Autotuning for delay systems: An algebraic approach

In this paper, principles for continuous-time controllers with utilization in autotuning schemes are studied. Design and tuning of proposed controllers is performed by algebraic tools where transfer functions are regarded as elements of the field of fractions associated with an appropriate ring according to the desired properties. The emphasis of designed autotuners is laid to SISO systems with time delays. Autotuners then represent a combination of a relay feedback identification test and some control design method. Within the scope of this contribution, models with up to three parameters are estimated by means of a single asymmetrical relay experiment. Then a stable low order transfer function with a time delay term is identified. Then, the control design is based on the ring of proper and stable rational functions (R_PS). Controller parameters are derived through a general solution of a linear Diophantine equation and a generalization for a two degree of freedom (2DOF) control structure is performed. A final controller can be tuned by a scalar real parameter m>0. The presented philosophy covers a generalization of PID controllers. The analytical simple rule is derived for aperiodic control response in the R_PS case. Autotuning principles then combine asymmetrical relay feedback tests with a control synthesis. A Matlab program for automatic design and simulation was developed and various simulations performed and analyzed.