On a modification of the PID controller
The paper considers the controlled system \[ x^{(n)}+ a_nx^{(n-1)}+ \cdots + a_2x' +a_1x =u(t) \] and the finite-memory controller \[ u= -c_1 \bigl(x(t) -x_d(t)\bigr)-c_2 \bigl(x'(t) -x_d'(t) \bigr)- c_3\int^t_{t- \sigma} \bigl(x (\tau)- x_d(\tau) \bigr)d \tau \] \(x_d(t)\) being the reference signal. This controller is shown to have several advantages (stability and robustness) with respect to the standard PID controller.
scientific article; zbMATH DE number 1046295