Robust Nonlinear Control Design Research Articles

Robust nonlinear multivariable tracking control design to a manipulator with unknown uncertainties using operator-based robust right coprime factorization

In this paper, an operator-based robust nonlinear multivariable tracking control for a manipulator with uncertainties is proposed by using a robust right coprime factorization approach. In general, there exist unknown modelling errors in measuring structural parameters of the manipulator and external disturbances in real situations. In the present control system design, the effect of the modelling errors and disturbance on system performance is considered to be uncertainties in the manipulator dynamics. Considering the uncertainties, an operator-based robust nonlinear multivariable tracking control using robust right coprime factorization is studied. That is, firstly a robustly stable control based on robust right coprime factorization is designed. Secondly, a robust nonlinear multivariable tracking system is proposed for improving the trajectory of the manipulator, and the output tracking performance is evaluated based on the exponential iteration theorem. Finally, the effectiveness of the designed system is confirmed by simulation results.

Robust Optimal Control of MAV Based on Linear-Time Varying Decoupled Model Dynamics

This paper discusses a nonlinear robust control design procedure to micro air vehicle that uses the singular value (μ) and μ-synthesis technique. The optimal robust control law that combines a linear parameters varying (LPV) of UAV (unmanned aerial vehicle) are realized by using serial connection of the Kestrel autopilot and the Gumstix microprocessor. Thus, the robust control feedback loops, which handle the uncertainty of aerodynamics derivatives, are used to ensure robustness stability of the UAV local dynamics in longitudinal and lateral control directions.

Robust non-linear control design to an ionic polymer metal composite with hysteresis using operator-based approach

In this article, robust non-linear control design to an ionic polymer metal composite (IPMC) with hysteresis, uncertainties and input constraints is studied. The IPMC is a novel smart polymer material, and many potential applications for low mass high displacement actuators in biomedical and robotic systems have been shown. In general, the IPMC has highly non-linear property and hysteretic behaviour, and the control input is subject to some constraints to ensure safety and longer service life of IPMC. Moreover, there exist uncertainties caused by identifying some physical parameters and approximate calculation in dynamic model. As a result, considering measurement error of parameters and model error, a practical non-linear model is obtained, and a non-linear robust control design with hysteresis, uncertainties and input constraints using operator-based robust right coprime factorisation is proposed for an IPMC setup, where, the Prandtl–Ishlinskii (PI) model is used to describe the hysteresis, and which is identified using experimental data. The effectiveness of the proposed control method based on obtained non-linear model is confirmed by simulation and experimental results.

Feedback linearization-based robust nonlinear control design for hypersonic flight vehicles

A new approach to designing a robust nonlinear controller for longitudinal flexible body models of canard configured air-breathing hypersonic flight vehicles with significant couplings and interactions is presented. The methodology uses a robust feedback linearization method to feedback linearize the nonlinear air-breathing hypersonic flight vehicle model with 24 uncertainty parameters. Using this approach, a linearized uncertainty model of the air-breathing hypersonic flight vehicle is obtained in the first step by considering an upper bound on each uncertain parameter. In the second step, a minimax linear quadratic regulator-based velocity and altitude robust tracking controller is synthesized for the linearized model. Simulation studies are conducted using the original nonlinear model of the air-breathing hypersonic flight vehicle with a large flight envelope and time-varying uncertainties. Simulation results show that the feedback linearization-based minimax linear quadratic regulator controller effectively achieves the tracking requirement and robustly stabilizes the air-breathing hypersonic flight vehicle.

