This thesis is mainly concerned with two-degree-of-freedom (2DOF) controllers. 2DOF controllers appeared in the early days when feedback control first became a widely used practice. However, it was not until the 1980s that the superiority of 2DOF controllers over one-degree-of-freedom (1DOF) controllers was re-recognized by some researchers. The philosophy of 2DOF controllers is to use a feedback controller to meet the requirements of internal stability, disturbance rejection, measurement noise attenuation, and sensitivity minimization, then apply a prefilter controller on the reference signal to optimize the response of the overall system to the reference input. On the basis of such a configuration, 2DOF controllers are superior to conventional 1DOF controllers in dealing with...[ Read more ]

This thesis is mainly concerned with two-degree-of-freedom (2DOF) controllers. 2DOF controllers appeared in the early days when feedback control first became a widely used practice. However, it was not until the 1980s that the superiority of 2DOF controllers over one-degree-of-freedom (1DOF) controllers was re-recognized by some researchers. The philosophy of 2DOF controllers is to use a feedback controller to meet the requirements of internal stability, disturbance rejection, measurement noise attenuation, and sensitivity minimization, then apply a prefilter controller on the reference signal to optimize the response of the overall system to the reference input. On the basis of such a configuration, 2DOF controllers are superior to conventional 1DOF controllers in dealing with various problems, such as tracking and disturbance rejection optimal design, zero overshoot design and minimal error tracking design.

For the part of theoretical study, we first show the internal stability of a system with a 2DOF controller, then introduce the parametrization of all stabilizing 2DOF controllers. Based on the above works, we deal with the 2DOF H₂-optimal controller design. We put forward an algorithm to design a 2DOF H₂-optimal controller for a given plant in each of two situations: the first is impulse disturbance and impulse noise, the second is step disturbance and impulse noise. We further prove that the 2DOF H₂-optimal controller designed by our algorithm is optimal in each situation. Finally, we show that the minimal tracking error design is a special case of our algorithm.

For the part of experimental study, we perform the zero overshoot design to a ball-beam system. By experiment we demonstrate that a 2DOF controller can achieve zero overshoot, while a 1DOF controller cannot for certain class of systems.

The new contributions of our work are mainly twofold as follows:

First, our problem formulation is very general. In the H₂ cost function, both tracking performance and control energy in response to reference, disturbance and noise are taken into consideration. Two situations are studied. One involves step reference, impulse disturbance and impulse noise, the other involves step reference, step disturbance and impulse noise. In both situations the analytical solutions to the H₂-optimal control problem are given .

Second, our algorithm is straightforward. No advanced mathematical knowledge is required. It can be easily applied by engineers in practice. Only four or five simple steps are needed to get the optimal 2DOF controllers and the optimal value of the cost function.