Comparison of Optimal Control Designs for a 5 MW Wind Turbine

Optimal controllers, namely Model Predictive Control (MPC), H∞ Control (H∞), and Linear Quadratic Gaussian control (LQG), are designed for a 5 MW horizontal-axis variable-speed wind turbine. The control design models required as part of the optimal control design are obtained by using a high fidelity aeroelastic model (i.e., DNV Bladed). The optimal controllers are eventually designed in three operating modes: below-rated, just below-rated, and above rated-wind speeds, based on linearized control design models. The linearized models are reduced by using a model reduction technique to facilitate the design of optimal controllers. The controllers are analyzed not only in the time domain but also in the frequency domain and on the torque/speed plane. Simulation results demonstrated that optimal controllers perform better than the standard proportional-integral-derivative (PID) controller, particularly for removing oscillation due to the drive-train mode without incorporating a drive-train damper.

СИНТЕЗ СИСТЕМ УПРАВЛІННЯ ЕЛЕКТРОПРИВОДАМИ З КОВЗНИМИ РЕЖИМАМИ

Synthesis of electric drive control systems by methods of the theory of analytical design of optimal controllers (ACOR) allows to obtain structures with sliding modes, which are characterized by high dynamic performance and the property of roughness relative to parametric and coordinate perturbations. At the same time, due to the presence of a relay regulator operating in sliding mode, such systems are nonlinear, described by differential equations with a discontinuous right-hand side. At the same time, one of the problems of ACOR is the problem of choosing the weights of optimizing functionals, which has not received an acceptable solution for designers: the choice of these coefficients is not predetermined by physically clear recommendations. If in the linear case the selection of weights of quadratic criteria can be organized by computer simulation of transients in a closed linear system, then in the nonlinear case such an approach is mathematically incorrect. This is due to the well-known fact that for nonlinear systems the principle of superposition is false, and their behavior in contrast to linear depends significantly on the initial conditions. In this regard, choosing as a result of modeling a nonlinear system on a computer those or other seemingly appropriate weights of the relevant criteria, you can get almost inoperable nonlinear system, because under other initial conditions, its behavior can change qualitatively. Surprisingly, this well-known fact in the literature is obscured, although its influence on the behavior of synthesized systems is fundamental.There are methods for constructing optimal systems based on the synthesis of regulators based on setting the desired quality indicators of transients, taking into account the known behavior of the system with a certain characteristic equation. The article substantiates the method of finding the feedback coefficients of the relay controller from the condition of providing the dynamic characteristics of the system, given the desired characteristic equation.

Recurrent-iterative algorithm for control synthesis of spacecraft terminal reorientation based on the method for analytical design of optimal controllers

The paper considers the application of the method for analytical design of optimal controllers as formulated by of A.A. Krasovsky (optimization according to the criterion of generalized work) for the control synthesis of spacecraft reorientation from an arbitrary angular position to a given attitude during a fixed time period. A predictive algorithm model was selected as a numerical implementation for the analytical design according to the generalized performance criterion. In order to investigate the angular motion optimization methods experimentally, a model of the spacecraft reorientation control process was developed and implemented in C#. Numerical experiments demonstrated that the generic algorithm does not ensure the specified accuracy of the final orientation, and an increase in the weight coefficients in the terminal member in order to reduce the orientation errors leads to a loss of stability of the dynamic process. The paper proposes a modification of the prediction algorithm — a recurrent-iterative algorithm for exact reorientation of a spacecraft in a fixed time period. The approach used in this case involves organizing an iterative procedure for synthesizing the optimal control of the spacecraft reorientation based on a prediction algorithm. The optimal control calculated at each iteration is used at the next step of the iterative procedure as the next additive component of programmable control. Numerical experiments demonstrated that the recursive-iterative method for reorienting a spacecraft ensures the angular motion stability of the spacecraft and the specified accuracy of the final orientation in a wide range of boundary conditions. The scope of the proposed algorithm is limited to control objects with continuum end-effectors. An example of such a control object is a remote sensing satellite with power gyroscopes (gyrodines) in the orientation system.

Two-channel time-optimal control of nonstationary heat conductive process with account for response time of boundary control actions

The task of organization a closed time-optimal control system of linear object with distributed parameters of parabolic type is considered. The object has two lumped internal controls for the power of heat sources excited in the electromagnetic field of an inductor. The proposed method for the synthesis of optimal controllers uses an alternance method for calculating the optimal program controls for each of the control actions. An example of the construction of a quasi-optimal time control system for the process of periodic induction heating of a metal workpiece with constant values of the feedback coefficients calculated for the most characteristic initial spatial distribution is given.

Using Division Method to Convert the K-Input MIMO System to SISOs System Combined with Optimal Algorithm Application to Control of a Flexible Link System for the Oscillation (K =1,2)

The flexible link system (FLS) was a highly nonlinear model, multivariable and absolutely unstable dynamic system. In practice, it is common to integrate multiple subsystems into the main system with dynamically turned k-input signals (k =1, 2,…, N) to diversity the functionality of the main system. The flexibility of the division method to convert k-input MIMO system to SISOs system combined with the optimal algorithm creates a powerful tool that can be applied to many different MIMO nonlinear systems with high success rates. The optimal controllers can be created in the future for the flexible system is implemented on an experiment system using Arduino UNO micro-controller KIT. This paper describes division method to convert the k-input MIMO system to SISOs system, after that combined with the optimal algorithm to control for the flexible link system. Specifically, the author will conduct oscillating component analysis of a system with k input pairs (k =1, 2) so that the author can better understand the nature of sub-components as they interact with the system.

Design of Optimal Controllers for Unknown Dynamic Systems through the Nelder–Mead Simplex Method

This paper presents an efficient method for designing optimal controllers. First, we established a performance index according to the system characteristics. In order to ensure that this performance index is applicable even when the state/output of the system is not within the allowable range, we added a penalty function. When we use a certain controller, if the state/output of the system remains within the allowable range within the preset time interval, the penalty function value is zero. Conversely, if the system state/output is not within the allowable range before the preset termination time, the experiment/simulation is terminated immediately, and the penalty function value is proportional to the time difference between the preset termination time and the time at which the experiment was terminated. Then, we used the Nelder–Mead simplex method to search for the optimal controller parameters. The proposed method has the following advantages: (1) the dynamic equation of the system need not be known; (2) the method can be used regardless of the stability of the open-loop system; (3) this method can be used in nonlinear systems; (4) this method can be used in systems with measurement noise; and (5) the method can improve design efficiency.