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FOTF Toolbox/Contents.m
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FOTF Toolbox/Contents.m
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%FOTF Toolbox - A MATLAB Toolbox for the modeling, analysis and design of fractional-order systems
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%
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% (c) Professor Dingy\"u Xue, Northeastern University, Shenyang, China
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% Email: xuedingyu@mail.neu.edu.cn
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% Date of last modification, 23 December, 2016
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%
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% This newly modified toolbox is written for the monograph,
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%
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% @BOOK{bkXueDFOCS,
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% Author = {Xue Dingy\"u},
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% Address = {Berlin},
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% Publisher = {de Gruyter Press},
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% Title = {Fractional-order Control Systems - Fundamentals and Numerical Implementations},
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% Year = {2017}
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% }
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%
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% Multivariable fractional-order systems are fully supported in the classes FOTF and FOSS
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% and low-level numerical algorithms are replaced by $O(h^p)$ precision ones.
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% For details in theory and programming, please refer to the monograph.
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% (I) Special functions and fundamentals in numerical computation
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% beta_c - beta function evaluation for complex arguments
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% common_order - compute the common order
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% fence_shadow - draw the shawdows on the walls
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% fmincon_global - a global constrained optimisation problem solver
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% funmsym - evaluate symbolic matrix functions
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% gamma_c - Gamma function evaluation for complex arguments
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% kronsum - compute Kronecker sum
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% mittag_leffler - symbolic evaluation of Mittag-Leffler functions
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% ml_func - numerical evaluation of Mittag-Leffler functions and derivatives
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% more_sols - find possible all solutions of nonlinear matrix equations
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% more_vpasols - symbolic version of more_sols, high precision solutions
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% new_inv - simple matrix inverse function, not recommended in applications
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%
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%(II) Numerical evaluations of fractional-order derivatives and integrals
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% caputo - computation of Caputo derivatives with interpolation, not recommended
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% caputo9 - evaluation of Caputo derivatives with $O(h^p)$, recommended
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% genfunc - computation of generating function coefficients symbolically
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% get_vecw - computation of $O(h^p)$ weighting coefficients
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% glfdiff0 - evaluation of GL derivatives, not recommended
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% glfdiff - standard evaluation of GL derivatives, with $O(h)$
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% glfdiff2 - evaluation of $O(h^p)$ GL derivatives, not recommended
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% glfdiff9 - evaluation of $O(h^p)$ GL derivatives, recommended
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% glfdiff_fft - evaluation of $O(h^p)$ GL derivatives with FFT, not recommended
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% glfdiff_mat - matrix version of glfdiff, not recommended for large samples
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% glfdiff_mem - GL derivative evaluation with short-memory effect
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% rlfdiff evaluation of RL derivatives, not recommended, use glfdiff9 instead
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%
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%(III) Numerical evaluations of linear fractional-order differential equations
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% caputo_ics - equivalent initial condition reconstruction, called by fode_caputo9
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% fode_caputo0 - simple Caputo FODE solver with nonzero initial conditions
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% fode_caputo9 - $O(h^p)$ solution of Caputo equations with nonzero ICs
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% fode_sol - closed-form solution of FODE with zero initial conditions
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% fode_solm - matrix version of fode_sol, not recommended for large samples
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% fode_sol9 - $O(h^p)$ version of fode_sol
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% ml_step3 - numerical solution of step response of 3-term models
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%
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%(IV) Numerical evaluations of nonlinear fractional-order differential equations
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% INVLAP_new - closed-loop response evaluation with inverse Laplace transform
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% nlfode_mat - matrix-based solutions of implicit nonlinear FODEs
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% nlfode_vec - nonlinear fractional-order extended state space equation solver
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% nlfode_vec1 - a different version of nlfode_vec, not recommended
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% nlfec - $O(h^p)$ corrector solution of nonlinear multi-term FODEs
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% nlfep - $O(h^p)$ predictor solution of nonlinear multi-term fractional-order ODEs
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% pepc_nlfode - numerical solutions of single-term nonlinear FODE with PCPE algorithm
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%
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%(V) Filter design for fractional-order derivatives and systems
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% carlson_fod - design of a Carlson filter
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% charef_fod - design of a Charef filter
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% charef_opt - design of an optimal Charef filter
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% cont_frac0 - continued-fraction interface to irrational functions
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% matsuda_fod - design of Matsuda-Fujii filter
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% new_fod - design of a modified Oustaloup filter
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% opt_app - optimal IO transfer approximation of high-order models
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% ousta_fod - design of a standard Oustaloup filter
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%
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%(VI) FOTF object design and overload functions
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% base_order - find the base order from an FOTF object
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% bode - Bode diagram analysis
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% diag - diagonal FOTF matrix creation and extraction
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% display - overload function to display a MIMO FOTF object
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% eig - find all the poles, including extraneous roots
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% eq - checks whether two FOTF blocks equal or not
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% feedback - overload the feedback function for two FOTF blocks
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% foss_a - convert an FOTF to an extended FOSS object
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% fotf - creation of an FOTF class
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% fotf2cotf - convert an FOTF object into commensurate form
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% fotf2foss - low-level conversion function of FOTF to FOSS object
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% fotfdata - extract all the fields from an FOTF object
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% freqresp - low-level frequency response function of an FOTF object
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% high_order - high-order IO transfer function approximation of FOTF objects
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% impulse - evaluation of impulse response of an FOTF object
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% inv - inverse FOTF matrix
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% isstable - check whether an FOTF object stable or not
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% iszero - check whether an FOTF object is zero or not
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% lsim - time response evaluation to arbitrary input signals
