1 Introduction to Proportional-Integral Controller (PI) Design
A PI-Lead controller is a proportional gain in parallel with an integrator; both in series with a lead controller. The proportional gain provides fast error response. The integrator drives the system to a 0 steady-state error.
2 Mathematics of the Proportional-Integral Controller
The Proportional-Integral (PI) Controller is a proportional controller (simple gain ) and an integrator . Examples of PI controllers with different zeros are on the right.
The MATLAB command to create a PI controller is
PIcomp = @(z) tf([1 z],[1 0]);
- z is the zeros in a PI controller.
The MATLAB command presented ignores the proportional gain, . The proportional gain is set so that the open loop system can achieve the desired open loop crossover frequency.