Nonlinear Control Analysis Research Articles

Partial Control of a Continuous Bioreactor: Application to an Anaerobic System for Heavy Metal Removal

This work presents a control strategy for a continuous bioreactor for heavy metal removal. For this aim, regulation of the sulfate concentration, which is considered the measured and controlled state variable, allowed diminishing the cadmium concentration in the bioreactor, where the corresponding controller was designed via nonlinear bounded function. Furthermore, a nonlinear controllability analysis was done, which proved the closed-loop instability of the inner or uncontrolled dynamics of the bioreactor. A mathematical model, experimentally corroborated for cadmium removal, was employed as a benchmark for the proposed controller. Numerical experiments clearly illustrated the successful implementation of this methodology; therefore, cadmium removal amounted to more than 99%, when the initial cadmium concentration was up to 170 mg/L in continuous operating mode.

Agent Based Fuzzy T-S Multi-Model System and Its Applications

Based on the basic concepts of agent and fuzzy T-S model, an agent based fuzzy T-S multi-model (ABFT-SMM) system is proposed in this paper. Different from the traditional method, the parameters and the membership value of the agent can be adjusted along with the process. In this system, each agent can be described as a dynamic equation, which can be seen as the local part of the multi-model, and it can execute the task alone or collaborate with other agents to accomplish a fixed goal. It is proved in this paper that the agent based fuzzy T-S multi-model system can approximate any linear or nonlinear system at arbitrary accuracy. The applications to the benchmark problem of chaotic time series prediction, water heater system and waste heat utilizing process illustrate the viability and the efficiency of the mentioned approach. At the same time, the method can be easily used to a number of engineering fields, including identification, nonlinear control, fault diagnostics and performance analysis.

Absolute stability analysis of non‐linear active disturbance rejection control for single‐input–single‐output systems via the circle criterion method

This study focuses on the stability analysis of non-linear active disturbance rejection control (ADRC) for single-input–single-output systems. Firstly, a non-linear ADRC system for a linear plant is transformed into a Lurie system. Secondly, two extended circle criteria are obtained, and two numerical examples are presented to illustrate the absolute stability analysis, including both stable and unstable linear plants. Thirdly, local asymptotic stability of a non-linear ADRC system for a non-linear plant is also performed through linearisation by Taylor expansion. Finally, a comparison with the existed processing methods is further made, including the describing function method and time domain stability analysis method. It can be concluded that the circle criterion method is more convenient and practical for its frequency domain and graphical interpretation. The circle criterion method can also be extended to the stability analysis of a control system which applies linear ADRC to a plant with one non-linear term.

Modeling and Analysis of Robust Nonlinear Controller for Three Phase Grid Connected System Under Structured Uncertainties

Modeling and Analysis of Robust Nonlinear Controller for Three Phase Grid Connected System Under Structured Uncertainties

Numerical Time-Scale Separation for Rotorcraft Nonlinear Optimal Control Analyses

This paper proposes a numerical technique for an efficient nonlinear optimal control analysis in which the system dynamics presents multiplicity in its time scale corresponding to a high-fidelity rotorcraft model. For this purpose, the integration of the fast dynamics is carried out separately from the integration of the slow dynamics using a pseudospectral method. The resultant nonlinear programming problem can be efficiently solved with a small number of computational nodes for the slow dynamics without degrading the fidelity of the original model. The integration process of each dynamics uses different nodes and shares the information for the states and controls by means of local Lagrange interpolation. In the algorithm implementation, the moving horizon approach and residualization method are investigated to guarantee solution convergence and to preserve the sensitivity of the cost and constraint functions to the slow states, respectively. To verify the proposed approach, two simulation studies are presented. First, the dynamic responses of the Bo-105 helicopter due to longitudinal doublet inputs are analyzed, which successfully provide the same level of integration accuracy as the Runge–Kutta method. Second, an optimal autorotational landing problem is considered as an example to prove the effectiveness of the proposed time-scale separation technique.

