Input-output Linearization Research Articles

Disturbance decoupling by measurement feedback

The paper addresses the disturbance decoupling problem for MIMO discrete-time nonlinear systems. A sufficient conditions are derived to solve the problem by dynamic measurement feedback, i.e. the feedback that depends on measurable outputs only. The solution to the disturbance decoupling problem, described in this paper, is based on the input-output linearization, which is used to linearize certain functions. Two examples are added to illustrate the results.

A New Robust Controller with Applications to Bioreactors

In this work an anaerobic digester is controlled using input-output linearization and Lyapunov-like function methods. It is assumed that model parameters are unknown, time-varying, and bounded, and upper or lower bounds are also unknown. To tackle the effect of input saturation, a state observer is designed. The tracking and observer errors are defined in terms of the noisy measured output instead of ideal output, given by the mathematical model. The design of the observer mechanism and the update laws is based on the Lyapunov-like function technique, whereas the design of the control law is based on the input-output linearization method. In this paper two important properties of the controlled system are proven. First, the observer error converges asymptotically to a residual set whose size is user-defined, and such convergence is not disrupted, neither by the input saturation nor by the parameter uncertainties. Second, when the control input is nonsaturated the tracking error converges to a residual set whose size is user-defined. The model parameter uncertainties are included to prove the convergence of errors. Finally, a numerical example to validate the developed control is presented.

Distributed Cooperative Current-Sharing Control of Parallel Chargers Using Feedback Linearization

We propose a distributed current-sharing scheme to address the output current imbalance problem for the parallel chargers in the energy storage type light rail vehicle system. By treating the parallel chargers as a group of agents with output information sharing through communication network, the current-sharing control problem is recast as the consensus tracking problem of multiagents. To facilitate the design, input-output feedback linearization is first applied to transform the nonidentical nonlinear charging system model into the first-order integrator. Then, a general saturation function is introduced to design the cooperative current-sharing control law which can guarantee the boundedness of the proposed control. The cooperative stability of the closed-loop system under fixed and dynamic communication topologies is rigorously proved with the aid of Lyapunov function and LaSalle invariant principle. Simulation using a multicharging test system further illustrates that the output currents of parallel chargers are balanced using the proposed control.

Voltage Control Of Three Phase Ac/Dc Pwm Converters Using Feedback Linearisation

This paper proposes a voltage control strategy for a three level PWM converter based on feedback linearization in order to control dc bus voltage. Incorporating the power balance of the input and output sides in system modeling, a nonlinear model of the PWM converter is derived with state variables such as ac input currents and dc output voltage. Feedback linearization transforms a nonlinear system into a linear system. Then by input-output feedback linearization, the system is linearized and a state feedback control law is obtained by pole placement. For robust control to parameter variations, integrators are added to the exact feedback control law. Since the fast voltage control is feasible for load changes, it is shown that the capacitor size can be reduced remarkably. The input current is regulated to be sinusoidal and the source power factor can be controlled at unity. This feedback linearization technique can be extended for permanent magnet synchronous generator wind power system at the grid voltage sag. The proposed method is tested and the results of simulation are observed using MATLAB/SIMULINK. I. Introduction In this paper, simulation of dc machine speed control which is fed by three - phase voltage source rectifier under input - output linearization nonlinear control, is realized. The speed Control loop is combined with input-output linearization nonlinear control. By means of the simulation, power factor, line currents, harmonic distortions and dc machine speed are presented. In nature, most of the systems are nonlinear. But, most of them are thought as linear and the control structures are realized with linear approach. Because, linear control methods are so strong to define the stability of the systems. However, linear control gives poor results in large operation range and the effects of hard nonlinearities cannot be derived from linear methods. Furthermore, designing linear controller, there must not be uncertainties on the parameters of system model because this causes performance degradation or instability. For that reasons, the nonlinear control are chosen. Nonlinear control methods also provide simplicity of the controller. Considering a three phase supply for every voltage source there will be some impedance drop, after measuring for rectification process to eliminate third and fifth harmonics we use six pulse bridge converters, after rectification this gets stored in capacitor, this is called DC link voltage. To control DC link voltage in this paper we used insulated gate bipolar transistor (IGBT'S) other than SCR because it has high holding capability compared to SCR'S. IGBT'S reduce the low harmonics depending on pulse width modulation (PWM) technique it generates gate pulses. PWM technique is nothing but decreasing width of pulse. To reduce the switching losses we go for SVPWM i.e. in IGBT parameters we consider voltage and current feedback and their magnitude is derived and the magnitude is converted into polar form, this technique is called parks transformation technique. Feedback linearization transforms a non-linear system into a linear one, then by input output feedback linearization the system is linearized and a state feedback control law is obtained by pole placement. Since the fast voltage control is feasible for load changes, it is shown that the capacitor size can be reduced remarkably. The input current is regulated to be sinusoidal and the source power factor can be controlled at unity. This can be extended by permanent magnet synchronous generator connected wind power system to maintain the voltage constant when the total system is connected generator side as well as grid side with the help of dc capacitor.

