Twin Rotor MIMO System Research Articles

Fixed-Time Fault-Tolerant Adaptive Neural Network Control for a Twin-Rotor UAV System with Sensor Faults and Disturbances

This paper presents a fixed-time fault-tolerant adaptive neural network control scheme for the Twin-Rotor Multi-Input Multi-Output System (TRMS), which is challenging due to its complex, unstable dynamics and helicopter-like behavior with two degrees of freedom (DOFs). The control objective is to stabilize the TRMS in trajectory tracking in the presence of unknown nonlinear dynamics, external disturbances, and sensor faults. The proposed approach employs the backstepping technique combined with adaptive neural network estimators to achieve fixed-time convergence. The unknown nonlinear functions and disturbances of the system are processed via an adaptive radial basis function neural network (RBFNN), while the sensor faults are actively estimated using robust terms. The developed controller is applied to the TRMS using a decentralized structure where each DOF is controlled independently to simplify the control scheme. Moreover, the parameters of the proposed controller are optimized by the gray-wolf optimization algorithm to ensure high flight performance. The system’s stability analysis is proven using a Lyapunov approach, and simulation results demonstrate the effectiveness of the proposed controller.

Robust PI-PD Controller Design: Industrial Simulation Case Studies and a Real-Time Application

PI-PD controllers have superior performance compared to traditional PID controllers, especially for controlling unstable and integrating industrial processes with time delays. However, computing the four tuning parameters of this type of controller is not an easy task. Recently, there has been significant interest in determining the tuning rules for PI-PD controllers that utilize the stability region. Currently, most tuning rules for the PI-PD controller are presented graphically, which can be time-consuming and act as a barrier to their industrial application. There is a lack of analytical tuning guidelines in the literature to address this shortfall. However, the existing analytical tuning guidelines do not consider a rigorous design approach. This work proposes new robust analytical tuning criteria based on predefined gain and phase margin bounds, as well as the centroid of the stability region. The proposed method has been tested using various simulation studies related to a DC–DC buck converter, a DC motor, and a heat exchanger. The results indicate that the proposed tuning rules exhibit strong performance against parameter uncertainty with minimal overshoots. Furthermore, the suggested technique for simultaneous control of yaw and pitch angles has been tested in a real-time application using the twin rotor multi-input multi-output system (TRMS). Real-time results indicate that, compared to other methods under investigation, the suggested approach provides nearly minimal overshoots.

Metaheuristic Algorithm-Based Proportional–Integrative–Derivative Control of a Twin Rotor Multi Input Multi Output System

Metaheuristic algorithms are computational techniques based on the collective behavior of swarms and the study of organisms acting in communities. These algorithms involve different types of organisms. Finding controller values for nonlinear systems is a challenging task using classical approaches. Hence, using metaheuristics to find the controller values of a twin rotor multi-input multi-output system (TRMS), one of the nonlinear systems studied in the literature, seems to be more appropriate than using classical methods. In this study, different types of metaheuristic algorithms were used to find the PID controller values for a TRMS, including a genetic algorithm (GA), a dragonfly algorithm, a cuckoo algorithm, a particle swarm optimization (PSO) algorithm, and a coronavirus optimization algorithm (COVIDOA). The obtained graphs were analyzed based on certain criteria for the main rotor and tail rotor angles to reach the reference value in the TRMS. The experimental results show that when the rise and settlement times of the TRMS are compared in terms of performance, the GA took 1.5040 s (seconds) and the COVIDOA took 9.59 s to increase the pitch angle to the reference value, with the GA taking 0.7845 s and the COVIDOA taking 2.4950 s to increase the yaw angle to the reference value. For the settling time, the GA took 11.67 s and the COVIDOA took 28.01 s for the pitch angle, while the GA took 14.97 s and the COVIDOA took 26.69 s for the yaw angle. With these values, the GA and COVIDOA emerge as the foremost algorithms in this context.

