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Control System Toolbox™ Reference R2017a How to Contact MathWorks Latest news: www.mathworks.com Sales and services: www.mathworks.com/sales_and_services User community: www.mathworks.com/matlabcentral Technical support: www.mathworks.com/support/contact_us Phone: 508-647-7000 The MathWorks, Inc. 3 Apple Hill Drive Natick, MA 01760-2098 Control System Toolbox™ Reference © COPYRIGHT 2001–2017 by The MathWorks, Inc. The software described in this document is furnished under a license agreement. The software may be used or copied only under the terms of the license agreement. No part of this manual may be photocopied or reproduced in any form without prior written consent from The MathWorks, Inc. FEDERAL ACQUISITION: This provision applies to all acquisitions of the Program and Documentation by, for, or through the federal government of the United States. 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Revision History June 2001 Online only New for Version 5.1 (Release 12.1) July 2002 Online only Revised for Version 5.2 (Release 13) June 2004 Online only Revised for Version 6.0 (Release 14) March 2005 Online only Revised for Version 6.2 (Release 14SP2) September 2005 Online only Revised for Version 6.2.1 (Release 14SP3) March 2006 Online only Revised for Version 7.0 (Release 2006a) September 2006 Online only Revised for Version 7.1 (Release 2006b) March 2007 Online only Revised for Version 8.0 (Release 2007a) September 2007 Online only Revised for Version 8.0.1 (Release 2007b) March 2008 Online only Revised for Version 8.1 (Release 2008a) October 2008 Online only Revised for Version 8.2 (Release 2008b) March 2009 Online only Revised for Version 8.3 (Release 2009a) September 2009 Online only Revised for Version 8.4 (Release 2009b) March 2010 Online only Revised for Version 8.5 (Release 2010a) September 2010 Online only Revised for Version 9.0 (Release 2010b) April 2011 Online only Revised for Version 9.1 (Release 2011a) September 2011 Online only Revised for Version 9.2 (Release 2011b) March 2012 Online only Revised for Version 9.3 (Release 2012a) September 2012 Online only Revised for Version 9.4 (Release 2012b) March 2013 Online only Revised for Version 9.5 (Release 2013a) September 2013 Online only Revised for Version 9.6 (Release 2013b) March 2014 Online only Revised for Version 9.7 (Release 2014a) October 2014 Online only Revised for Version 9.8 (Release 2014b) March 2015 Online only Revised for Version 9.9 (Release 2015a) September 2015 Online only Revised for Version 9.10 (Release 2015b) March 2016 Online only Revised for Version 10.0 (Release 2016a) September 2016 Online only Revised for Version 10.1 (Release 2016b) March 2017 Online only Revised for Version 10.2 (Release 2017a) Contents Class Reference 1 Functions — Alphabetical List 2 Block Reference 3 v 1 Class Reference TuningGoal.ConicSector TuningGoal.ControllerPoles TuningGoal.Gain TuningGoal.LoopShape TuningGoal.LQG TuningGoal.Margins TuningGoal.MinLoopGain TuningGoal.MaxLoopGain TuningGoal.Overshoot TuningGoal.Passivity TuningGoal.Poles TuningGoal.Rejection TuningGoal.Sensitivity TuningGoal.StepRejection TuningGoal.StepTracking TuningGoal.Tracking TuningGoal.Transient TuningGoal.Variance TuningGoal.WeightedPassivity TuningGoal.WeightedGain TuningGoal.WeightedVariance 1 Class Reference TuningGoal.ConicSector class Package: TuningGoal Sector bound for control system tuning Description A conic sector bound is a restriction on the output trajectories of a system. If for all nonzero input trajectories u(t), the output trajectory z(t) = (Hu)(t) of a linear system H satisfies: for all T ≥ 0, then the output trajectories of H lie in the conic sector described by the symmetric indefinite matrix Q. Selecting different Q matrices imposes different conditions on the system response. When tuning a control system with systune, use TuningGoal.ConicSector to restrict the output trajectories of the response between specified inputs and outputs to a specified sector. For more information about sector bounds, see “About Sector Bounds and Sector Indices”. Construction Req = TuningGoal.ConicSector(inputname,outputname,Q) creates a tuning goal for restricting the response H(s) from inputs inputname to outputs outputname to the conic sector specified by the symmetric matrix Q. The tuning goal constrains H such that its trajectories z(t) = (Hu)(t) satisfy: for all T ≥ 0. (See “About Sector Bounds and Sector Indices”.) The matrix Q must have as many negative eigenvalues as there are inputs in H. T To specify frequency-dependent sector bounds, set Q to an LTI model that satisfies Q(s) = Q(–s). 1-2 T T Ú0 z(t) Q z(t)dt < 0, TuningGoal.ConicSector class Input Arguments inputname Input signals for the tuning goal, specified as a character vector or, for multiple-input tuning goals, a cell array of character vectors. • If you are using the tuning goal to tune a Simulink® model of a control system, then inputname can include: • Any model input. • Any linear analysis point marked in the model. • Any linear analysis point in an slTuner interface associated with the Simulink model. Use addPoint to add analysis points to the slTuner interface. Use getPoints to get the list of analysis points available in an slTuner interface to your model. For example, suppose that the slTuner interface contains analysis points u1 and u2. Use 'u1' to designate that point as an input signal when creating tuning goals. Use {'u1','u2'} to designate a two-channel input. • If you are using the tuning goal to tune a generalized state-space (genss) model of a control system, then inputname can include: • Any input of the genss model • Any AnalysisPoint location in the control system model For example, if you are tuning a control system model, T, then inputname can be any input name in T.InputName. Also, if T contains an AnalysisPoint block with a location named AP_u, then inputname can include 'AP_u'. Use getPoints to get a list of analysis points available in a genss model. If inputname is an AnalysisPoint location of a generalized model, the input signal for the tuning goal is the implied input associated with the AnalysisPoint block: 1-3 1 Class Reference For more information about analysis points in control system models, see “Mark Signals of Interest for Control System Analysis and Design”. outputname Output signals for the tuning goal, specified as a character vector or, for multiple-output tuning goals, a cell array of character vectors. • If you are using the tuning goal to tune a Simulink model of a control system, then outputname can include: • Any model output. • Any linear analysis point marked in the model. • Any linear analysis point in an slTuner interface associated with the Simulink model. Use addPoint to add analysis points to the slTuner interface. Use getPoints to get the list of analysis points available in an slTuner interface to your model. For example, suppose that the slTuner interface contains analysis points y1 and y2. Use 'y1' to designate that point as an output signal when creating tuning goals. Use {'y1','y2'} to designate a two-channel output. • If you are using the tuning goal to tune a generalized state-space (genss) model of a control system, then outputname can include: • Any output of the genss model • Any AnalysisPoint location in the control system model For example, if you are tuning a control system model, T, then outputname can be any output name in T.OutputName. Also, if T contains an AnalysisPoint block with a location named AP_u, then outputname can include 'AP_u'. Use getPoints to get a list of analysis points available in a genss model. If outputname is an AnalysisPoint location of a generalized model, the output signal for the tuning goal is the implied output associated with the AnalysisPoint block: 1-4