Control Toolbox In Matlab Research Articles

Robust PID control of a two-rotor aerodynamical system with decoupling

Abstract In this work, robust PID design via μ synthesis for controlling a MIMO two-rotor aerodynamic system manufactured by the Polish company Inteco is presented. The controller consists of a decoupling system and two PID controllers. The aim is to demonstrate an approach enabling further fine-tuning based on an already synthesized controller structure. Tools from Robust Control Toolbox in MATLAB are used. The PIDs are constructed as tunablePID objects, and the decoupler is also tunable and has the preset structure of a static gain matrix (tunableGain) or dynamic state-space system with a given number of states (tunableSS). The model contains some parameters with structured uncertainty. Several variants of the controller with a fixed structure have been created, and their performance has been tested by simulation and on the laboratory set-up.

Comparing the Performance of Robust Controllers for Vibration Suppression in Long Rotor Systems

In this paper, the vibration control of the multivariable model of rotor bearing systems is considered for investigation. Some simply structured controllers that can suppress vibrational disturbances are tested for their robustness via the H∞ optimality criteria. Initially, intelligent optimisation techniques are used to minimize the H∞ mixed-sensitivity norm of the Linear Fractional Transformation (LFT) of the simple two-term PI controllers acting on the rotor system models. This results in some controllers that can suppress the vibration but with a slow oscillatory response. After this, an appropriate interpretation of the Bode plot singular values of the combined sensitivity and control effort matrix is used to explain the performance shortcomings of this controller. Moreover, the existing simply structured controllers in the literature exhibiting a faster performance are examined by using singular value plots. It is shown that when the maximum singular value of the control effort matrix drops below the 0 db line, the performance will be boosted. Finally, the H∞ controllers are designed by using the robust control toolbox in MATLAB. This resulted in rapid disturbance rejection, with the vibration amplitude diminishing to zero after 0.3 s due to double-step disturbances. However, these controllers in the frequency domain have an order of eight and may not be realizable to be implemented in practice. It is concluded that examining the Bode plot of the maximum singular value of the control effort matrix is a useful tool for evaluating performance in the frequency domain. However, designing robust controllers by toolboxes in the time domain can lead to superb performance with higher-order controllers.

Robust control of wind turbines to reduce wind power fluctuation

AbstractThe wind power generation system of a 5 MW horizontal axis wind turbine has a high wind energy conversion efficiency. The proportion of installed capacity in practical production applications is increasing year on year, so that the stability of its operation becomes a central factor in determining the productivity of the wind farm in question. This paper takes a 5 MW wind turbine as the research object and proposes a parameter‐adaptive robust model predictive control method to achieve self‐optimization of controller parameters through a Bayesian optimization approach. A robust model predictive control strategy, aiming to reduce the power fluctuation while maximizing the power output, is developed in this paper to enhance the dynamic economic performance under uncertain wind speed variation. A Bayesian algorithm is used in this paper to optimize the parameters of the controller. Moreover, wind speeds are simulated using TurbSim for different turbulence intensities of 5%, 10%, and 15% turbulence. Finally, the robust model predictive control toolbox in MATLAB is designed and simulated. The results show that the operational instability of the wind energy system is overcome. Meanwhile, the robustness of the wind energy system operation is improved compared to the traditional model predictive control approach.

Sampled-data controller scheme for multi-agent systems and its Application to circuit network

The objective of this study is to investigate the synchronization criteria under the sampled-data control method for multi-agent systems (MASs) with state quantization and time-varying delay. Currently, a looped Lyapunov–Krasovskii Functional (LKF) has been developed, which integrates information from the sampling interval to ensure that the leader system synchronizes with the follower system, resulting in a specific condition in the form of Linear Matrix Inequalities (LMIs). The LMIs can be easily solved using the LMI Control toolbox in Matlab. Finally, the proposed approach’s feasibility and effectiveness are demonstrated through numerical simulations and comparative results.

