org/10.1109/ACC.1989.4173454","url":null,"abstract":"Midcourse guidance is examined for an air-to-air missile featuring boost-coast-sustain propulsion. A vertical-plane, point-mass model is studied with load factor as a control variable and coasting time as a parameter. Time-range-energy optimal trajectories are computed, open-loop, via the usual necessary conditions and a multiple-shooting algorithm. A requirement on terminal velocity magnitude is examined for its effect on firing range. One of the major results for the missile studied is that, it is not optimal to add a coasting phase between the boost and the sustain phases.","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":"124334331","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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