Complex‐step derivative‐based extended Kalman filter for state estimation in twin rotor MIMO system

AbstractThis paper presents the design of a complex‐step extended Kalman filter (CS‐EKF) to estimate the states of the twin‐rotor MIMO system (TRMS) which is a non‐linear system. Since the model of TRMS is quite complex and contains discontinuous functions, it is very difficult to calculate the Jacobian matrix in the TRMS analytically by hand. This makes it difficult to implement control methods that require Jacobian matrix calculation for TRMS. Herein, to calculate the Jacobian matrix, the CS‐EKF uses the complex‐step derivative approach, which is a numerical technique and offers near‐analytical accuracy in a single function evaluation. The effectiveness of the CS‐EKF is demonstrated through simulation and real‐time experiments. Also, The CS‐EKF is compared to the finite‐difference extended Kalman filter (FD‐EKF) and the unscented Kalman filter (UKF) in terms of estimation accuracy, computational load, and ease of implementation.

Survey of Advanced Nonlinear Control Strategies for UAVs: Integration of Sensors and Hybrid Techniques.

This survey paper explores advanced nonlinear control strategies for Unmanned Aerial Vehicles (UAVs), including systems such as the Twin Rotor MIMO system (TRMS) and quadrotors. UAVs, with their high nonlinearity and significant coupling effects, serve as crucial benchmarks for testing control algorithms. Integration of sophisticated sensors enhances UAV versatility, making traditional linear control techniques less effective. Advanced nonlinear strategies, including sensor-based adaptive controls and AI, are increasingly essential. Recent years have seen the development of diverse sliding surface-based, sensor-driven, and hybrid control strategies for UAVs, offering superior performance over linear methods. This paper reviews the significance of these strategies, emphasizing their role in addressing UAV complexities and outlining future research directions.

Improved Set-point Tracking Control of an Unmanned Aerodynamic MIMO System Using Hybrid Neural Networks

Artificial neural networks (ANN), an Artificial Intelligence (AI) technique, are both bio-inspired and nature-inspired models that mimic the operations of the human brain and the central nervous system that is capable of learning. This paper is based on a system that optimizes the performance of an uncertain unmanned nonlinear Multi-Input Multi-Output (MIMO) aerodynamic plant called Twin Rotor MIMO System (TRMS). The pitch and yaw angles which are challenging to control and optimize in practice, are being used as the input to the Nonlinear Auto-Regressive with eXogenous (NARX) model, and eventually trained. The training features use the Matlab Deep Learning Toolbox. The NARX structure has its core in the neural networks’ architecture. Data is collected from the TRMS testbed which is used to train the network. ANN as a Hybrid intelligent control strategy of ANN in combination with Pattern Search and Genetic Algorithm, is then utilized to optimize the parameters of the neural networks. At the end it was validated, tested and the optimized system run in simulation and compared with other intelligent and conventional controllers, with the proposed controller outperforming them, giving a very fast tracking control, stable and optimal performance that satisfactorily met all our design requirements.

A flexible mixed-optimization with H∞ control for coupled twin rotor MIMO system based on the method of inequality (MOI)- An experimental study.

This article introduces a cutting-edge H∞ model-based control method for uncertain Multi Input Multi Output (MIMO) systems, specifically focusing on UAVs, through a flexible mixed-optimization framework using the Method of Inequality (MOI). The proposed approach adaptively addresses crucial challenges such as unmodeled dynamics, noise interference, and parameter variations. Central to the design is a two-step controller development process. The first step involves Nonlinear Dynamic Inversion (NDI) and system decoupling for simplification, while the second step integrates H∞ control with MOI for optimal response tuning. This strategy is distinguished by its adaptability and focus on balancing robust stability and performance, effectively managing the intricate cross-coupling dynamics in UAV systems. The effectiveness of the proposed approach is validated through simulations conducted in MATLAB/Simulink environment. Results demonstrated the efficiency of the proposed robust control approach as evidenced by reduced steady-state error, diminished overshoot, and faster system response times, thus significantly outperforming traditional control methods.

