Bernstein polynomials based compensator design for actuator saturated coupled tank level control system

One of the major problems encountered in the studies dealing with the controller design in physical systems is that the mathematical model of the system is not sufficiently accurate enough and can not be obtained analytically in some cases. A well-known method used in the literature when faced with such problems is system identification algorithms. System identification techniques aim to construct a mathematical model that describes the existing physical system as well as possible by using different approaches and algorithms. A major method highly used in system identification studies are identification functions. The main purpose of using identification functions can be defined as the approach where different types of signals are applied as the input to the system and as a result of the analysis of the system output, the analysis of dynamic structures within the system model is carried out via different algorithms. One of the subclasses of describing functions can be defined as Higher Order Sinusoidal Input Describing Functions (HOSIDFs) which become a popular approach in control literature especially in the last decade. The controller design for a couple tank system with actuator saturation is carried out via HOSIDFs in this study. HOSIDF approach aims to define linear and nonlinear structures of the system via the analysis of system output where a sinusoidal input signal with predefined amplitude and frequency is applied to the system. When a sinusoidal input signal is applied to a stable, linear time invariant, single input single output and causal system, the periodic sinusoidal system output has the same frequency with the applied input signal. If the linear system is replaced with a nonlinear system in the aforementioned assumption, the system output consists of different spectral components in addition to the main spectral line at the fundamental frequency of the applied sinusoidal input signal. These components, expressed as harmonics, are considered as the results of the presence of non-linear structures in the system. At this point, the aforementioned algorithm should aim to suppress these harmonics or minimize the amplitude values. As the magnitude values of the harmonics are reduced, the effect of the non-linear sturctures on the system output is also reduced and the performance of the predefined conventional linear controllers in the system is highly increased. It is aimed in this approach to reduce the effect of non-linear characteristics in the system to the output and increase the controller performance via the implementation of a secondary compensator on the already existing feedback controller in the system without harming the closed-loop stability. In this study, the most important reason to utilize HOSIDF approach can be considered as its high applicability to real-time physical systems. For this reason, the implementation of the proposed algorithm in the study is illustrated on the couple tank level control system including actuator saturation. The main contribution of the research can be defined as the application of HOSIDF approach for the systems where there exist significant limitation due to actuator saturation, especially in terms of controller performance. In addition to the studies already existing in the literature, the compensator parameters are calculated by using a frequency based optimization algorithm in order to be implemented into the HOSIDF based compensator. At this point, the compensator structure is first constructed via Chebyshev polynomials that are also used in the existing literature and Bernstein polynomials are utilized for the proposed controller structure in the study which can be considered as a contribution to the literature. There exist two main control loops in the couple tank level control system. The existing actuator saturations acting on the control signal applied to the system reduces the performance of the controller significantly. Therefore, in addition to the existing controller structure in the system, a secondary HOSIDF-based compensator design is designed to reduce the performance degrading effect of the actuator saturation on the reference tracking performance of the system. The system output is defined as the liquid level of the tank in the lower section whereas the applied reference input is defined as the nonconstant setpoint values for the tank level in the lower section. Time domain and frequency domain simulation results obtained in the study are also given in order to illustrate the performance of proposed controller. The simulation results include the time domain plot of the system output in order to represent the reference tracking performance of the system, the harmonic plots that represent the frequency domain representation of the system output and Integrated Squared Error(ISE) tables.