Comparative Analysis of H2 and H∞ Robust Control Design Approaches for Dynamic Control Systems

This paper discusses using H2 and H∞ robust control approaches for designing control systems. These approaches are applied to elementary control system designs, and their respective implementation and pros and cons are introduced. The H∞ control synthesis mainly enforces closed-loop stability, covering some physical constraints and limitations. While noise rejection and disturbance attenuation are more naturally expressed in performance optimization, which can represent the H2 control synthesis problem. The paper also applies these two methodologies to multi-plant systems to study the stability and performance of the designed controllers. Simulation results show that the H2 controller tracks a desirable closed-loop performance, while the H∞ controller guarantees robust stability for the closed-loop system. The validation of the techniques is demonstrated through the robust and performance gamma index, where the H∞ controller achieved a robust gamma index of 0.8591, indicating good robustness and the H2 controller achieved a performance gamma index of 2.1972, indicating a desirable performance. The robust control toolbox of MATLAB is used for simulation purposes. Overall, the paper shows that selecting a suitable, robust control strategy is crucial for designing effective control systems, and the H2 and H∞ robust control approaches are viable options for achieving this goal.

Robust stability and passivity analysis for discrete-time neural networks with mixed time-varying delays via a new summation inequality

<abstract><p>The summation inequality is essential in creating delay-dependent criteria for discrete-time systems with time-varying delays and developing other delay-dependent standards. This paper uses our rebuilt summation inequality to investigate the robust stability analysis issue for discrete-time neural networks that incorporate interval time-varying leakage and discrete and distributed delays. It is a novelty of this study to consider a new inequality, which makes it less conservative than the well-known Jensen inequality, and use it in the context of discrete-time delay systems. Further stability and passivity criteria are obtained in terms of linear matrix inequalities (LMIs) using the Lyapunov-Krasovskii stability theory, coefficient matrix decomposition technique, mobilization of zero equation, mixed model transformation, and reciprocally convex combination. With the assistance of the LMI Control toolbox in Matlab, numerical examples are provided to demonstrate the validity and efficiency of the theoretical findings of this research.</p></abstract>

Noise and Disturbance Rejection Performance Evaluation on Explicit Model Predictive Control Technique Applied to Inverted Pendulum with Various Test Scenarios

An inverted pendulum on a cart (IPC) system, which is a widely used test environment for controller design due to ease of applicability, has the opportunity to be applied in different fields with nonlinear and under-actuated characteristics. In this study, the performance of the explicit MPC control method has been examined against the noise and disturbances by using two test cases and analysis approaches. Different trajectory tracking, disturbance, and noise situations have been taken into account in the elaborated scenarios. The numerical applications have been performed by the model predictive control toolbox of Matlab®/Simulink®. The advantages and drawbacks of the controller have been discussed in terms of time-domain specifications.

New delay-dependent conditions for finite-time extended dissipativity based non-fragile feedback control for neural networks with mixed interval time-varying delays

This paper studies the delay-dependent conditions for finite-time extended dissipativity based non-fragile feedback control for neural networks with mixed interval time-varying delays. By applying Jensen’s inequality, an extended Jensen’s double integral inequality, and a free matrix form inequality to the Lyapunov–Krasovskii functional (LKF), delay-dependent conditions are derived and solved by the Matlab control toolbox in terms of linear matrix inequalities (LMIs). By stability criteria, this paper is less conservative than the other works. In addition, we demonstrate the advantage of our obtained methods by five numerical examples. One practical example shows a real-world approach: the quadruple-tank process system (QTPS).

Adaptive Control and Estimation of the Condition of a Small Unmanned Aircraft Using a Kalman Filter

The article was motivated by the design of adaptive control algorithms for the control of a a fixed wing unmanned aerial vehicle (UAV). An adaptive system is a system that, with its structure or parameters, adapts to changes in the behavior of the object and based on the knowledge of variable properties, maintains the quality of its regulatory transition. The knowledge gained on this small UAV can be applied to larger aircraft. The creation of the proposed adaptive control into the UAV consisted of the creation of a simulation model of the aircraft based on known physical laws, the properties of the aircraft and a mathematical description. An adaptive PID controller for stabilization with changing coefficients based on the airspeed of the aircraft was designed and simulated. A validated control of the mathematical model of an unmanned aircraft was designed and simulated using the methods of estimation and identification of the UAV model parameter based on measured data from flight tests. Identifying dynamic parameters is a challenging task due to several factors, such as random vibration noise, interference, and sensor measurement uncertainty. The designed adaptive UAV control provides very promising results in improving the controllability of the aircraft while reducing the effect of speed changes on the stability and controllability of the system compared to the conventional PID controller. The comparison was performed on three selected types of PID controllers. The first type had fixed coefficients for the entire range of speeds calculated using the Control toolbox in MatLab. The second type also had constant coefficients over the entire range of speeds calculated using the Naslin method. The third adaptive type of PID controller had variable coefficients based on approximate polynomials dependent on the change in flight speed. The reason for the comparison was to show an increase in margin of stability using the method of variable coefficients of the PID controller based on the change of flight speeds. The obtained results show that the proposed adaptive control algorithm is robust enough to control the movement of the aircraft in the longitudinal plane and due to the introduced process and measurement errors, while the used Kalman filter effectively eliminates these errors.

