Robust adaptive control using disturbance observer for the system with actuator of first order time lag

The disturbance observer is widely used in various applications, since it can effectively reject the external disturbances. And it also compensates the plant uncertainties if the system has matched uncertainties. Actual system has actuator to regulate the physical control input. Generally, the response time of actuator is very small enough to be ignored. But, in case of high power system, the response time of actuator is relatively long to affect system properties, and it's often described approximately in first order time lag. Since the disturbance observer rejects the disturbance and uncertainties by subtracting the estimated value of disturbance from the system input, the time lag of actuator increases the disturbance compensation error. So effect of actuator should be considered to design the disturbance observer. In this paper, matched uncertainty system with input actuator is considered and robust control method using disturbance observer is proposed. The gain of robust control input is adaptively determined. All information - states, disturbance and uncertainties - needed for controller are obtained and estimated from system input and output. The relation between estimation error and output boundary is analyzed.