System Analysis-Time Domain

c2d (sys opt, t)	Function File
c2d (sys t)	Function File

Converts the system data structure describing: . x = Ac x + Bc u into a discrete time equivalent model: x[n+1] = Ad x[n] + Bd u[n] via the matrix exponential or bilinear transform. Inputs sys system data structure (may have both continuous time and discrete time subsystems) opt string argument; conversion option (optional argument; may be omitted as shown above) "ex" use the matrix exponential (default) "bi" use the bilinear transformation 2(z-1) s = ----- T(z+1) 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). t 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 dsys 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.

d2c (sys tol)	Function File
d2c (sys opt)	Function File

Convert a discrete (sub)system into a purely continuous one. The sampling time used is sysgettsam(sys). Inputs sys system data structure with discrete components tol Scalar value. Tolerance for convergence of default "log" option (see below) opt 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 csys continuous time system (same dimensions and signal names as in sys).

[dsys fidx] = dmr2d (sys, idx, sprefix, ts2, cuflg)

Function File

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 sys discrete time system; dmr2d exits with an error if sys is not discrete idx indices or names of states with sampling time sysgettsam(sys) (may be empty); see cellidx sprefix list of string prefixes of states with sampling time sysgettsam(sys) (may be empty) ts2 sampling time of states not specified by idx sprefix must be an integer multiple of sysgettsam(sys) cuflg "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 dsys 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) fidx 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.

damp (p tsam)

Function File

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.

dcgain (sys tol)

Function File

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)

[y t] = impulse (sys, inp, tstop, n)

Function File

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 sys System data structure. inp Index of input being excited tstop The argument tstop (scalar value) denotes the time when the simulation should end. n 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 y Values of the impulse response. t Times of the impulse response.

[y t] = step (sys, inp, tstop, n)

Function File

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 sys System data structure. inp Index of input being excited tstop The argument tstop (scalar value) denotes the time when the simulation should end. n 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 y Values of the step response. t Times of the step response. When invoked with the output parameter y the plot is not displayed.