Feedback Linearization with Fuzzy Compensation for Uncertain Nonlinear Systems

This paper presents a nonlinear controller for uncertain single-input-single-output (SISO) nonlinear systems. The adopted approach is based on the feedback linearization strategy and enhanced by a fuzzy inference algorithm to cope with modeling inaccuracies and external disturbances that can arise. The boundedness and convergence properties of the tracking error vector are analytically proven. An application of the proposed control scheme to a second-order nonlinear system is also presented. The obtained numerical results demonstrate the improved control system performance

Sensitivity-based robust feedback linearizing control of hydraulically actuated system

Feedback linearization is an effective controller-design methodology for nonlinear systems where it is difficult to obtain a finite number of operating points to linearize the system for designing well-known linear robust controllers. Feedback linearization becomes one of very limited methodologies that can be used for control of such systems. Traditional implementations of feedback linearization technique are not robust, which means this control methodology does not account for system uncertainties. The reason being that the control law methodology assumes accurate knowledge of nonlinear dynamics of the system. Recently, in [1] a new methodology was proposed which adds robustness to feedback linearization. The methodology uses sensitivity dynamics-based control synthesis. The methodology was demonstrated on a simple proof-of-concept single actuator mass-spring-damper model. This research is focused on application of robust feedback linearization technique to real life complex hydraulically actuated physical systems. In particular, the methodology is applied to the problem of controlling mechanical linkage configuration in excavator machines. The problem addressed is controlling of bucket angle of excavator such that the bucket is always kept parallel to ground irrespective of boom motion to avoid spilling of the load. The dynamics of systems such as excavator linkage actuated by hydraulic actuator are often complex and application of robust feedback linearization (RFL) methodology gets tedious and cumbersome. The work in this thesis is intended for demonstrating the applicability of RFL methodology for such complex systems and also to lay foundation for development of an automated user-friendly toolbox to enable easy use of such control technique in day-to-day practice. The uncertain parameter considered in the development in this thesis is the bulk modulus of the system as it is the most common uncertainty in the system. The modeling process also considers portability of models from some known commercial software tools such as SimHydraulics and SimMechanics. The results presented show that the RFL methodology is very effective in achieving robust control of hydraulically actuated systems with uncertainties in hydraulic parameters

Modelling of an electro-hydraulic actutor using extended adaptive distance gap statistic approach

The existence of high degree of non-linearity in Electro-Hydraulic Actuator (EHA) system has imposed a challenging task in developing its model so that effective control algorithm can be proposed. In general, there are two modelling approaches available for EHA system, which are the dynamic equation modelling method and the system identification modelling method. Both approaches have disadvantages, where the dynamic equation modelling is hard to apply and some parameters are difficult to obtain, while the system identification method is less accurate when the system’s nature is complicated with wide variety of parameters, nonlinearity and uncertainties. This thesis presents a new modelling procedure of an EHA system by using fuzzy approach. Two sets of input variables are obtained, where the first set of variables are selected based on mathematical modelling of the EHA system. The reduction of input dimension is done by the Principal Component Analysis (PCA) method for the second set of input variables. A new gap statistic with a new within-cluster dispersion calculation is proposed by introducing an adaptive distance norm in distance calculation. The new gap statistic applies Gustafson Kessel (GK) clustering algorithm to obtain the optimal number of cluster of each input. GK clustering algorithm also provides the location and characteristic of every cluster detected. The information of input variables, number of clusters, cluster’s locations and characteristics, and fuzzy rules are used to generate initial Fuzzy Inference System (FIS) with Takagi-Sugeno type. The initial FIS is trained using Adaptive Network Fuzzy Inference System (ANFIS) hybrid training algorithm with an identification data set. The ANFIS EHA model and ANFIS PCA model obtained using proposed modelling procedure, have shown the ability to accurately estimate EHA system’s performance at 99.58% and 99.11% best fitting accuracy compared to conventional linear Autoregressive with External Input (ARX) model at 94.97%. The models validation result on different data sets also suggests high accuracy in ANFIS EHA and ANFIS PCA model compared to ARX model

Neural network based feedback linearization control of a servo-hydraulic vehicle suspension system

This paper presents the design of a neural network based feedback linearization (NNFBL) controller for a two degree-offreedom (DOF), quarter-car, servo-hydraulic vehicle suspension system. The main objective of the direct adaptive NNFBL controller is to improve the system's ride comfort and handling quality. A feedforward, multi-layer perceptron (MLP) neural network (NN) model that is well suited for control by discrete input-output linearization (NNIOL) is developed using input-output data sets obtained from mathematical model simulation. The NN model is trained using the Levenberg- Marquardt optimization algorithm. The proposed controller is compared with a constant-gain PID controller (based on the Ziegler-Nichols tuning method) during suspension travel setpoint tracking in the presence of deterministic road disturbance. Simulation results demonstrate the superior performance of the proposed direct adaptive NNFBL controller over the generic PID controller in rejecting the deterministic road disturbance. This superior performance is achieved at a much lower control cost within the stipulated constraints

Neural network based feedback linearization control of a servo-hydraulic vehicle suspension system