Voltage-Oriented Input-Output Linearization Controller as Maximum Power Point Tracking Technique for Photovoltaic Systems

This paper presents a robust input-output linearization controller as maximum power point tracking (MPPT) technique in a photovoltaic (PV) buck dc-dc converter with applications to dc microgrids, solar vehicles, or stand-alone systems. Due to the control structure proposed in this paper, the MPPT control system is able to track very fast irradiance changes. Meanwhile, the internal stability of the overall closed-loop system is guaranteed for different load scenarios. A sector condition is only required for the load current, which is satisfied for most of the current PV applications. In turn, this condition implies the robustness against oscillations in the dc bus voltage. Finally, the MPPT control system is validated through experimental results, where the closed-loop performance is evaluated under abrupt irradiance and set-point changes, parametric uncertainty, and dc bus load variations.

On-line implementation of decoupled input-output linearizing controller in Baker's yeast fermentation

Baker's yeast fermentation is influenced by the relative concentration of glucose and dissolved oxygen (DO) in the reactor. The process is sensitive to the oxidative capacity of the cells and exhibits a range of metabolic regimes depending on available glucose and oxygen. The time profiles of cell mass, glucose, ethanol and DO concentrations possess strong nonlinear characteristics. A decoupled input-output linearizing controller (DIOLC), which exhibited satisfactory performance in simulation experiments, was implemented online for validation. Our results showed that the DIOLC was capable of negating the interaction between glucose and dissolved oxygen, and executed satisfactory control action in experiments carried out in a 5 liter bioreactor. The performance of DIOLC was better compared to that of a PID controller implemented under identical test conditions.

LUT Controller Design with Piecewise Bilinear Systems Using Estimation of Bounds for Approximation Errors

We propose the stabilization of nonlinear control systems approximated by Piecewise Bilinear (PB) models. The approximated model is fully parametric and a Look-Up-Table (LUT) represents its controller. Input-Output (I/O) feedback linearization is applied to stabilize PB control systems. We further propose PB modeling combined with conventional feedback linearization as a very powerful tool for analyzing and synthesizing nonlinear control systems. We also propose a method for designing robust stabilization controllers taking modeling error into consideration. Examples confirm the feasibility of our proposals.

Avoiding a Voltage Sag Detection Stage for a Single-Phase Multilevel Rectifier by Using Control Theory Considering Physical Limitations of the System

The use of control theory in power electronics applications is aimed toward several objectives, which include, obtaining a good dynamic response, stabilizing in an operation point, regulation of state variable, reference tracking, rejecting of disturbances and robustness against parametric variations. It is also possible to eliminate stages that represent computational effort via control theory without loss of the main desirable characteristics. However, it should be considered the physical limitations of the topology given that even with sophisticated controllers they cannot achieve the established objectives if these limitations are exceeded. This paper aims at highlighting the importance of physical limitations of a single-phase multilevel rectifier (SPMR) using a nonlinear controller, an aspect not considered in previous works published by the authors. Thus, the design here presented is based on input-output linearization via feedback combined with a generalized PI controller. These controllers are used because they allow avoiding a voltage sag detection stage without changing the main characteristics of the topology. The procedure to reproduce these results is shown and the feasibility of the method is demonstrated by simulation and experimental results in a 1 kVA SPMR prototype.

Model based control of a small-scale biomass boiler

Because of increased efforts to reduce CO2 emissions a significant step in the development of small-scale (residential) biomass boilers for space heating has been achieved in recent years. Currently, the full potential for low-emission operation at high efficiencies, which is in principle possible due to optimized furnace geometries as well as combustion air staging strategies, cannot be exploited since there is still the need to enhance the controllers applied. For this reason, a model based control strategy for small-scale biomass boilers was developed and successfully implemented in a commercially available system. Thereby, appropriate mathematical models were developed for all relevant parts of the furnace and connected to an overall model subsequently used for the control unit design. The resulting controller is based on the input–output linearization and the state variables are estimated by an extended Kalman filter. Finally, the new control was implemented at a commercially available small-scale biomass boiler and the experimental verification showed a significant improvement of the operating behaviour in comparison to the conventional control.

PASSIVITY-BASED PARAMETER ESTIMATION AND COMPOSITE ADAPTIVE POSITION CONTROL OF INDUCTION MOTORS

In the rotor reference frame, the input-output linearization theory was adopted to decouple the rotor position and rotor flux. We then designed two adaptation laws to estimate the rotor resistance and mechanical parameters of the motor. The passive properties of the negative feedback connection from the rotor flux observer to the rotor resistance estimator, and the position controller were analyzed according to the passivity theorem. The overall control system was proved to be globally stable. Finally, experimental results show that the proposed scheme is robust to the variations of the rotor resistance and load torque disturbances. Furthermore, the estimated parameters can converge to the actual values.