Nonlinear robust control of integrated vehicle dynamics

A new methodology to design the vehicle GCC (global chassis control) nonlinear controller is developed in this paper. Firstly, to handle the nonlinear coupling between sprung and unsprung masses, the vehicle is treated as a mechanical system of two-rigid-bodies which has 6 DOF (degree of freedom), including longitudinal, lateral, yaw, vertical, roll and pitch dynamics. The system equation is built in the yaw frame based on Lagrange's method, and it has been proved that the derived system remains the important physical properties of the general mechanical system. Then the GCC design problem is formulated as the trajectory tracking problem for a cascade system, with a Lagrange's system interconnecting with a linear system. The nonlinear robust control design problem of this cascade interconnected system is divided into two H ∞ control problems with respect to the two sub-systems. The parameter uncertainties in the system are tackled by adaptive theory, while the external uncertainties and disturbances are dealt with the H ∞ control theory. And the passivity of the mechanical system is applied to construct the solution of nonlinear H ∞ control problem. Finally, the effectiveness of the proposed controller is validated by simulation results even during the emergency manoeuvre.

Robust Nonlinear Control Design with Application to a Marine Cooling System

In this paper we consider design of control laws for a marine cooling system with flow dependent delays by use of principles from feedback linearization. To deal with model uncertainties and delay mismatches, a robust linear H∞ controller is designed for the feedback linearized system. In this context, we apply a bilinear transformation to obtain a well-posed H∞ problem. Robustness of performance for the resulting robust nonlinear control design is evaluated through a simulation example where a comparison is made to a linear control design.

Operator-based robust nonlinear control and its realization for a multi-tank process by using a distributed control system

In this paper, a robust nonlinear control design method using an operator-based robust right coprime factorization approach and its realization based on a distributed control system (DCS) device are considered for a multi-tank process. In detail, for the multi-tank process, consisting of a water-level process and a water-flow process, theoretical models are developed according to the Bernoulli theorem. Based on the obtained models, a robust nonlinear feedback control design is presented by using robust right coprime factorization for the multi-tank process. Further, from a large-scale industrial application viewpoint, the realization of the designed operator-based robust right coprime factorization controllers is considered by using a DCS device. Because there are some nonlinear functions in the designed controllers which cannot be realized straightforwardly in the DCS device such that the designed controllers need to be realized approximately. That is, there exist some parasitic terms for the approximated realization of the controllers in the real system. As a result, the parasitic terms and processes’ unknown uncertainties should be considered simultaneously. In this paper, a robust condition is derived to guarantee robust stability of the nonlinear feedback control system with the parasitic terms and the uncertainties. Moreover, tracking controller design problem for the multi-tank process is discussed. Finally, by using a DCS device (CENTUM CS3000), experimental results are given to confirm the effectiveness of the proposed design scheme.

Operator-based robust nonlinear control and fault detection for a Peltier actuated thermal process

In this paper, operator-based robust nonlinear control design scheme and fault detection technique using robust right coprime factorization approach are considered for a Peltier actuated thermal process. The Peltier actuated thermal process is a typical nonlinear control affine system, where the process temperature depends not only on input current, but also on the square of the input current. In addition, the real system is likely to contain a fault signal owing to various factors. As a result, it is difficult to stabilize the control system and to achieve high accurate control performance, and to detect the fault signal to guarantee the engineering safety when a fault occurs. In this paper, for pursuing robust stability and tracking performance of the nonlinear closed-loop control system, a design scheme of operator-based robust tracking control system is proposed by using robust right coprime factorization approach. Then, for the tracking operator control system, a fault detection design technique based on robust right coprime factorization approach is also investigated. Finally, simulation and experimental results are given to confirm the effectiveness of the proposed method.

Robust stabilization for nonholonomic systems with state delay and nonlinear drifts

This paper presents a control strategy for stabilization of the nonholonomic control systems with strongly nonlinear drifts and state delay. Applying a novel Lyapunov functional and backstepping recursive method, the design of robust nonlinear state feedback controllers is proposed, which can guarantee the stability of the closed-loop systems. Finally, a numerical example is provided to show the effectiveness of the method.