This paper presents the design of a neural network based feedback linearization (NNFBL) controller for a two degree-offreedom (DOF), quarter-car, servo-hydraulic vehicle suspension system. The main objective of the direct adaptive NNFBL controller is to improve the system’s ride comfort and handling quality. A feedforward, multi-layer perceptron (MLP) neural network (NN) model that is well suited for control by discrete input-output linearization (NNIOL) is developed using input-output data sets obtained from mathematical model simulation. The NN model is trained using the Levenberg– Marquardt optimization algorithm. The proposed controller is compared with a constant-gain PID controller (based on the Ziegler–Nichols tuning method) during suspension travel setpoint tracking in the presence of deterministic road disturbance. Simulation results demonstrate the superior performance of the proposed direct adaptive NNFBL controller over the generic PID controller in rejecting the deterministic road disturbance. This superior performance is achieved at a much lower control cost within the stipulated constraints

Modeling and Robust Control of Integrated Ride and Handling of Passenger Cars

Vehicle industries in the last decade have focused on improving ride quality and safety of passenger cars. To achieve this goal, modeling and simulation of dynamic behaviour of vehicles have been widely studied to design model based and robust control strategies. This PhD work presents a new integrated vehicle model and a nonlinear robust controller. The thesis is divided into two main sections: dynamic modeling and controller design. A new fourteen Degrees of Freedom integrated ride and handling vehicle model is proposed using Lagrangian method in terms of quasi-coordinates. The governing equations are derived considering the interaction between the ride and handling systems, Euler motion of the frames attached to the wheels and body, the load transfer among the wheels, acceleration and braking. A non-dimensional factor called coupling factor is introduced to study the coupling among different DOFs of the dynamic system for a defined vehicle maneuver. The coupling factor is considered as an indicator parameter to demonstrate the advantages of the developed model over the existing dynamic models. The improved model is validated using ADAMS/Car for different manoeuvres. The simulation results confirm the accuracy of the improved dynamic model in comparison with the ADAMS/Car simulations and the models available in the literature. Considering the proposed nonlinear integrated ride and handling vehicle model, a nonlinear robust controller is designed for an intermediate passenger car. The H∞ robust control strategy is designed based on the Hamiltonian-Jacobi-Isaacs (HJI) function, Linear Matrix Inequality and State Feedback techniques. In order to improve the ride and handling quality of the vehicle, a Magneto-rheological (MR) damper and a differential braking system are used as control devices. A frequency dependent MR damper model is proposed based on the Spencer MR damper model. The parameters of the model are identified using a combination of Genetic algorithms and Sequential Quadratic Programming approaches based on the experimental data. A mathematical model is validated using the experimental results which confirm the improvement in the accuracy of the model and consistency in the variation of damping with frequency. Based on the proposed MR damper model, an inverse model for the MR damper is designed. A differential braking system is designed to assign desired braking action. The dynamic behavior of the controlled vehicle is simulated for single lane change and bump input, considering three different road conditions: dry, rainy and snowy. The robustness of the designed controller is investigated when the vehicle is under these road conditions. The simulation results confirm the interactive nature of the ride and handling systems and the robustness of the designed control strategy

Controle em cascata de um atuador hidráulico utilizando redes neurais

No presente trabalho, é realizada a modelagem e identificação de um serovoposicionador hidráulico de uma bancada de testes. As expressões analíticas tradicionalmente utilizadas em uma estratégia em cascata aplicada ao controle de trajetória de posição são obtidas. A estratégia em questão utiliza, conjuntamente, a linearização por realimentação como lei de controle do subsistema hidráulico e a lei de controle de Slotine e Li no subsistema mecânico. Com base na mesma estratégia, um controlador em cascata neural é proposto. Em tal controlador, a função analítica que representa o mapa inverso, presente na linearização por realimentação, e a função de compensação de atrito utilizada na lei de Slotine e Li são substituídas por funções constituidas por meio de redes neurais de perceptrons de múltiplas camadas. Essas redes neurais têm como entradas os estados do sistema e também a temperatura do fluido hidráulico. O novo controlador é apresentado em uma versão onde as redes neurais são aplicadas sem modificações on-line e em outra, onde são apresentadas leis de controle adaptativo para as mesmas. A prova de estabilidade do sistema em malha fechada é apresentada em ambos os casos. Resultados experimentais do controle de seguimento de trajetórias de posição em diferentes temperaturas do fluido hidráulico são apresentados. Esses resultados demonstram a maior efetividade do controlador proposto em relação aos controladores clássicos PID e PID+feefforward e ao controlador em cascata com funções analíticas fixas. Os experimentos são realizados em duas situações: quando não ocorrem variações paramétricas importantes no sistema, onde é utilizado o controlador em cascata neural fixo e quando ocorrem essas variações, onde se utiliza o controlador em cascata neural adaptativo.In this work, the modeling and identification of a hydraulic actuator testing setup are performed and the analytical expressions that are used in a cascade control strategy applyied in a position trajectory tracking control are designed. Such cascade strategy uses the feedback linearization control law in the hydraulical subsystem and the Slotine and Li control law in the mechanical one. Based on this cascade strategy, a neural cascade controller is proposed, for which the analytical function used as inversion set in the feedback linearization control law and the friction function compensation of the Slotine and Li control law are replaced by multi layer perceptrons neural networks where the inputs are the states of the system and the hydraulic fluid temperature. The novel controller is introduced in two different aproachs: the first one where the neural networks do not have on-line modifications and the second one where adaptive control laws are proposed. For both of them the stability proof of the closed-loop system is presented. Experimental results about some position tracking controls performed in different fluid temperature are showed. The results show that the novel controller is more efective than the classical PID, PID+feedforward and the traditional analytical cascade controller. The experiments are performed in two different setups: considering the system without importants parametric variations where is applied the non adaptive cascade neural controller and in the presence of parametric variations where is applied the adaptive cascade neural controller