Minimum Variance Pole Placement in Uncertain Linear Control Systems

The pole-placement issue for linear multi-input multi-output (MIMO) dynamic systems with uncertain parameters has been addressed in this article. A static feedback matrix has been designed for minimizing variances of closed-loop poles (CLPs) and for assigning poles to the nominal system at the desired places. It is assumed that the joint probability density function (PDF) of uncertain parameters is known and the system has more than one input. A new unknown vector is used like an eigenvector for a stochastic closed-loop system matrix to state the problem. The variances of poles are considered as cost functions, and the means of poles are termed constraints. This form of the problem statement has helped us to simply find a solution. In the first step, the optimization problem with constraints was handled by solving the equality constraint, and then, the problem was converted to a classic extended eigenvalue optimization problem. Later, the eigenvalue optimization problem was solved by the Rayleigh quotient and the feedback matrix was accomplished. Finally, this approach was simulated and validated using the MATLAB simulations, and the results were compared with a robust pole-placement method, which MATLAB control toolbox uses. The Monte Carlo simulations showed lower covariance for CLPs around the mean poles as compared to the robust pole-placement method.

Computing $\mu$-values for LTI Systems

In this article we consider certain linear time-varying control systems and investigate their stability using structured singular values ($\mu$-values). We use the low rank ordinary differential equations based methodology to compute the lower bounds for $\mu$-values. The inner-outer algorithm computes the local extremizer of an admissible perturbation and adjusts the desired perturbation level. Further, we present a comparison of our results via the well-known MATLAB routine mussv which is available in MATLAB control toolbox.

Stability Analysis of Linear Feedback Systems in Control

This article presents a stability analysis of linear time invariant systems arising in system theory. The computation of upper bounds of structured singular values confer the stability analysis, robustness and performance of feedback systems in system theory. The computation of the bounds of structured singular values of Toeplitz and symmetric Toeplitz matrices for linear time invariant systems is presented by means of low rank ordinary differential equations (ODE’s) based methodology. The proposed methodology is based upon the inner-outer algorithm. The inner algorithm constructs and solves a gradient system of ODE’s while the outer algorithm adjusts the perturbation level with fast Newton’s iteration. The comparison of bounds of structured singular values approximated by low rank ODE’s based methodology results tighter bounds when compared with well-known MATLAB routine mussv, available in MATLAB control toolbox.

On Instability Analysis of Linear Feedback Systems

The numerical approximation of the μ -value is key towards the measurement of instability, stability analysis, robustness, and the performance of linear feedback systems in system theory. The MATLAB function mussv available in MATLAB Control Toolbox efficiently computes both lower and upper bounds of the μ -value. This article deals with the numerical approximations of the lower bounds of μ -values by means of low-rank ordinary differential equation (ODE)-based techniques. The numerical simulation shows that approximated lower bounds of μ -values are much tighter when compared to those obtained by the MATLAB function mussv.

A delay‐dependent asymptotic stability criteria for uncertain BAM neural networks with leakage and discrete time‐varying delays: A novel summation inequality

AbstractThis proposed research work aims to investigate the problem of uncertain BAM neural networks with leakage and discrete time‐varying delays in the sense of asymptotic stable by applying convex combination approach, discrete‐time Wirtinger inequality. It is pointed out that a novel summation inequality is entrenched based on discrete type Wirtinger based inequality. By the aid of novel inequality, reciprocally convex combination technique, time‐varying delays are examined to certify the stability of neural networks. Here, the uncertainties are considered as a randomly occurring parameter uncertainties and it conforms certain mutually uncorrelated Bernoulli‐distributed white noise sequences. The important feature of the results reported here is that the probability of occurrence of the parameter uncertainties are known a priori. To demonstrate the theoretical results of this research paper, numerical examples are given to expo the validity and efficiency of our results with the help of LMI Control toolbox in matlab.

