Pub Date : 1988-06-15DOI: 10.23919/ACC.1988.4790096
A. Iyer, Sahjendra N. Singh
This paper considers control of a class of uncertain nonlinear systems which can be decoupled by state variable feedback. A variable structure control (VSC) law is derived such that in the closed-loop system the output variable asymptotically tracks a given output trajectory in spite of the uncertainty in the system. Based on this result, a control law is derived for the attitude control of an orbiting spacecraft in the presence of uncertainty using reaction jets. The controlled outputs are the three Euler angles which describe the orientation of the spacecraft relative to an orbital frame. Simulation results are presented to show that in the closed-loop system precise attitude control is accomplished in spite of the uncertainty in the system.
{"title":"Variable Structure Control of Decoupleable Systems and Attitude Control of Spacecraft in Prescence of Uncertainty","authors":"A. Iyer, Sahjendra N. Singh","doi":"10.23919/ACC.1988.4790096","DOIUrl":"https://doi.org/10.23919/ACC.1988.4790096","url":null,"abstract":"This paper considers control of a class of uncertain nonlinear systems which can be decoupled by state variable feedback. A variable structure control (VSC) law is derived such that in the closed-loop system the output variable asymptotically tracks a given output trajectory in spite of the uncertainty in the system. Based on this result, a control law is derived for the attitude control of an orbiting spacecraft in the presence of uncertainty using reaction jets. The controlled outputs are the three Euler angles which describe the orientation of the spacecraft relative to an orbital frame. Simulation results are presented to show that in the closed-loop system precise attitude control is accomplished in spite of the uncertainty in the system.","PeriodicalId":6395,"journal":{"name":"1988 American Control Conference","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1988-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85112117","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 : 1988-06-15DOI: 10.23919/ACC.1988.4789954
J. Zhu, C. Johnson
Let A(t) be a real-valued matrix function on [0, + ¿]. A (time-varying) Linear Dynamical Systems (LDS) of the form x=A(t)x is said to be well-defined if A(t) is Lebesgue integrable on every finite subinterval of [0, + ¿], and is called proper if A(t)=f(t,G) for some constant generating matrix G and scalar primitive function f(t, ¿) (see [13], [15]). According to a recent result obtained in [17], every well-defined LDS is reducible to a proper one by a D-similarity transformation. Therefore, it is interesting to study the stability of the reduced (proper) LDS as a means for uncovering new stability information for well-defined LDS. In this paper we use some recent results on proper LDS (see [13], [14], [15], [16]), to derive new necessary and sufficient stability criteria for proper time-varying LDS in terms of the conventional (time-varying) eigenvalues of A(t) and a new entity we have named co-eigenvalues of A(t). The notion of stability index for proper A(t) with Laplace transformable elements is also introduced and serves to unify the well-known stability criteria for time-invariant LDS and periodic proper LDS which are based on the eigenvalues of A and the Floquet characteristic exponents of A(t), respectively.
{"title":"New Results for the Stability Analysis of Time-Varying Linear Systems Part I: The Case of Reduced Systems","authors":"J. Zhu, C. Johnson","doi":"10.23919/ACC.1988.4789954","DOIUrl":"https://doi.org/10.23919/ACC.1988.4789954","url":null,"abstract":"Let A(t) be a real-valued matrix function on [0, + ¿]. A (time-varying) Linear Dynamical Systems (LDS) of the form x=A(t)x is said to be well-defined if A(t) is Lebesgue integrable on every finite subinterval of [0, + ¿], and is called proper if A(t)=f(t,G) for some constant generating matrix G and scalar primitive function f(t, ¿) (see [13], [15]). According to a recent result obtained in [17], every well-defined LDS is reducible to a proper one by a D-similarity transformation. Therefore, it is interesting to study the stability of the reduced (proper) LDS as a means for uncovering new stability information for well-defined LDS. In this paper we use some recent results on proper LDS (see [13], [14], [15], [16]), to derive new necessary and sufficient stability criteria for proper time-varying LDS in terms of the conventional (time-varying) eigenvalues of A(t) and a new entity we have named co-eigenvalues of A(t). The notion of stability index for proper A(t) with Laplace transformable elements is also introduced and serves to unify the well-known stability criteria for time-invariant LDS and periodic proper LDS which are based on the eigenvalues of A and the Floquet characteristic exponents of A(t), respectively.","PeriodicalId":6395,"journal":{"name":"1988 American Control Conference","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1988-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85291590","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 : 1988-06-15DOI: 10.23919/ACC.1988.4789877
Paul H. Gusciora, A. Foss
Taylor dispersion in a fixed bed reactor results from heat exchange between the flowing reactant stream and the fixed thermal capacitances of the catalyst particles and reactor wall. The Taylor approximation transforms the hyperbolic partial differential equations representing deviations of the energy balance from steady-state into a single parabolic partial differential equation encompassing convection and diffusion. The hybrid Taylor diffusion model developed here incorporates spatially varying heat generation by reaction into the parabolic partial differential equation and couples it to a material balance on the fluid. A third or fourth order spatial discretization of this model provides a good approximation of the frequency response, and was used for online control and optimization.