Position and Current Control of an Interior Permanent-Magnet Synchronous Motor by Using Loop-Shaping Methodology: Blending of H∞ Mixed-Sensitivity Problem and T–S Fuzzy Model Scheme

This paper presents a robust mixed-sensitivity H∞ controller design via loop-shaping methodology for a class of multiple-input multiple-output (MIMO) uncertain nonlinear systems. In order to design this controller, the nonlinear plant is first modeled as several linear subsystems by Takagi and Sugeno's (T–S) fuzzy approach. Both loop-shaping methodology and mixed-sensitivity problem are then introduced to formulate frequency-domain specifications. Afterward for each linear subsystem, a regional pole-placement output-feedback H∞ controller is employed by using linear matrix inequality (LMI) approach. The parallel distributed compensation (PDC) is then used to design the controller for the overall system. Several experimental results show that the proposed method can effectively meet the performance requirements like robustness, good load disturbance rejection, and both tracking and fast transient responses even in the presence of parameter variations and load disturbance for the three-phase interior permanent-magnet synchronous motor (IPMSM). Finally, the superiority of the proposed control scheme is approved in comparison with the input–output linearization (I/O linearization) and the H2/H∞ controller methods.

Lyapunov and Hurwitz based controls for input–output linearisation applied to nonlinear vessel steering

This paper focuses on the Lyapunov, Hurwitz and PID based control approaches for an input–output linearisation applied nonlinear vessel steering system. A mathematical model of the vessel steering system is derived considering a second-order Nomoto model with nonlinear manoeuvrability features. In general, the control design process of the nonlinear vessel steering system is affected by the nonlinearities that are related to rudder angle, rudder rate and vessel heading angle. Therefore, to simplify the nonlinear vessel steering system, input–output linearisation is proposed in this study. During this process (i.e. input–output linearization), the system is divided in a system with linear dynamics and a system with internal dynamics. Furthermore, the stability conditions of internal dynamics are analysed to observe overall stability of the vessel steering system. The Lyapunov, Hurwitz and PID based controllers are proposed for course keeping and course changing manoeuvres in vessel steering. Furthermore, the overall stability conditions of the proposed Lyapunov and Hurwitz based controller are analysed, considering a Lyapunov candidate function and the Hurwitz conditions, respectively. Finally, the proposed control algorithms are simulated on a vessel steering system and successful results with respect to course keeping and course changing manoeuvres are presented in this paper.

Modeling and Simulation on Temperature Control System for Hot Pressure Welding

Hot pressure welding (HPW) is one of the inner lead bonding process which is widely used in microelectronics manufacturing. This paper presents a practical digital temperature controller for HPW. Based on the step response, an identification method is developed to obtain a nonlinear time-delay model for heating-up control design. The input-output linearization problem is solved by means of second-order Pade approximation and static inverse transform, and an optimal controller is obtained for the welding machine. The experimental equipment on the temperature control is designed based on LabVIEW and data acquisition card. Simulation and experimental results show that the dynamic performance, steady stage error and overshoot satisfy the designed requirements.

Indirect output voltage regulation of DC–DC buck/boost converter operating in continuous and discontinuous conduction modes using adaptive backstepping approach

In this study, an adaptive non-linear controller is designed for DC-DC buck/boost converter which is robust and stable against converter load changes, input voltage variations and parameter uncertainties. The proposed controller is developed based on input-output linearisation using an adaptive backstepping approach. The controller can be applied in both continuous and discontinuous conduction modes (CCM and DCM). Owing to non-minimum phase nature of buck/boost converter, the output voltage of this converter is indirectly controlled by tracking the inductor reference current. The inductor reference current is generated by a conventional PI controller. Using a MATLAB/Simulink toolbox and a stand-alone TMS320F2810 digital signal processor from Texas Instruments, some simulations and practical results are presented to verify the capability and effectiveness of the proposed control approach.

On the need of nonlinear control for efficient model-based wake stabilization

The mitigation of oscillatory vortex shedding behind a cylinder is chosen as a well-investigated benchmark problem to compare model-based feedback flow control approaches. The flow is sensed by a single velocity signal in the wake and is manipulated via a single volume force actuator. A low-dimensional proper orthogonal decomposition Galerkin model is adopted as a control-oriented fluid flow representation. An extended Kalman filter is used as an effective means for online dynamic state estimation. Investigated strategies of linear and nonlinear controller design include pole placement, linear parameter-varying, input–output linearization, Lyapunov-based backstepping, and nonlinear model predictive control. These strategies are applicable to a large class of flows with oscillatory dynamics and to experimental conditions, where variants have already been used. Controllers are evaluated and compared based on their application to the full plant, that is, to the direct numerical simulation of the wake, emulating an experiment with a single hot-wire sensor. Overall, nonlinear closed-loop control is shown to be distinctly superior to linear approaches. As is often the case, physics dictates a similarity of successful control commands, irrespective of the design approach, and differentiates these controllers, as a group, from less successful approaches.

