State space system interface functions

ss (a b, c, d, tsam, n, nz, stname, inname, outname, outlist)

Function File

Create system structure from state-space data. May be continous discrete or mixed (sampled data) Inputs a b c d usual state space matrices. default: d = zero matrix tsam sampling rate. Default: tsam = 0 (continuous system) n nz number of continuous discrete states in the system If tsam is 0 n = rows(a), nz = 0. If tsam is greater than zero n = 0, nz = rows(a) see below for system partitioning stname cell array of strings of state signal names default (stname=[] on input): x_n for continuous states xd_n for discrete states inname cell array of strings of input signal names default (inname = [] on input): u_n outname cell array of strings of input signal names default (outname = [] on input): y_n outlist list of indices of outputs y that are sampled If tsam is 0 outlist = []. If tsam is greater than 0 outlist = 1:rows(c). Unlike states discrete/continous outputs may appear in any order. sys2ss returns a vector yd where yd(outlist) = 1; all other entries of yd are 0. Outputs outsys = system data structure System partitioning Suppose for simplicity that outlist specified that the first several outputs were continuous and the remaining outputs were discrete. Then the system is partitioned as x = [ xc ] (n x 1) [ xd ] (nz x 1 discrete states) a = [ acc acd ] b = [ bc ] [ adc add ] [ bd ] c = [ ccc ccd ] d = [ dc ] [ cdc cdd ] [ dd ] (cdc = c(outlist1:n), etc.) with dynamic equations: d/dt xc(t) = acc*xc(t) + acd*xd(k*tsam) + bc*u(t) xd((k+1)*tsam) = adc*xc(k*tsam) + add*xd(k*tsam) + bd*u(k*tsam) yc(t) = ccc*xc(t) + ccd*xd(k*tsam) + dc*u(t) yd(k*tsam) = cdc*xc(k*tsam) + cdd*xd(k*tsam) + dd*u(k*tsam) Signal partitions | continuous | discrete | ---------------------------------------------------- states | stname(1:n:) | stname((n+1):(n+nz),:) | ---------------------------------------------------- outputs | outname(cout:) | outname(outlist,:) | ---------------------------------------------------- where cout is the list of in 1:rows(p) that are not contained in outlist. (Discrete/continuous outputs may be entered in any order desired by the user.) Example octave:1> a = [1 2 3; 4 5 6; 7 8 10]; octave:2> b = [0 0 ; 0 1 ; 1 0]; octave:3> c = eye (3); octave:4> sys = ss (a b, c, [], 0, 3, 0, {"volts", "amps", "joules"}); octave:5> sysout(sys); Input(s) 1: u_1 2: u_2 Output(s): 1: y_1 2: y_2 3: y_3 state-space form: 3 continuous states 0 discrete states State(s): 1: volts 2: amps 3: joules A matrix: 3 x 3 1 2 3 4 5 6 7 8 10 B matrix: 3 x 2 0 0 0 1 1 0 C matrix: 3 x 3 1 0 0 0 1 0 0 0 1 D matrix: 3 x 3 0 0 0 0 0 0 Notice that the D matrix is constructed by default to the correct dimensions. Default input and output signals names were assigned since none were given.

[a b, c, d, tsam, n, nz, stname, inname, outname, yd] = sys2ss (sys)

Function File

Extract state space representation from system data structure. Input sys System data structure. Outputs a b c d State space matrices for sys. tsam Sampling time of sys (0 if continuous). n nz Number of continuous discrete states (discrete states come last in state vector x). stname inname outname Signal names (lists of strings); names of states inputs and outputs, respectively. yd Binary vector; yd(ii) is 1 if output y(ii) is discrete (sampled); otherwise yd(ii) is 0. A warning massage is printed if the system is a mixed continuous and discrete system. Example octave:1> sys=tf2sys([1 2][3 4 5]); octave:2> [ab,c,d] = sys2ss(sys) a = 0.00000 1.00000 -1.66667 -1.33333 b = 0 1 c = 0.66667 0.33333 d = 0