{"title":"A Reduced-Order Model of a Fixed-Bed Reactor based on Novel Application of the Taylor-Dispersion Approximation","authors":"Paul H. Gusciora, A. Foss","doi":"10.23919/ACC.1988.4789877","DOIUrl":"https://doi.org/10.23919/ACC.1988.4789877","url":null,"abstract":"Taylor dispersion in a fixed bed reactor results from heat exchange between the flowing reactant stream and the fixed thermal capacitances of the catalyst particles and reactor wall. The Taylor approximation transforms the hyperbolic partial differential equations representing deviations of the energy balance from steady-state into a single parabolic partial differential equation encompassing convection and diffusion. The hybrid Taylor diffusion model developed here incorporates spatially varying heat generation by reaction into the parabolic partial differential equation and couples it to a material balance on the fluid. A third or fourth order spatial discretization of this model provides a good approximation of the frequency response, and was used for online control and optimization.","PeriodicalId":6395,"journal":{"name":"1988 American Control Conference","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1988-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81848556","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}
This paper considers the optimal control of structural systems with quadratic performance indices. The proposed approach approximates each configuration variable of a structural model by the sum of a fifth order polynomial and a finite term Fourier-type series. In contrast to standard linear optimal control approaches which typically require the solution of Riccati equations, the method adopted here is a near optimal approach in which the necessary and sufficient condition of optimality is derived as a system of linear algebraic equations. These equations can be solved directly by a method such as Gaussian elimination. The proposed approach is computationally efficient and can be applied to structural systems of high dimension and/or to structural systems with fixed (or highly penalized) terminal states without numerical difficulties.
{"title":"A Fourier-Based Optimal Control Approach for Structural Systems","authors":"V. Yen, M. Nagurka","doi":"10.2514/3.20546","DOIUrl":"https://doi.org/10.2514/3.20546","url":null,"abstract":"This paper considers the optimal control of structural systems with quadratic performance indices. The proposed approach approximates each configuration variable of a structural model by the sum of a fifth order polynomial and a finite term Fourier-type series. In contrast to standard linear optimal control approaches which typically require the solution of Riccati equations, the method adopted here is a near optimal approach in which the necessary and sufficient condition of optimality is derived as a system of linear algebraic equations. These equations can be solved directly by a method such as Gaussian elimination. The proposed approach is computationally efficient and can be applied to structural systems of high dimension and/or to structural systems with fixed (or highly penalized) terminal states without numerical difficulties.","PeriodicalId":6395,"journal":{"name":"1988 American Control Conference","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1988-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83863632","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 : 1988-06-15DOI: 10.23919/ACC.1988.4790020
Cheng Chen, R. Walker, Chin-Hu Feng
Multiple-target tracking is used to identify the traveling paths of multiple point targets from a set of detected measurements. Since all the detected measurements often have a uniform look, it becomes difficult to distinguish one target from another, and targets from false alarms. Based on the statistical information about channel noise, target initiation rate, false alarm rate and probability of detection, a multiple-hypothesis testing can be formulated to associate each measurement with a specific source. However, this association process is a computationally explosive problem. By converting the association problem to an equivalent assignment problem, a branch-and-bound algorithm can be applied to provide an efficient method for generating hypotheses, evaluating their likelihood, and identifying the leading N most likely hypotheses. The modularity of the branch-and-bound algorithm leads naturally to a parallel computer implementation using the best-first search strategy.