Synchronous Pitch and Yaw Orientation Control of a Twin Rotor MIMO System Using State Varying Gain Sliding Mode Control

Synchronous Pitch and Yaw Orientation Control of a Twin Rotor MIMO System Using State Varying Gain Sliding Mode Control

Synthesis of Adaptive Sliding Mode Control for Twin Rotor MIMO System with Mass Uncertainty based on Synergetic Control Theory

In this paper, the authors present a new method to synthesize an adaptive sliding controller for Twin Rotor MIMO System (TRMS) based on Synergetic Control Theory (SCT). This system represents a prototype of a helicopter with two degrees of freedom and is widely used in automatic control laboratories. The complexity of the control problem is due to the nonlinear cross-coupling between the main and tail rotors. Uncertainty in system parameters further increases the complexity of the control problem. In Synergetic Control Theory, manifolds are designed for each channel. The control law is found based on sequential manifolds and the Analytical Design of Aggregated Regulators (ADAR) method. The adaptive law when the parameters are uncertain is given based on the analysis of system stability thanks to the Lyapunov function of the first manifold. Finally, the effectiveness of the proposed controller is demonstrated by numerical simulation results and comparison with conventional Sliding Mode Control (SMC).

Bio-Inspired Jumping Spider Optimization for Controller Tuning/ Parameter Estimation of an Uncertain Aerodynamic MIMO System

The practical near impossibility of empirical attempts in estimating optimal controller gains makes the use of metaheuristics strategies inevitable to automatically obtain these gains by an iterative, heuristic simulation procedure. The convergence of the gains values to the local or global solutions occur with ease. In designing controllers for the Twin-Rotor MIMO System (TRMS), Jumping Spider Optimization Algorithm (JSOA), a novel neoteric population-based bio-inspired metaheuristic approach is used to obtain optimum values for the Proportional, Integral and Derivative (PID) controllers. With the k,p,i controller gains as the decision variables, the JSOA solution to a nonlinear multi-objective optimization problem subject to some intrinsic constraints spawned optimal values for the controllers’ variables. Counter to other algorithms (deterministic and stochastic) that get caught in local minima, JSOA evolved a solution after searchingly rummaging the entire solution search space in a vectorized fashion for an optimal value. Compared with several other versatile controllers (using GA, PSO, Pattern Search and Simulated Annealing), statistical results obtained showed JSOA technique provided a unique solution and found the gains of the PID controllers, marginally in relation to the others (optimization methods).

Multiple-model adaptive explicit predictive control for nonlinear MIMO system

This work is to develop a blending-based multiple model adaptive explicit predictive control scheme for nonlinear MIMO systems that can handle parametric uncertainties. Here, for each identification model, an explicit nonlinear model predictive control (ENMPC) law is computed in advance for the corresponding model. The generated control inputs from the set of ENMPC controllers are being blended online using a weighting vector that is continuously updated by the proposed adaptive identification schemes. The proposed control scheme is used to govern the tracking of a highly nonlinear helicopter model known as the twin rotor MIMO system (TRMS). Here, an extended Kalman filter (EKF) is used to estimate the unavailable states of the TRMS. Finally, simulation and experimental results are presented to prove that the proposed controller gives better performance than some reported works in the literature. The effectiveness of the proposed controller is demonstrated by experimental studies of the TRMS model.

Design of sliding mode control with state varying gains for a Benchmark Twin Rotor MIMO System in Horizontal Motion

In this paper, a sliding mode control (SMC) with state-varying gains is proposed to control the yaw orientation of the Twin Rotor MIMO System (TRMS). This proposed SMC algorithm reduces the chattering effect without affecting the properties of the robustness of the sliding modes. The salient feature of this control is that the magnitude of the variable gains depends on the absolute values of the states and tracking error. This design exhibits a relation between first-order and higher-order sliding mode control algorithms. Besides, the developed control strategy does not overestimate disturbances. Hence, the energy utilized by the control effort is reduced significantly. The stability analysis is accomplished by considering the TRMS model in the horizontal plane to illustrate the asymptotic stability condition. Further, a comparison between the twisting algorithm and the proposed control law is highlighted. However, it is evinced that the proposed variable gain SMC is a combination of a twisting algorithm and conventional SMC. Simulations studies are carried out to highlight the efficacies of the proposed controller using MATLAB/Simulink environment.