Simulation Analysis of Non-Linear Fuzzy PID Temperature Controller

The objectives of the project are to simulate linear Mamdami type fuzzy temperature controller and non-linear Takegi-Sugeno type fuzzy temperature controllers using MATLAB and Simulink, and to compare the performance between the two controllers. A case study has been created to test the controllers involved a water boiler, where the system is modeled using Joules Law and Law of Thermodynamics. A Proportional-Integral-Derivative (PID) controller was tuned and the PID parameters were then used to obtain the gain of the fuzzy controllers. Simulation results confirmed that non-linear fuzzy controller has smaller overshoot and faster settling time compared to the linear fuzzy controller and PID controller, although an extra derivative gain may be needed for the non-linear fuzzy controller if the integral term is huge enough to affect the stability of the system.

Simulation and Experimentation of a Precise Nonlinear Tracking Control Algorithm for a Rotary Servo-Hydraulic System With Minimum Sensors

The dynamics of hydraulic systems involves slow and fast modes. These modes are associated with the mechanical components and those involving fluid flow, respectively. As such, controllers for electro-hydraulic servo systems (EHSS) can be designed and analyzed using singular perturbation theory. In this paper, a singular perturbation control (SPC) algorithm is proposed and investigated on a rotary EHSS modeled based on a two-time-scale behavior of the system. For modeling, the components of the hydraulic system, specifically the nonlinear model of the orifice in servo valve, are modeled. A mathematical modeling and nonlinear control analysis that validated by experiment is presented. The controlled system with the SPC algorithm tracks a fairly smooth trajectory with very small error. As well, the control algorithm is successfully verified by experiment as the main contribution of the paper. In addition, this is robust to variations in the hydraulic fluid bulk modulus such that only its nominal value is sufficient. Furthermore, the proposed control design will not require derivatives of the control pressures and any output acceleration feedback. Hence, it can be implemented easier in the real system setup. The controller design approach addresses the nonlinearities of the rotary EHSS. The parameters of the real system model are experimentally identified using the continuous recursive least square method.

Analysis of Bifurcation and Nonlinear Control for Chaos in Gear Transmission System

In order to study the bifurcation characteristics and control chaotic vibration of the gear transmission system. The complex dynamics characters of gear transmission system are studied. The dynamical equation and the state equation of gear transmission system are established according to Newton's rule. The route to chaos of the system is studied by the bifurcation diagram, phase portrait, time course diagram and Poincaré map. A method of controlling chaos by nonlinear feedback controller is developed to guide chaotic motions towards regular motions. Numerical simulation shows that with the increase of meshing stiffness, gear transmission system will be from the periodic motion to chaotic motion by doubling bifurcation, the effectiveness and feasibility of the strategy to get rid of chaos by stabilizing the related unstable periodic orbit.

Nonlinear Model-Based Approach for Accurate Stability Prediction of One-Bit Higher-Order Delta–Sigma Modulators

The current approaches on predicting the stability of delta-sigma (Δ-Σ) modulators are mostly confined to dc inputs. This poses limitations as practical applications of Δ-Σ modulators involve a wide range of signals other than dc. In this paper, a quasi-linear model for Δ-Σ modulators with nonlinear feedback control analysis is presented, which accurately predicts the stability of higher-order single-loop 1-bit Δ-Σ modulators for various types of input signals, such as single sinusoids, dual sinusoids, multiple sinusoids, and Gaussian. Theoretical values are shown to match closely with simulation results. The results of this paper would significantly speed up the design and evaluation of higher-order single-loop 1-bit Δ-Σ modulators for various applications, including those that may require multiple-sinusoidal inputs or any general input composed of a finite number of sinusoidal components, circumventing the need to perform detailed time-consuming simulations to quantify stability limits. By using the proposed method, the difference between the predicted and the actual stable amplitude limits results in an error of less than 1 dB in the in-band signal-to-noise ratio for the third-order and higher-order Δ-Σ modulators for single-sinusoidal inputs. For single-sinusoidal, dual-sinusoidal, multiple-sinusoidal, and Gaussian inputs, the error is less than 2 dB for the fifth-order modulator and reduces to less than 1 dB for the sixth-order and higher-order Δ-Σ modulators.

