1.3 DISTURBANCE RESISTANT
• In real systems we expect that certain events will occur that are not part of our system model.
• In this case we assume that the system control is happening as expected, and we add in a new disturbance input.
• The block diagram below shows one of these systems, with a disturbance injected between the controller and the process.
• Notice that in the above form we are reducing the problem by finding differences (basically a partial differential solution) which will be a good approximation when the disturbance is not too fast or large.
• We can develop an equation for the controller, based on the desired system response to the disturbance,
• The closed form expression can be calculated by replacing the desired transfer function,
• These systems are often called regulators, and can be used when a system is subject to unexpected noise. Examples of possible applications would include plumbing systems, electrical power supplies, etc.
1.3.1 Disturbance Minimization
• We can use an approach similar to the deadbeat controller, but we still need to know the type of disturbance expected to develop a controller.
• Consider a case where the disturbance is a step function
• We can examine the previous controller for stability as well,
• If we have a first order system we only need to have a sample time that is shorter than the system time constant.