{"title":"A Branch-and-Bound Algorithm for Multiple-Target Tracking and its Parallel Implementation","authors":"Cheng Chen, R. Walker, Chin-Hu Feng","doi":"10.23919/ACC.1988.4790020","DOIUrl":"https://doi.org/10.23919/ACC.1988.4790020","url":null,"abstract":"Multiple-target tracking is used to identify the traveling paths of multiple point targets from a set of detected measurements. Since all the detected measurements often have a uniform look, it becomes difficult to distinguish one target from another, and targets from false alarms. Based on the statistical information about channel noise, target initiation rate, false alarm rate and probability of detection, a multiple-hypothesis testing can be formulated to associate each measurement with a specific source. However, this association process is a computationally explosive problem. By converting the association problem to an equivalent assignment problem, a branch-and-bound algorithm can be applied to provide an efficient method for generating hypotheses, evaluating their likelihood, and identifying the leading N most likely hypotheses. The modularity of the branch-and-bound algorithm leads naturally to a parallel computer implementation using the best-first search strategy.","PeriodicalId":6395,"journal":{"name":"1988 American Control Conference","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1988-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82256052","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 : 1988-06-15DOI: 10.1109/ACC.1988.4173060
J. Connally, J. Hubbard
This paper presents the theoretical and experimental results of active vibration control of a cantilevered S-Glass composite beam using PVF2 film as a low authority distributed control actuator. The beam is approrximately ¿ in. × ¿ in. × 12 in. with a small mass mounted at the free end. The Lyapunov stability criteria is used to derive a control algorithm for the active damper based on angular rate feedback of the free end of the beam. The algorithm is stable for all vibrational modes of the beam. Experimental results are presented which show the increase in damping produced by the PVF2 actuators for the first two modes of vibration of the beam. The damping ratio for the first mode was increased from .2061 to .6588, and the increase for the second mode was from .1402 to .5482 (these results are with the electromagnetic excitation source oriented in the +y direction).
{"title":"Low Authority Control of a Composite Cantilever Beam in Two Dimensions","authors":"J. Connally, J. Hubbard","doi":"10.1109/ACC.1988.4173060","DOIUrl":"https://doi.org/10.1109/ACC.1988.4173060","url":null,"abstract":"This paper presents the theoretical and experimental results of active vibration control of a cantilevered S-Glass composite beam using PVF2 film as a low authority distributed control actuator. The beam is approrximately ¿ in. × ¿ in. × 12 in. with a small mass mounted at the free end. The Lyapunov stability criteria is used to derive a control algorithm for the active damper based on angular rate feedback of the free end of the beam. The algorithm is stable for all vibrational modes of the beam. Experimental results are presented which show the increase in damping produced by the PVF2 actuators for the first two modes of vibration of the beam. The damping ratio for the first mode was increased from .2061 to .6588, and the increase for the second mode was from .1402 to .5482 (these results are with the electromagnetic excitation source oriented in the +y direction).","PeriodicalId":6395,"journal":{"name":"1988 American Control Conference","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1988-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80223000","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 : 1988-06-15DOI: 10.1109/ACC.1988.4172889
A. Calise, G. Bae
A three-state model is presented for analyzing the problem of optimal changes in heading with minimum energy loss for a hypersonic gliding vehicle. A further model order reduction to a single state model is examined using singular perturbation theory. the optimal solution for the reduced problem defines an optimal altitude profile dependent on the current energy of the vehicle. A separate boundary layer analysis is used to account for altitude and flight path angle dynamics, and to obtain lift and bank angle control solutions. By considering alternative approximations to solve the boundary layer problem, three guidance laws are obtained, each having a feedback form. The guidance laws are evaluated for a hypothetical vehicle, and compared to an optimal solution obtained using a multiple shooting algorithm.
{"title":"Optimal Reentry Guidance for Aeroassisted Orbit Transfer Vehicles","authors":"A. Calise, G. Bae","doi":"10.1109/ACC.1988.4172889","DOIUrl":"https://doi.org/10.1109/ACC.1988.4172889","url":null,"abstract":"A three-state model is presented for analyzing the problem of optimal changes in heading with minimum energy loss for a hypersonic gliding vehicle. A further model order reduction to a single state model is examined using singular perturbation theory. the optimal solution for the reduced problem defines an optimal altitude profile dependent on the current energy of the vehicle. A separate boundary layer analysis is used to account for altitude and flight path angle dynamics, and to obtain lift and bank angle control solutions. By considering alternative approximations to solve the boundary layer problem, three guidance laws are obtained, each having a feedback form. The guidance laws are evaluated for a hypothetical vehicle, and compared to an optimal solution obtained using a multiple shooting algorithm.","PeriodicalId":6395,"journal":{"name":"1988 American Control Conference","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1988-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83096371","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 : 1988-06-15DOI: 10.23919/ACC.1988.4789865
C. Chuang, Q. Wang, J. Speyer
For a reasonable model of a hypersonic scramjet cruiser, the optimum fuel cruise trajectories are determined. Two local minimums are obtained which give nearly the same fuel consumption. One local minimum is periodic which has amplitude variations of about 25,000 feet and a mean of about 100,000 feet. The other local minimum is a static path where the maximum thrust is just equal to the aerodynamic drag. This static path seems to be unobtainable except possibly asymptotically. However, for the periodic path which is realizable, a periodic neighboring optimum regulator is derived. This regulator includes variations in the control variables of lift coefficient and thrust switch times. Furthermore, the mass change of the vehicle which is tacitly assumed negligible in producing the nominal path is included explicitly in this regulator. The performance of this regualtor due to variations both in initial conditions and mass of the vehicle is very impressive.