Guaranteed cost control of stochastic uncertain systems with slope bounded nonlinearities via the use of dynamic multipliers

This paper presents a new approach to constructive output feedback robust nonlinear guaranteed cost controller design. The approach involves a class of controllers which include copies of the slope bounded nonlinearities occurring in the plant. Dynamic multipliers are introduced to exploit these repeated nonlinearities. The linear part of the controller is synthesized using minimax LQG control theory.

Non-linear robust adaptive excitation controller design in power systems based on a new back-stepping method

This study provides a new method for non-linear robust adaptive excitation controller design for power systems. This method can be developed by using the back-stepping technique, but needs fewer conditions than the conventional methods, which is more desirable in power systems. This method is guaranteed to be robust in the presence of model errors and disturbances, and will adapt to uncertain parameters. Meanwhile, the over-parameterisation problem that usually appears in some adaptive methods is avoided. Simulations on a 4-machine-2-area power system and the East China power system demonstrate the effectiveness of the suggested method.

Operator-based robust nonlinear control system design for MIMO nonlinear plants with unknown coupling effects

In this article, operator-based robust nonlinear control system design for multi-input multi-output (MIMO) plants with unknown coupling effects is considered. That is, by using operator-based robust nonlinear control design, coupling effects existing in the MIMO nonlinear plants can be decoupled based on a feedback design and robust right coprime factorisation approach, the coupling effects caused by controllers and plant outputs can be stabilised by using definition of Lipschitz operator and contraction mapping theorem, and output tracking performance can be realised by a tracking design scheme. Finally, a simulation example about temperature control process of 3-input/3-output aluminum plate is given to support the theoretical analysis.

Multi-Timescale Nonlinear Robust Control for a Miniature Helicopter

A new nonlinear control approach, which is applied to a miniature aerobatic helicopter through a multi-timescale structure, is proposed. Because of the highly nonlinear, unstable, and underactuated nature of a miniature helicopter, it is a challenge to design an autonomous flight control system that is capable of operating in the full flight envelope. To deal with unstable internal dynamics, the translational, rotational, and flapping dynamics of the helicopter (eleven degrees of freedom) are organized into a three-timescale, nonlinear model. The concepts of dynamic inversion and sliding manifold are combined together such that 1) the controller proposed is robust with respect to functional and parametric uncertainties, and 2) the settling time in faster modes is guaranteed to be less than the fixed step size of slower modes. A time-varying feedback gain, derived according to global stability and sliding manifold variations, is proved to be uniquely solvable based on the Perron-Frobenius Theorem. Partial uncertainties are explicitly taken into account in the nonlinear robust control design, and Monte Carlo simulations are used for validations under other sensor noises, model uncertainties, and a Federal Aviation Administration suggested gust condition.

Nonlinear robust control of a small-scale helicopter on a test bench

A nonlinear robust controller design procedure is presented, which is designed to simultaneously satisfy multiple conflicting closed-loop performance specifications. Significantly, a robust performance specification for the experimental system, developed for studying the attitude control of a small-scale helicopter in our previous work, is discussed quantitatively. The robust performance specifications and nominal multiple closed-loop performance specifications are conflicting. Use of the Convex Integrated Design (CID) method can provide, where feasible, a single closed-loop controller which satisfies a set of multiple conflicting performance specifications. However, the resultant controller has a complex form. Here, the standard CID method is extended to a more general control system framework to solve the conflicting simultaneous performance design problem. When compared with the standard CID design, the extended CID design procedure generates a relatively simple closed-loop controller. Finally, the synthesised controller is tested in simulation and is validated with an experimental small-scale test helicopter, demonstrating the performance of the proposed controller.

Robust non-linear control and tracking design for multi-input multi-output non-linear perturbed plants

Robust non-linear control and tracking design scheme for multi-input multi-output (MIMO) non-linear perturbed plants are considered, that is, robust stability and output tracking performance are studied by using operator-based robust right coprime factorisation approach. Some sufficient conditions for the MIMO non-linear perturbed plants are derived. By using these conditions, the obtained control and tracking systems are robustly stable, and the desired output tracking performance is realised. Finally, two general examples and one example about the application to a three-input/three-output aluminium plate are given to initially demonstrate the theoretical analysis.