Exponential stability of discrete-time uncertain neural networks with multiple time-varying leakage delays

In this paper, we investigate a new exponential stability criterion for uncertain discrete-time neural networks with both multiple leakage time-varying delays and discrete time-varying delays. Here for the first time leakage time varying delay is taken to be a multiple one and this does not exist in the literature. Based on the discrete-type Halanay inequality and some inequality techniques, a novel exponential stability criterion for uncertain discrete-time neural networks is derived in terms of LMIs. Then the LMIs can be easily manipulated by using LMI Control toolbox in Matlab. Finally few numerical examples along with simulative responses are given to strengthen our proposed stability results.

F13FUNCTIONAL ANALYSIS OF THE SCHIZOPHRENIA ASSOCIATED GENE AS3MT IN SH-SY5Y NEUROBLASTOMA CELLS

In this paper, we investigate a new exponential stability criterion for uncertain discrete-time neural networks with both multiple leakage time-varying delays and discrete time-varying delays. Here for the first time leakage time varying delay is taken to be a multiple one and this does not exist in the literature. Based on the discrete-type Halanay inequality and some inequality techniques, a novel exponential stability criterion for uncertain discrete-time neural networks is derived in terms of LMIs. Then the LMIs can be easily manipulated by using LMI Control toolbox in Matlab. Finally few numerical examples along with simulative responses are given to strengthen our proposed stability results.

Computing Structured Singular Values for Sturm-Liouville Problems

In this article we present numerical computation of pseudo-spectra and the bounds of Structured Singular Values (SSV) for a family of matrices obtained while considering matrix representation of SturmLiouville (S-L) problems with eigenparameter-dependent boundary conditions. The low rank ODE's based technique is used for the approximation of the bounds of SSV. The lower bounds of SSV discuss the instability analysis of linear system in system theory. The numerical experimentation show the comparison of bounds of SSV computed by low rank ODE'S technique with the well-known MATLAB routine mussv available in MATLAB Control Toolbox.

Numerical Computation of Lower Bounds of Structured Singular Values

In this article we consider the numerical approximation of lower bounds of Structured Singular Values, SSV. The SSV is a wellknown mathematical quantity which is widely used to analyse and syntesize the robust stability and instability analysis of linear feedback systems in control theory. It links a bridge between numerical linear algebra and system theory. The computation of lower bounds of SSV by means of ordinary differential equations based technique is presented. The obtained numerical results for the lower bounds of SSV are compared with the well-known MATLAB function mussv available in MATLAB control toolbox.

Enhanced result on stability analysis of randomly occurring uncertain parameters, leakage, and impulsive BAM neural networks with time‐varying delays: Discrete‐time case

SummaryIn real‐world problems, neural networks play an increasingly important role in terms of both theory and applications. In this paper, the asymptotic stability analysis issue is investigated for uncertain impulsive discrete‐time bidirectional associative memory neural networks with leakage and time‐varying delays. With the assistance of novel summation inequality, reciprocally convex combination technique, and triple Lyapunov‐Krasovskii functionals terms, many cases of time‐varying delays are examined to certify the stability of neural networks. Here, the uncertainties are considered as a randomly occurring parameter uncertainty, and it conforms certain mutually uncorrelated Bernoulli‐distributed white noise sequences. An important feature of the results reported here is that the probability of occurrence of the parameter uncertainties specify a priori estimate. Finally, numerical examples are proposed to expose the capability and efficiency of our research work with the help of the LMI control toolbox in MATLAB.

Design of Fuzzy Control for Tracking in Free Space Optical Communication

In order to track the beacon facular precisely in real time, a new method based on the self adjusting fuzzy-PID control is presented, which is suitable for ATP (acquisition, tracking, pointing) servo system for optical space communication. The advantages of fuzzy control and traditional PID control were combined in this method. The design method of fuzzy-PID controller is discussed. The design and simulation of the system were implemented by using the fuzzy control tool box in MATLAB. The comparison of the obtained result with that of the conventional PID controller was carried out. The simulation results show that the system is much better than the conventional PID controller, and the LOS (liner of light) stability of ATP system is improved.