Ekstremum seeking control and applications in electric drive systems

The goal of thesis is to provide better performance in electrical drive systems with using Extremum Seeking Control. In the direction of this goal, firstly, Extremum Seeking Control (ESC) has been researched and the different approaches to ESC algorithm are defined in detail. The different types of ESC algorithm in the literature are separated under two main classes. First class is named as Analog Based Extremum Seeking Control and the second class is Numerical Optimization Based Extremum Seeking Control. The methods, which are observed under first class, Analog Based Extremum Seeking Control, are Sliding Mode Based Extremum Seeking Control, Gradient Based Extremum Seeking Control and Perturbation Based Extremum Seeking Control. The second type of ESC, which is observed in the class of Numerical Optimization Based Extremum Seeking Control, is given in detail with the different types of the numerical optimization methods. Then, implementation examples exists in the literature are researched in the scope of the different ESC techniques. One of the implementation example is ABS system, which provides life-saving protection for the people and the sector. This implementation example is not only a very critical technological improvement, but also a spotlight to make ESC understandable in this thesis. The other implementation example for the ESC is maximum power point tracking systems for solar energy systems. These implementation examples then determined for making comparison of the different ESC methods. After making comparison, the objective of the thesis become clear. By researching different types of ESC, it is clarified that using only ESC as a control method of the electrical drive system may not meet the drive's real time optimization requirements. For this reason, Model Predictive Control (MPC), which is another optimization method, is observed. Furthermore, the research become deeper in the objective of using MPC with integration of ESC as a real time optimization control method. In this thesis, the permanent magnet synchronous motor is considered, which will be driven by the electrical drive. This kind of motor become popular because of its innovative technology. With the improvement of the permanent magnet technology, this kind of motors become more feasible than classical asynchronous motors. It allows to a better speed control of the loads. Due to its high torque output at the low speed, it is not necessary to use extra reduction units such as gearboxes. By this way, it is possible to make more reliable and economical systems with eliminating an equipment from a drive system. For this thesis, the equivalent circuits of the permanent magnet synchronous motor are given. In the spotlight of the equivalent circuits, motor's state-space equations are obtained. This state-space equations then used as system model in model predictive control. It should be mentioned that the system model and controllers in this thesis are in linear form. MPC is a model based control method that is based on prediction of the controlled system's behaviors on next time steps. In order to achieve this goal, a prediction horizon is defined within MPC. In MPC using larger horizons has the great potential to give better performance, but requires more computational effort at each sampling period to solve optimization problem. Electrical drives are an interesting application area for MPC at least two reasons • It can be obtained its linear model both by analytical means and by identification techniques. • Limits on drive variables are important for the drive system dynamics. The presence of the system constraints is one of the main reasons why state-space controllers have limited application in electrical drives. Despite MPC has this kind of advantages for the electrical drive systems, MPC applications to electrical drives are still largely unexplored. In this thesis, system constraints, which are very important for MPC, are defined carefully. The control of an electrical drive, which drives a permanent magnet synchronous motor with MPC, is simulated via MATLAB/SIMULINK in this thesis. First, system model is created on an m-file then it is sent to the MATLAB workspace. Then, the discrete-time state-space system, which is ready on the workspace, is introduced to the MPC controller, which takes place on SIMULINK. After introducing the system model to the controller, the prediction horizon, the control horizon, constraints and tuning parameters such as weights are defined. Then the control system is simulated with two different simulation scenarios. In the first scenario, while the system works normally in its reference speed, the load is changed (increased). By this way, the MPC controller is tested in varying load conditions. The second scenario is a little different from the normal conditions. In this scenario, system has uncertainties on the parameters of inertia and friction of the rotor. By this way, the MPC controller is tested on a system, which has an uncertainty. To achieve the goal of this thesis, a simulation in MATLAB/SIMULINK is done for simulating an ESC controller in the electrical drive application. As mentioned before, ESC and MPC controllers are integrated and applied to an electrical drive system. The idea that is introduced in this thesis is that the performance of a model based MPC controller can be combined with the robustness of a model-free ESC algorithm for simultaneous identification and control of linear discrete time systems with structural uncertainties. While regulation and identification are conflicting objectives, by identifying the system dynamics online and updating the MPC prediction model, the closed loop performance is improved relative to a standard MPC controller. ESC&MPC controller, which combines two different methods together, merges a model based linear MPC algorithm with a model free ESC algorithm to realize an iterative learning MPC that adjusts to structured model uncertainties. In the simulation of the ESC&MPC controller in MATLAB/SIMULINK, very similar to the MPC controller's simulation, first an m-file is compiled to define system's nominal operating point. Then, in order to combine ESC algorithm with the MPC, a code generated in a Matlab Function on a SIMULINK model with appropriate input-output configuration. On the other hand, the MPC controller must allow updating the defined system model. For this reason, Adaptive MPC Controller block is used for the simulation. To complete the integration of two controllers, the system model parameters that comes from ESC Matlab Function Block are arranged with the correct order for the Adaptive MPC controller. The MPC parameters such as constraints and weights are adjusted and the two different simulation scenarios that are defined above are applied for ESC&MPC controller. In order to make a comparison between the simulation results of the MPC controlled electrical drive and ESC&MPC controlled electrical drive, same simulation steps are applied to both of the controllers. Both of the controllers are seems successful for normal conditions in speed control of the PMSM electrical drive. They both follow the reference speed without any problem. To make the simulation harder, a load is applied to the motor while it is operating. In the second simulation scenario, the system that will be controlled is become a system which contains uncertainties. These uncertainties are added to the system parameters and simulated with both of the controllers. In Simulation of the MPC controller is lost its speed reference and never tried to catch the reference again. Oppositely, in simulation of the ESC&MPC controller, system tried to catch the reference again and finally – within very short time period- catches the reference again and succeeds to eliminate the structural uncertainties. To conclusion, when the MPC controller is supported with a real time optimization algorithm ESC, it became highly effective controller even with the parametric uncertainties. However, a big problem must be solved before make this controller usable in the real life. ESC&MPC controllers need very high computational capabilities in very short time steps. Therefore, implementation of this controller for real applications would be possible when faster and much capable microprocessors will be produced.