{"title":"Periodic Neighboring Optimum Regulator Applied to a Hypersonic Scramjet Cruiser","authors":"C. Chuang, Q. Wang, J. Speyer","doi":"10.23919/ACC.1988.4789865","DOIUrl":"https://doi.org/10.23919/ACC.1988.4789865","url":null,"abstract":"For a reasonable model of a hypersonic scramjet cruiser, the optimum fuel cruise trajectories are determined. Two local minimums are obtained which give nearly the same fuel consumption. One local minimum is periodic which has amplitude variations of about 25,000 feet and a mean of about 100,000 feet. The other local minimum is a static path where the maximum thrust is just equal to the aerodynamic drag. This static path seems to be unobtainable except possibly asymptotically. However, for the periodic path which is realizable, a periodic neighboring optimum regulator is derived. This regulator includes variations in the control variables of lift coefficient and thrust switch times. Furthermore, the mass change of the vehicle which is tacitly assumed negligible in producing the nominal path is included explicitly in this regulator. The performance of this regualtor due to variations both in initial conditions and mass of the vehicle is very impressive.","PeriodicalId":6395,"journal":{"name":"1988 American Control Conference","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1988-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81417969","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 : 1988-06-15DOI: 10.1109/ACC.1988.4172826
M. Nikolaou, V. Manousiouthakis
The computation of the optimal operating profile for batch processes through the maximum principle depends on the model involved. The real process, however may deviate from the assumed model due to external disturbances or parameter variations. In this paper we examine the effect of the above on the value of the objective function, when the nominal optimal policy is applied, as well as the effect on the optimum of the objective function. We present relations between quantities of the perturbed and the nominal problems and demonstrate their use through a number of examples.
{"title":"Robust Control of Batch Processes","authors":"M. Nikolaou, V. Manousiouthakis","doi":"10.1109/ACC.1988.4172826","DOIUrl":"https://doi.org/10.1109/ACC.1988.4172826","url":null,"abstract":"The computation of the optimal operating profile for batch processes through the maximum principle depends on the model involved. The real process, however may deviate from the assumed model due to external disturbances or parameter variations. In this paper we examine the effect of the above on the value of the objective function, when the nominal optimal policy is applied, as well as the effect on the optimum of the objective function. We present relations between quantities of the perturbed and the nominal problems and demonstrate their use through a number of examples.","PeriodicalId":6395,"journal":{"name":"1988 American Control Conference","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1988-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82525435","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 : 1988-06-15DOI: 10.1109/ACC.1988.4172863
P. Khargonekar, M. Rotea
New results on coprime factorizations for continuous-time linear time-varying systems are presented. It is shown that a linear time-varying system admits a coprime factorization if and only if it is stabilizable and detectable, or if and only if it is internally stabilizable via dynamic output feedback. State-space formulae for coprime factorizations are given.
{"title":"Coprime Factorization for Linear Time-Varying Systems","authors":"P. Khargonekar, M. Rotea","doi":"10.1109/ACC.1988.4172863","DOIUrl":"https://doi.org/10.1109/ACC.1988.4172863","url":null,"abstract":"New results on coprime factorizations for continuous-time linear time-varying systems are presented. It is shown that a linear time-varying system admits a coprime factorization if and only if it is stabilizable and detectable, or if and only if it is internally stabilizable via dynamic output feedback. State-space formulae for coprime factorizations are given.","PeriodicalId":6395,"journal":{"name":"1988 American Control Conference","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1988-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83262657","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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