| Polynomial Toolbox and H-infinity Optimization |
We would like to insert this corner in the EUROPOLY Newsletter periodically to give tips on how the Polynomial Toolbox 2.0 for Matlab can be employed for solving various control problems via polynomial design methods. This time we will show how the closed-loop poles can be moved to the desired location using dynamical feedback controller. |
Given a SISO plant with the transfer function P = n/d, both continuous time and sampled, the controller C = y/x placing the closed loop poles to the desired location can be computed using the macro pplace.
Consider for instance the plant P with numerator n(s) = s+1 and denominator d(s) = s2-3s+2, with two unstable poles 1 and 2. The controller C(s) = y(s)/x(s), assigning the closed loop the poles –1, -1+j and –1-j, is achieved by the command
[y,x]=pplace(s+1,-s^2-3*s+2,[-1,-1+j,-1-j])
returning
y =
5s (controller‘s numerator)
x =
1 + s (controller‘s denominator)
For MIMO systems the macro works similarly, accepting both left and right polznomisl mstrix fractions and allowing the user to specify the whole set of invariant polynomials, not only the overall characteristic polynomial.
| EUROPOLY Newsletter | Number 2 - April 1999 |