The Lagrange Mechanization and Application of Multi-Machine Power System

The fast development of Hamilton system theory provides a powerful tool for the nonlinear control and stability analysis of power system. The construction of Hamilton function plays an important role in Hamilton realization. Based on Hamilton canonical equations, the energy integration of system is given. This paper expands the odd-order power system to even-order system and gives the responding conditions of Hamilton realization by using the self-adjoint methods of analytical mechanics. Besides, the standard Hamilton form of power system is derived by the combinations of Lagrange mechanization and Hamilton theory, and the form of Hamilton function is also given. Based on non-conservative analytical mechanical principles, the controllers are designed in allusion to the characteristics of power system and Matlab program is realized in IEEE3-9 standard system. The simulation effects are discussed in the transient conditions of three-phase fault by comparison of different approaches, which proves the effectiveness of the control strategy. This approach to construct Hamilton function and design the controllers has an extensive prospect of application

Observer-Based Nonlinear Feedback Controls for Heartbeat ECG Tracking Systems

The analysis and design of observed-based nonlinear control of a heartbeat tracking system is investigated in this paper. Two of Zeeman’s heartbeat models are investigated and modified by adding the control input as a pacemaker, thereby creating the control-affine nonlinear system models that capture the general heartbeat behavior of the human heart. The control objective is to force the output of the heartbeat models to track and generate a synthetic electrocardiogram (ECG) signal based on the actual patient reference data, obtained from the William Beaumont Hospitals, Michigan, and the PhysioNet database. The formulations of the proposed heartbeat tracking control systems consist of two phases: analysis and synthesis. In the analysis phase, nonlinear controls based on input-output feedback linearization are considered. This approach simplifies the difficult task of developing nonlinear controls. In the synthesis phase, observer-based controls are employed, where the unmeasured state variables are estimated for practical implementations. These observer-based nonlinear feedback control schemes may be used as a control strategy in electronic pacemakers. In addition, they could be used in a software-based approach to generate a synthetic ECG signal to assess the effectiveness of diagnostic ECG signal processing devices.

Accurate stability prediction of one-bit higher-order delta–sigma modulators for multiple-sinusoidal inputs

The present approaches on predicting stability of delta-sigma (Δ-Σ) modulators are mostly confined to DC inputs. This poses limitations as practical applications of Δ-Σ modulators involve a wide range of signals other than DC such as multiple-sinusoidal inputs for speech modelling. In this study, a quasi-linear model for Δ-Σ modulators with non-linear feedback control analysis is presented that accurately predicts stability of single-loop one-bit higher-order Δ-Σ modulators for multiple sinusoids. Theoretical values are shown to match closely with the simulation results. The results of this study would significantly speed up the design and evaluation of higher-order single-loop Δ-Σ modulators with increased dynamic ranges for various applications that require multiple-sinusoidal inputs or any general input composed of a finite number of sinusoidal components.

Efficient Nonlinear Wind-Turbine Modeling For Control Applications

AbstractA simple nonlinear model for variable pitch wind turbines is described. The model is aimed specifically at nonlinear control design and analysis. We propose a parametric model and subsequently describe a method to determine the parameters for any turbine that falls into the scope of the model. The result is a model that describes a turbine rotor, which is free to move in all six degrees of freedom. This freedom is required to model the new breed of floating offshore turbines. The resulting model is compared to experimental data with good results. Cyclic forces at large yaw offsets are not modeled well, however. Limitations of the model are discussed.

Stability Analysis of Constrained Nonlinear Model Predictive Control with Terminal Weighting

This paper investigates stability of model predictive control (MPC) for nonlinear constrained systems. New stability results for the MPC algorithms with terminal weighting are proposed using the dynamic programming method, which gives new criteria for choosing state, control and terminal weighting in the performance index to achieve stability of MPC algorithms. Illustrative examples are given to show that by combining this condition with existing ones, much less conservative results can be generated.

Nonlinear Control and Model Analysis of Trirotor UAV Model

AbstractThis paper reveals the minimal number of inputs for hovering control from the perspective of nonlinear control system theory. Then, a nonlinear controller is designed to obtain meaningful motion for an underactuated UAV with the consideration of the limitation acknowledged through the model analysis. Throughout this paper, a particular UAV model having three rotors is considered as a controlled object. First, nonlinear state equations are computed with valid assumptions. Next, the model analysis reveals that hovering control is impossible for not only the proposed model but also a generic three-inputs model through the argument of Locally Asymptotically Stabilizability(LAS). Finally, numerical simulation confirms that position control is realizable via Output Zeroing Control along with preferable attitude.