Constrained Model Predictive Control With Integral Action for Twin Rotor MIMO Systems

Abstract This paper describes the design and successful implementation of a constrained model predictive controller with integral action for the control of a Twin Rotor MIMO System (TRMS). The integral action guarantees zero steady-state error in set-point tracking with robustness toward perturbations of the nominal system parameters. In addition to saturation constraints on the input variables, hard constraints are imposed on the controlled output variables, i.e., on pitch and yaw angular positions, to avoid collisions with obstacles. The model predictive controller was designed using a high-fidelity nonlinear model of the TRMS developed in previous work. As an intermediate step, exact linearized models of the TRMS are obtained and their closed-form expressions are reported. The controller was tested experimentally, also showing its effectiveness in ensuring actual collision avoidance by the TRMS when physical obstacles were present.

Pitch orientation control of twin-rotor MIMO system using sliding mode controller with state varying gains

This work presents the controlling of the pitch orientation of a twin-rotor multi-input multi-output system (TRMS) using the sliding mode control (SMC) technique with variable gains. In this, the SMC is designed using variable gains where the pitch orientation error of the vertical dynamics of the TRMS system is intended to render the control law. The magnitude of the variable gains is related to the absolute value of the tracking error. Further, this technique minimised the chattering effect by ensuring the robustness property of the sliding modes. This design establishes a relationship between first and higher-order SMCs. The proposed controller is adapted from the twisting algorithm (TA) and conventional SMC. The control algorithm does not overestimate disturbances, resulting in a large reduction in control energy. Finally, a Lyapunov stability analysis is devised to demonstrate asymptotic stability. Simulations demonstrate the pitch orientation control and robustness of the proposed control scheme.

Real-time robust generalized dynamic inversion based optimization control for coupled twin rotor MIMO system

This work is used to design a novel robust optimization control law augmented with Robust Generalized Dynamic Inversion (RGDI) for continuous varying perturbations in the Twin Rotor MIMO System (TRMS). The perturbations like coupling effect, un-known states, gyroscopic disturbance torque, parametric uncertainties and parametric disturbances are considered as unwanted signal which should be optimized by an efficient controller. The variable structured systems like the TRMS (prototype) have great focus due to its high computational cost with a higher order non-linear behavior. The RGDI based controller designed to remove nonlinear dynamics as well as to avoid singularity issue with the augmentation of stability based mathematical operations (lyapunov stability analysis, controllability and observability matrices ) in the presence of considered perturbations during implementation. In this paper, we develop estimation of state deviation calculation between control angles and desired angles known as Euclidean error norm. The next step was to design RGDI based controller [Sliding Mode Control (SMC) and {H_infty } optimization] to minimize considered perturbations as well as the computational cost. The sharp (rapid) chattering phenomena in RGDI based SMC reduce the actuators performance that goes towards the failure of actuators. While the RGDI based {H_infty } optimization overcome the computational cost and minimizes {H_infty } norm that’s guaranteeing the robust stability as well as robust performance. The robustness of the optimization control technique validated by taking its worst case via MATLAB-Simulation. A real-time implementation applied to evaluate the worth of novel dynamic approach.

Nonlinear disturbance observer-based adaptive nonlinear model predictive control design for a class of nonlinear MIMO system

Model predictive control with less prior knowledge of system uncertainty and external disturbance is a long-standing theoretical and practical problem. In this paper, a solution is presented by proposing a disturbance observer-based adaptive nonlinear model predictive control scheme for a class of nonlinear MIMO systems. Our scheme requires the state and parameterdependent state-space model to linearise the nonlinear system along the prediction horizon. To cope with the unknown system uncertainty, the multiple estimation model and the concept of second-level adaptation [Pandey, V. K., Kar, I., & Mahanta, C. (2014). Multiple models and second level adaptation for a class of nonlinear systems with nonlinear parameterisation. In Industrial and Information Systems (ICIIS), 2014 9th International Conference on (pp. 1–6). IEEE.] technique for the nonlinear system is used. To ensure the boundedness of the estimated parameter, a projection-based adaptive law [Hovakimyan, N., & Cao, C. (2010). L1 adaptive control theory: Guaranteed robustness with fast adaptation. SIAM.] is used. Using a twin-rotor MIMO system (TRMS), the effectiveness of the proposed control algorithm has been verified. Simulation and real-time results show that the proposed control algorithm performs better than the existing control algorithm in the presence of unknown external disturbance and parameter uncertainties.

