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Converts the system data structure describing: into a discrete time equivalent model: via the matrix exponential or bilinear transform.
Inputs
system data structure (may have both continuous time and discrete time subsystems)
string argument; conversion option (optional argument; may be omitted as shown above)
"ex"
use the matrix exponential (default)
"bi"
use the bilinear transformation
FIXME: This option exits with an error if sys is not purely
continuous. (The ex
option can handle mixed systems.)
"matched"
Use the matched pole/zero equivalent transformation (currently only works for purely continuous SISO systems).
sampling time; required if sys is purely continuous.
Note: if the second argument is not a string, c2d()
assumes that the second argument is t and performs
appropriate argument checks.
Output
Discrete time equivalent via zero-order hold, sample each t sec.
This function adds the suffix _d
to the names of the new discrete states.
Convert a discrete (sub)system into a purely continuous one.
The sampling time used is sysgettsam(sys)
.
Inputs
system data structure with discrete components
Scalar value.
Tolerance for convergence of default "log"
option (see below)
conversion option. Choose from:
"log"
(default) Conversion is performed via a matrix logarithm. Due to some problems with this computation, it is followed by a steepest descent algorithm to identify continuous time a, b, to get a better fit to the original data.
If called as d2c (sys, tol)
, with tol
positive scalar, the "log"
option is used. The default value
for tol is 1e-8
.
"bi"
Conversion is performed via bilinear transform
z = (1 + s T / 2)/(1 - s T / 2) where T is the
system sampling time (see sysgettsam
).
FIXME: bilinear option exits with an error if sys is not purely discrete
Output
continuous time system (same dimensions and signal names as in sys).
convert a multirate digital system to a single rate digital system
states specified by idx, sprefix are sampled at ts2, all
others are assumed sampled at ts1 = sysgettsam (sys)
.
Inputs
discrete time system;
dmr2d
exits with an error if sys is not discrete
indices or names of states with sampling time
sysgettsam(sys)
(may be empty); see cellidx
list of string prefixes of states with sampling time
sysgettsam(sys)
(may be empty)
sampling time of states not specified by idx, sprefix
must be an integer multiple of sysgettsam(sys)
"constant u flag" if cuflg is nonzero then the system inputs are assumed to be constant over the revised sampling interval ts2. Otherwise, since the inputs can change during the interval t in [k ts2, (k+1) ts2], an additional set of inputs is included in the revised B matrix so that these intersample inputs may be included in the single-rate system. default cuflg = 1.
Outputs
equivalent discrete time system with sampling time ts2.
The sampling time of sys is updated to ts2.
if cuflg=0 then a set of additional inputs is added to the system with suffixes _d1, ..., _dn to indicate their delay from the starting time k ts2, i.e. u = [u_1; u_1_d1; ..., u_1_dn] where u_1_dk is the input k*ts1 units of time after u_1 is sampled. (ts1 is the original sampling time of the discrete time system and ts2 = (n+1)*ts1)
indices of "formerly fast" states specified by idx and sprefix; these states are updated to the new (slower) sampling interval ts2.
WARNING Not thoroughly tested yet; especially when cuflg == 0.
Displays eigenvalues, natural frequencies and damping ratios of the eigenvalues of a matrix p or the A matrix of a system p, respectively. If p is a system, tsam must not be specified. If p is a matrix and tsam is specified, eigenvalues of p are assumed to be in z-domain.
Returns dc-gain matrix. If dc-gain is infinite an empty matrix is returned. The argument tol is an optional tolerance for the condition number of the A Matrix in sys (default tol = 1.0e-10)
Impulse response for a linear system.
The system can be discrete or multivariable (or both).
If no output arguments are specified, impulse
produces a plot or the impulse response data for system sys.
Inputs
System data structure.
Index of input being excited
The argument tstop (scalar value) denotes the time when the simulation should end.
the number of data values.
Both parameters tstop and n can be omitted and will be computed from the eigenvalues of the A Matrix.
Outputs
Values of the impulse response.
Times of the impulse response.
Step response for a linear system.
The system can be discrete or multivariable (or both).
If no output arguments are specified, step
produces a plot or the step response data for system sys.
Inputs
System data structure.
Index of input being excited
The argument tstop (scalar value) denotes the time when the simulation should end.
the number of data values.
Both parameters tstop and n can be omitted and will be computed from the eigenvalues of the A Matrix.
Outputs
Values of the step response.
Times of the step response.
When invoked with the output parameter y the plot is not displayed.
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