Necessary and sufficient Lyapunov-like conditions for robust nonlinear stabilization

In this work, we propose a methodology for the expression of necessary and sufficient Lyapunov-like conditions for the existence of stabilizing feedback laws. The methodology is an extension of the well-known Control Lyapunov Function (CLF) method and can be applied to very general nonlinear time-varying systems with disturbance and control inputs, including both finite and infinite-dimensional systems. The generality of the proposed methodology is also reflected upon by the fact that partial stability with respect to output variables is addressed. In addition, it is shown that the generalized CLF method can lead to a novel tool for the explicit design of robust nonlinear controllers for a class of time-delay nonlinear systems with a triangular structure.

Robust Output Feedback Guaranteed Cost Control of Nonlinear Stochastic Uncertain Systems Via an IQC Approach

This technical note presents a new approach to constructive output feedback robust nonlinear controller design based on the use of IQCs and minimax LQG control. The approach involves a class of controllers which include copies of the nonlinearities in the controller. The linear part of the controller is synthesized using minimax LQG control theory which is closely related to H infin control theory.

Robust Nonlinear EGR and VGT Control with Integral Action for Diesel Engines

A robust non-linear multivariable control design with integral action is proposed and investigated for control of EGR valve and VGT position in heavy duty diesel engines. The main control goal is to regulate oxygen/fuel ratio and intake manifold EGR-fraction. These are chosen as main performance variables since they are strongly coupled to the emissions. A recently developed non-linear control design based on feedback linearization is extended with integral action. The nonlinear controller gives an inner loop with good stability and robustness properties. It is shown that integral action is necessary to handle model errors so that the controller can track the performance variables specified in the outer loop. In particular the control design method utilizes a control Lyapunov function and inverse optimal control, which results in a control law with robustness properties interpretable as gain and phase margins. Furthermore, comparisons by simulation also show that the proposed control design successfully handles non-linear effects.

Nonlinear observer and robust controller design for enhancement of vehicle lateral stability

This paper describes the design of a sliding mode controller to control wheel slip. A yaw motion controller (YMC), which uses a PID control method, is also proposed for controlling the brake pressure of the rear and inner wheels to enhance lateral stability. It induces the yaw rate to track the reference yaw rate, and it reduces a slip angle on a slippery road. A nonlinear observer is also developed to estimate the vehicle variables difficult to measure directly. The braking and steering performances of the anti-lock brake system (ABS) and YMC are evaluated for various driving conditions, including straight, J-turn, and sinusoidal maneuvers. The simulation results show that developed ABS reduces the stopping distance and increases the longitudinal stability. The observer estimates velocity, slip angle, and yaw rate very well. The results also reveal that the YMC improves vehicle lateral stability and controllability when various steering inputs are applied. In addition, the YMC enhances the vehicle safety on a split-μ road.

Adaptive Back-Stepping Design of TCSC Robust Nonlinear Control for Power Systems

Abstract The back-stepping design methodology of the nonlinear control theory is known to provide an efficient constructive tool for designing non-linear controllers for a wide range of systems engineering applications where it is crucial to employ non-lineaz models of the plants. A novel adaptive and robust non-linear control design for electrical power systems employing thyristor controlled series compensation has been solved by using this methodology. For the case of single machine to infinite bus system with TCSC having internal and external disturbances, storage functions of the system aze constructed via adaptive back-stepping design and a novel non-linear L2 gain disturbance attenuation controller along with the parameter update law were derived. Simulation results have demonstrated that the proposed control design possesses asymptotic stability with superior performances. The construction of feedback control law via associated storage functions is consistently systematic, which makes the proposed ...