A simple modelling strategy for integer order and fractional order interval type-2 fuzzy PID controllers with their simulation and real-time implementation

This paper presents a simple approach to the mathematical modelling of the Integer Order (IO) and Fractional Order (FO) Interval Type-2 Fuzzy Proportional Integral Derivative (IT2FPID) controllers. In this approach, the control effort produced by the IT2FPID controller is obtained by combining the individual control efforts generated by the Interval Type-2 Fuzzy Proportional (IT2FP), Interval Type-2 Fuzzy Integral (IT2FI), and Interval Type-2 Fuzzy Derivative (IT2FD) controllers. The analytical structures of each of the IT2FPID components are unveiled using one-dimensional (1D) input space and without using any AND or OR operator. To the best of the authors’ knowledge, such a strategy was never used and is completely new for the modelling of the IT2FPID controllers. Properties, computational issues, and design guidelines of the newly obtained controllers are discussed, and their applicability is delineated using five simulation examples and one experimental case study. A chemical reactor plant, two fractional order plants, a nonlinear plant, and a Twin Rotor Multi Input Multi Output System (TRMS) are considered in the simulation study. The experimental study is conducted on an unstable nonlinear Magnetic Levitation System (MLS). Moreover, to exhibit the usefulness of the newly derived controllers, simulation and real-time results are also compared with the existing results available in the literature. As the proposed controllers are plant model-free, they can be used for other control applications also.

Nonlinear disturbance observer‐based adaptive feedback linearized model predictive controller design for a class of nonlinear systems

AbstractAdaptive control with less prior information of a nonlinear system subjected to external disturbance and parametric uncertainties is a longstanding problem in the control community. In this paper, a nonlinear disturbance observer‐based adaptive feedback linearized model predictive control (NDO‐AFLMPC) technique is proposed for a class of nonlinear MIMO systems. In this approach, a nonlinear disturbance observer (NDO) is used to observe the external disturbance of the system. A suitable constraint mapping algorithm is developed to map the input–output constraints within the proposed control scheme. Here, a multiple estimation model and the concept of second‐level adaptation technique is used to handle the parametric uncertainty of the real‐time plant. The boundedness of the estimated parameter is solved by developing the projection‐based parameter adaptation laws. Using an aerodynamic laboratory set‐up, known as the twin‐rotor MIMO system (TRMS), the effectiveness of the proposed control algorithm is verified. The complete state information of the real‐time system is provided to the proposed adaptive controller from an extended Kalman filter (EKF)‐based state observer. The performance of the proposed control algorithm is compared with other existing nonlinear control algorithms in the presence of unknown external disturbance and parametric uncertainties.

Small signal model designing and robust decentralized tilt integral derivative TID controller synthesizing for twin rotor MIMO system

Small signal model designing and robust decentralized tilt integral derivative TID controller synthesizing for twin rotor MIMO system

Generalized discrete decoupling and control of MIMO systems

AbstractThis paper proposes an efficient discrete‐time decoupling algorithm for multiple input multiple output (MIMO) systems having strong coupling between inputs and outputs. A design method for discrete decouplers is proposed to eliminate the cross‐coupling effects present in MIMO systems. The proposed decoupling technique is based on relative gain array (RGA) approach of MIMO system. In order to perform closed‐loop control, individual discrete‐time PID controllers are designed based on Kharitonov theorem for each of the SISO control loops of the resulting decoupled MIMO system. The closed‐loop performance of the MIMO system under consideration is investigated in simulation and in real time which illustrate that the proposed decoupling algorithm satisfactorily nullifies the interaction between the inputs and outputs. The control scheme exhibits perfect tracking of the reference commands even in presence of disturbances. Twin rotor MIMO system (TRMS) is considered as the real‐time example to validate the proposed method. Further, the performance of the compensated TRMS system is analyzed in frequency domain in presence of common actuator nonlinearities dead zone and saturation together. The performances of the controllers are found to be efficient even in presence of actuator nonlinearities.