Nonlinear Control Analysis of an ICU Model for Tight Glycaemic Control

AbstractIntensive care is one of the most challenging areas of modern medicine. Maintenance of glucose levels in intensive care unit (ICU) patients via control of insulin inputs is an active research field. Accurate metabolic system models are a critical element of automatic control. Different ICU models appeared in the literature some of them already validated in clinical trials. The current paper analyzes and gives a nonlinear synthesis of a frequently used ICU metabolic system model's redefined version. The model has been already validated in clinical trials. Global control characteristics are determined using nonlinear analysis. Results of reachability and observability are explained regarding physiological meanings, and then exact linearization is computed. Finally, quasi affine linear parameter varying (qALPV) modeling methodology is applied and compared with results obtained by exact linearization. It is demonstrated that inside the chosen scheduling parameters’ vertex the qAPLV model represents the nonlinear system itself without any approximation. Conclusions are drawn from this analysis for further robust nonlinear model based controller design.

Nonlinear multivariable control and performance analysis of an air-handling unit

To maintain satisfactory comfort conditions in buildings with low energy consumption and operation cost, control of air-conditioner units is required. In this paper, nonlinear control of an air-handling unit (AHU) is investigated and compared for two control approaches: gain scheduling and feedback linearization. A nonlinear multi input–multi output model (MIMO) of an air-handling unit (AHU) is considered. Both indoor temperature and relative humidity are controlled via manipulation of valve positions of air and cold water flow rates. Using an observer to estimate state variables, a hybrid control system including regulation system for disturbance rejection and nonlinear control system for tracking objectives is designed. Achievement of tracking objectives is investigated for various desired commands of indoor temperature and relative humidity; including a sequence of steps and ramps-steps. According to results, more quick time responses with a bit more overshoot in tracking set-points/paths are achieved by using feedback linearization method (especially for temperature). However, valves position as input control signals are associated with less oscillation (and consequently less energy consumption) when the controller designed based on gain scheduling approach is used. Finally, it is shown through phase portrait of the system that the controller designed based on feedback linearization shows a robust performance in the presence of random uncertainty in model parameters.

Nonlinear Control Analysis of Nonholonomic Kinematic Systems with Affine Constraints

Nonlinear Control Analysis of Nonholonomic Kinematic Systems with Affine Constraints

Stability analysis of genetic regulatory network with additive noises

BackgroundGenetic regulatory networks (GRN) can be described by differential equations with SUM logic which has been found in many natural systems. Identification of the network components and transcriptional rates are critical to the output behavior of the system. Though transcriptional rates cannot be measured in vivo, biologists have shown that they are alterable through artificial factors in vitro.ResultsThis study presents the theoretical research work on a novel nonlinear control and stability analysis of genetic regulatory networks. The proposed control scheme can drive the genetic regulatory network to desired levels by adjusting transcriptional rates. Asymptotic stability proof is conducted with Lyapunov argument for both noise-free and additive noises cases. Computer simulation results show the effectiveness of the control design and robustness of the regulation scheme with additive noises.ConclusionsWith the knowledge of interaction between transcriptional factors and gene products, the research results can be applied in the design of model-based experiments to regulate gene expression profiles.

Nonlinear control and stability analysis of spacecraft attitude recovery

The problem of automated attitude recovery of rigid and flexible spacecraft is investigated using feedback linearization control and a novel approach for generating the control error signal based on quaternion addition. The attitude and flexible dynamics equations for a class of spacecraft is presented. The resulting nonlinear and coupled equations of the system are implemented into a high-fidelity user-friendly simulation environment. The simulator is used for the investigation of attitude recovery of flexible spacecraft using the feedback linearization approach. Since the flexible spacecraft is underactuated, the input-output linearization technique was specifically used to break up the system into two distinct parts, namely 1) an external linearizable system for which a linear controller can be easily implemented, and 2) an internal nonlinear unobservable system for which the associated zero dynamics is shown to be asymptotically stable for two representative cases. The overall closed-loop stability of the flexible spacecraft is analyzed rigorously and shown to be asymptotically stable using Lyapunov's method