Model Predictive Control Toolbox

Uses a model in state-space format to calculate the step response of a SISO or MIMO system, in MPC step format.

Syntax

• plant = ss2step(phi,gam,c,d,tfinal) 
  plant = ss2step(phi,gam,c,d,tfinal,delt1,delt2,nout) 
  

Description
The input variables phi, gam, c, and d are assumed to be a state-space model of a process. The model can be either continuous time:

or discrete time:

    x(k + 1) = x(k) + u(k)

    y(k) = Cx(k) + Du(k)

where x is a vector of n state variables, u is a vector of nu inputs (usually but not necessarily manipulated variables), y is a vector of ny plant outputs, and , , etc., are constant matrices of appropriate size. The ss2step function calculates the step responses of all the outputs of this process with respect to all the inputs in u, and puts this information into the variable plant in MPC step format. The section for mod2step describes the step format in detail.

The input variable tfinal is the time at which you would like to end the step response calculation, and delt1 is the sampling period. For continuous systems, use delt1=0. If you do not specify delt1, the default is delt1=0.

The optional input variable delt2 is the desired sampling period for the step response model. If you use delt2=[ ] or omit it, the default is delt2=delt1 if delt1 is specified and delt1 neq 0; otherwise, the default is delt2=1.

The optional input variable nout is the output stability indicator. For stable systems, set nout equal to the number of outputs, ny. For systems with one or more integrating outputs, nout is a column vector of length ny with nout(i)=0 indicating an integrating output and nout(i)=1 indicating a stable output. If you use nout=[ ] or omit it, the default is nout=ny (only stable outputs).

Example
The following process has 3 inputs and 4 outputs (and is the same one used for the example in the mod2step section):

• phi=diag([0.3, 0.7, -0.7]); 
  gam=eye(3); 
  c=[1 0 0; 0 0 1; 0 1 1; 0 1 0]; 
  d=[1 0 0; zeros(3,3)];
  

• delt1=1.5; tfinal=3*1.5; 
  plant=ss2step(phi,gam,c,d,tfinal,delt1) 
  

See Also
plotstep, mod2step, tfd2step

ss2mod

svdfrsp