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% margin - compute the gain and phase margins
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% maxdelay - extract maximum delay from an FOTF object
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% mfrd - frequency response evaluation
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% minus - minus operation of two FOTF objects
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% mldivide - left-division function
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% mpower - power of an FOTF object
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% mrdivide - right-division function
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% mtimes - overload function of * operation of two blocks
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% nichols - Nichols chart
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% norm - H2 and Hinf evaluation
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% nyquist - Nyquist plot
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% plus - overload function of + operation of two blocks
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% residue - partial fraction expansion
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% rlocus - root locus analysis
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% sigma - singular value plots
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% simplify - simplification of an FOTF object
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% step - step response
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% uminus - unary minus of an FOTF object
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%
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%(VII) FOSS object design and overload functions
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% bode - Bode diagram analysis
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% coss_aug - FOSS augmentation
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% ctrb - controllability test matrix creation
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% display - overload function to display a MIMO FOSS object
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% eig - compute the poles of a FOSS object
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% eq - checks two FOSS blocks equal or not
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% feedback - overload the feedback function for two FOSS blocks
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% foss - FOSS class creation
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% foss2fotf - low-level conversion from FOSS to FOTF object
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% impulse - evaluation of impulse response of an FOSS object
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% inv - inverse of an FOSS object
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% isstable - check an FOSS object stable or not
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% lsim - time response evaluation to arbitrary input signals
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% margin - compute the gain and phase margins
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% mfrd - frequency response evaluation
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% minreal - minimum realisation of a FOSS object
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% minus - minus operation of two FOTF objects
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% mpower - power of an FOSS object
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% mtimes - overload function of * operation of two blocks
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% nichols - Nichols chart
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% norm - H2 and Hinf evaluation
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% nyquist - Nyquist plot
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% obsv - construct observability test matrix
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% order - find the orders of an FOSS object
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% plus - overload function of + operation of two blocks
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% rlocus - root locus analysis
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% size - find the numbers of inputs, outputs and states
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% ss_extract - extract integer-order state space object from FOSS
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% step - step response
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% uminus - unary minus of an FOSS object
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%
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%(VIII) Simulink models
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% fotflib - Simulink blockset for FOTF Toolbox
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% fotf2sl - multivariable FOTF to Simulink block convertor
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% sfun_mls - S-function version of Mittag-Leffler function
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% slblocks - default Simulink description file
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% c9mvofuz - Simulink model for variable-order fuzzy PID control systems
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% c9mvofuz2 - Simulink model for variable-order fuzzy PID systems with variable delays
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% c10mpdm2 - Simulink model for multivariable PID control system
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% c10mpopt - Simulink model for multivariable parameter optimisation control systems
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% fPID_simu - Simulink model fractional-order PID controller for single-variable system
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%
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%(IX) Fractional-order and other controller design
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% c9mfpid - fractional-order PID controller design with equation solution techniques
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% c9mfpid_con - constraints in optimum FOPID design of FOPDT plants
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% c9mfpid_con1 - constraints in optimum FOPID design of FOIPDT plants
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% c9mfpid_con2 - constraints in optimum FOPID design of FO-FOPDT plants
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% c9mfpid_opt - objective function in optimum FOPID design of FOPDT plants
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% c9mfpid_opt1 - objective function in optimum FOPID design of FOIPDT plants
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% c9mfpid_opt2 - objective function in optimum FOPID design of FO-FOPDT plants
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% ffuz_param - S-function for parameter setting of fuzzy fractional-order PIDs
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% fopid - construct a \fPID{} controller from parameters
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% fpidfun - an example of objective function for optimum fractional-order PIDs
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% fpidfuns - objective function for fractional-order PID controller design
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% fpidtune - design of optimum fractional-order PID controllers
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% gershgorin - draw Nyquist plots with Gershgorin bands
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% get_fpidf - build string expression of the open-loop model
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% mfd2frd - convert MFD data into FRD data
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% optimfopid - GUI for optimum fractional-order PID design
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% optimpid - GUI for optimum integer-order PID design
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% pseuduag - pseudodiagonalisation of multivariable systems
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%
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%(X) Dedicated functions and models for the examples
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% c2exnls - constraint function of an example
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% c8mstep - Simulink model of a multivariable fractional-order system
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% c8mfpid1 - Simulink model of a fractional-order PID control system
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% c8mchaos - vectorised Simulink model for fractional-order Chua system
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% c8mchaosd - data input file for c8mchaos
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% c8mchua - MATLAB description of fractional-order Chua equations
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% c8mchuasim - Simulink model for fractional-order Chua circuit
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% c8mblk2,3,5 - three Simulink models of a linear fractional-order equation
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% c8mcaputo - complicated Simulink model for nonlinear FODE
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% c8mexp2 - simpler Simulink model for nonlinear Caputo equations
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% c8mexp2m - MATLAB description of nonlinear Caputo equation
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% c8mnlf1, c8mnlf2 - two different Simulink models of a nonlinear FODE
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% c8mexp1x - MATLAB function for describing nonlinear Caputo equations
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% c8nleq - MATLAB description of a nonlinear single-term Caputo equation
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% c8mlinc1 - Simulink model of a linear fractional-order Caputo equation
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% c9ef1-c9ef3 - criteria for optimum fractional-order PID controllers
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% c9mplant - Simulink model used for optimpid design
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