L-Dissipativity of Hyperstable Repetitive Control Systems

In this research author proposed the method for constructing the hyperstable repetitive control systems for nonstrictly minimally phase linear dynamic plant which are subjects to the constant action of external periodic perturbations. To build a stable control system, the V.M. Popov's hyperstability criterion is used. Compensation of external disturbances and also adaptation to a periodic command action is carried out by the generator for periodic signals in the forward channel of the system. Ldissipativity of a hyperstable system is provided with the help of the high-speed dynamic correction filter which introduce into the main control loop. Main feature of the proposed solution is to provide the desired properties of the control system by bringing the relative degree of the control plant to a single value. At the same time, the operability of the system under consideration in the presence of a structural disturbance is ensured by fulfilling special conditions that impose requirements on the value of the time constant of the correction filter. The results of present research can be used in the development of hyperstable repetitive control systems for different complex classes of dynamic plants. For example, when the mathematical models of plant contain non-linear and/or non-stationary characteristics. In this case, the main problem will be to synthesize the dynamic feedback algorithms.