Robust control strategies for a class of nonlinear systems with an ill-defined relative degree

Differential geometry theory has become one of the most promising design tools for nonlinear processes in the past decade. Several differential geometry techniques, such as input–output linearization and input-state linearization, have received considerable attention in the literature. However, one of the main assumptions often needed in the design of nonlinear controller by means of differential geometry is a nonlinear system with a well-defined relative degree. Nonlinear systems with an ill-defined relative degree will have an input–output linearizing law with singularities. This problem restricts the application of the feedback linearization technique in many engineering systems. One approach to this problem is to use approximate linearization techniques but this tends to yield very sluggish responses. In this paper, we investigate the applicability of a composite control scheme consisting of heuristic-based approximate linearization and backstepping design for a nonlinear system with an ill-defined relative degree. Two procedures are used to deal with this problem. In the first step, a function approximates the Lie derivative of the process output along with the input function to avoid the occurrence of singularity. Then, a nonlinear controller with an integral action-based back-stepping design is proposed to ensure that both a stable process and improved performance are obtained. Numerical simulations that illustrate the effectiveness of this approach are given.

Design and Simulation of PMSM Feedback Linearization Control System

With the theory of AC adjustable speed as well as a new control theory research is unceasingly thorough, the permanent magnet synchronous motor control system requires high precision of control and high reliability of the occasion, access to a wide range of applications, in the modern AC motor has play a decisive role position. Based on the deep research on the feedback linearization technique based on, by choosing appropriate state transformation and control transform, PMSM model input output linearization, and the design of the feedback linearization controller, realized PMSM decoupling control based on Matlab, and PMSM feedback linearization control system simulation. The simulation results show that, the system in a certain range of speed than the traditional PI controller has better control performance, but to the parameter variation has strong sensitivity. It also determines the direction for future research. DOI: http://dx.doi.org/10.11591/telkomnika.v11i3.2192 Full Text: PDF

A Feedback Linearization Based Nonlinear Control Approach for Variable Speed Wind Turbines

This paper describes the design and implementation of a nonlinear control strategy for the control of the shaft speed of wind turbine systems. The proposed approach is based on input-output linearization techniques. Because wind turbine systems are highly nonlinear, feedback linearization constitutes a suitable optimal control design for those systems. Further, Electromechanical systems in general are good candidates for nonlinear control applications because the nonlinearities, being modeled on the basis of physical principles, are often significant and exactly known. The underlying design objective is to endow the wind turbine with high performance dynamics while maximizing power extraction when the wind turbine operates in the partial load regime. In addition to fulfilling the aforementioned control objectives, our control design aims to reduce the complexity of the control scheme, saving thereby the computation time of the control algorithm, which is an improvement over previous work found in the technical literature. Application of the proposed approach to an induction generator based variable speed wind turbine has led to optimum operations and maximization of power extraction when the wind turbine operates in the partial load regime.

Stabilization and Control of a Spherical Robot on an Inclined Plane

In this study, the dynamics and control aspects of a spherical robot rolling without slipping on an inclined plane are investigated. The planar dynamic model of the robot rolling ahead on an inclined plane is derived using Lagrangian dynamics. Based on the equivalent control method and Lyapunov stability theorem, a decoupled sliding mode control approach is presented for stable control of the planar motion. Utilizing the constrained Lagrange method the three-dimensional dynamics of the robot rolling on an inclined plane are deduced. Based on input-output feedback linearization, we develop a trajectory tracking control algorithm for the three-dimensional motion of the robot. The validity of the proposed controllers is demonstrated through numerical simulations.

Passivity-Based Parameter Estimation and Position Control of Induction Motors via Composite Adaptation

This paper proposes the parameters estimation and position control of an induction motor drive by using the composite adaptation scheme. First, in the rotor reference frame, the input-output linearization theory was employed to decouple the mechanical rotor position and the rotor flux amplitude at the transient state. An open-loop current model rotor flux observer was utilized for estimating the flux, and then the adaptive laws for estimating the rotor resistance, moment of inertia, viscous friction coefficient, and load torque. The passive properties of the flux observer, rotor resistance estimator, and composite adaptive position controller were analyzed based on the passivity theorem. According to the properties, the overall position control system was proved to be globally stable without using Lyapunov-type arguments. Experimental results are finally provided to show that the proposed method is robust to variations of the motor mechanical parameters, rotor resistance, and load torque disturbances. Moreover, good position tracking response and characteristics on parameter estimation can be achieved.