Model-Free Control Design for Nonlinear Mechanical Systems

Madadi, Elmira GND

As industrial processes and demands for precise process control and quality enhancement become more advance and complex, the demand of designing appropriate controllers increases continuously. Based on physical and mathematical knowledge about the system, well-established model-based control methods have been successfully applied to linear and nonlinear systems, well-known benchmarks, and industrial processes.
However, model-based schemes require detailed model knowledge and related modeling processes using first-order (theoretical) modeling or models identified by suitable approaches like recursive least-squares (RLS) or data-driven techniques. With the increasing scale of industrial plants and enterprises, production technology and processes also become complex, and the requirements on product quality are increasing. All these aspects which were previously not fully explored, cause considerable challenges to the theoretical studies and practical applications of model-based control theory.

To avoid the demanding and complex modeling procedures, model-free control methods are utilized as an efficient alternative, in which the accurate system manual modeling step is not required. Accordingly, model-free control technique can be a suitable technique targeting a high performance considering the following two key aspects: i) the dynamical behavior of the unknown system should be determined without the requirement of mathematical models of the system only using the data measured from the input and output of the system.
It is worth noting that the dynamical behavior of the system to be controlled should be estimated online to update the actual dynamics, and ii) an appropriate control input should be generated for the upcoming time steps.
Despite the strong researches and works in this area, there are still aspects to be improved. Therefore, this thesis focuses on improving the efficient design of model-free control methods and development of precise concepts to describe the nonlinear systems combined with the optimal time-varying parameters for possible general applications.

The Modified Model-Free Adaptive Control (Modified MFAC) method is introduced as the extended version of Model-Free Adaptive Control (MFAC) approach to overcome the disadvantages of MFAC and to realize a suitable control performance in the case of time delay systems. Accordingly, model-free dynamically linearization approaches including Compact Form Dynamically Linearization (CFDL) and Partial Form Dynamically Linearization (PFDL) are focused to realize an equivalent transformation of an original nonlinear system. A modified objective is defined so that the control performance and the related energy can be evaluated. Unlike MFAC method, Modified MFAC approach attempts to reduce time delay effects on the nonlinear system. Comparison between MFAC design has been done in the task of tracking trajectory considering a nonlinear well-known benchmark system.
The stability of the system is established considering the convergence of controller tracking error and the value of the Pseudo Partial Derivative. Experimental and simulation results for SISO and MIMO cases validate and verify the effectiveness of the proposed Modified MFAC in comparison to previous methods. Consequently, a general comparison of both proposed model-free approaches is provided based on the experimental results.

Furthermore, a novel model-free control approach is proposed to overcome the disadvantages/difficulties of Model-Free Adaptive Control approach. The idea of well-known classical PID control is taken into consideration to design a model-free intelligent PID controller. The proposed intelligent PID controller uses the input-output information of the system instead of a mathematical plant model.
The measured I/O data already contains information which describes the internal dynamics of the nonlinear system to eliminate the need for a precise plant model. In addition, the concept of using a robust sliding mode differentiator which can directly operate the original signal and achieve the derivative signal is introduced to estimate the derivative of output signal. The effectiveness of the proposed method is evaluated by experimental results using a three tank system test rig.

Moreover, this thesis provides a novel fully model-free controller as Model-Free Adaptive ILC to improve the position tracking performance of a nonlinear inverted elastic cantilever beam test rig as well as its robustness in the presence of external disturbances.
The structure of Modified MFAC is integrated into the Iterative Learning Control approach to achieve a control law that provides the desired performance. An equivalent transformation of the original nonlinear system is performed to integrate into the structure of Iterative Learning Control approach and weighting matrices design. Additionally, a new weighting matrices design approach considering Discrete Algebraic Ricatti Equation is proposed to achieve appropriate weighting matrices design and to eliminate the effects of related nonoptimal weighting matrices values.
The convergence analysis is considered in terms of the convergence rate. Experimental results validate the advantages of proposed Model-Free Adaptive ILC approach in comparison to standard NOILC and model-based standard IMC in the presence of external disturbances.

Finally, an iterative learning-based intelligent PI controller is proposed for a nonlinear MIMO system. The introduced model-free intelligent PI control approach is used in combination with a well-known PD-type ILC method. The tracking control procedure and its evaluation are detailed by simulation results defining different scenarios in the context of a nonlinear MIMO system.

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Madadi, Elmira: Model-Free Control Design for Nonlinear Mechanical Systems. 2019.

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