Input-output Feedback Linearization Research Articles

Nonlinear control of the permanent magnet synchronous motor PMSM using input-output linearization control and sliding mode control

Today, electric machines are becoming increasingly important in all sectors (industrial drives, the automotive industry, aviation, traction systems, and agriculture, etc.). Among these machines, permanent magnet synchronous machines (PMSMs) hold a significant place in the control of industrial mechanisms, automated systems, and in the fields of renewable energy like (wind energy, solar energy, and hybrid systems, etc ). Currently, in variable speed drives, the use of PMSM, especially for low power and certain special industrial applications, is replacing DC motors and asynchronous motors because they offer higher efficiency, power factor, and torque density. Moreover, PMSM do not have an excitation circuit in the rotor, which leads to reduced maintenance demands. The control of permanent magnet synchronous machines (PMSM) presents significant challenges due to their nonlinear behavior. Classical linear controllers, such as PI, perform well with linear systems that have constant parameters. However, for nonlinear systems with varying parameters, the conventional control methods may prove insufficient and exhibit a lack of robustness. To address the issues and achieve decoupled machine control, various methods have been proposed. Nonlinear robust control techniques have been extensively explored within the domain of power electronics and drive systems. Included in these, sliding mode control and nonlinear input-output feedback linearization (IOFL). Sliding mode control (SMC) is a control technique known for its excellent dynamic performance in PMSM drives. It offers high robustness and straightforward implementation in both software and hardware. However, a significant drawback of this method is the chattering phenomenon. By the way the input/output linearization control can provide good behavior in steady and dynamic regimes and also provides good decoupling between system variables. This article presents a design of tow control laws based on sliding mode and feedback linearization controller based on input-output feedback linearization to adjust the speed of a permanent magnet synchronous motor (PMSM). To highlight the effectiveness of the designed controllers, a comparison was carried out Matlab Simulink, revealing that the feedback linearization controller outperforms the SMC.

Stability analysis for passive robots walking on inclined surfaces with local angles

For common-legged robots with a kind of stiff joints, the human-like and consecutive gait shown by passive walking robots is a bit difficult to achieve because of varying degrees of control, which is usually accompanied by computational cost. Of course, passive dynamic walking undoubtedly has its inevitable disadvantages because of the lack of control, which is stability. At the same time, the significant nonlinearity of the passive gait increases the difficulty of realizing the walking stability of the passive robot. Therefore, the passive robot still needs certain control to achieve stable walking even on the natural plane or smooth slope. In this paper, a passive robot model walking on an inclined plane with a local angle is studied. First of all, the approximate solution of the nonlinear dynamic equation is given by the perturbation method, and the conditions for the robot to achieve stable walking without external forces are obtained. Further, the input-output feedback linearization control based on hybrid zero dynamics is employed to carry out virtual constraints on the passive robot during the swing stage of walking, facilitating the transition from the unstable state to the stable periodic state. From the result of the experiments, the walking stability of the passive robot is improved over a larger range of walking status values compared with the condition without external force control, and the use of this method reduces the complicated work of solving the fixed point. These findings possibly have reference value in passive walking stabilization control. Meanwhile, the simulation results obtained by designing and studying the minimum controlled walking model show that human walking is based on the uncontrolled mechanical process. The exploration of the mechanism of passive gait can provide some enlightenment to the research of human texture and the application of exoskeleton.

Making of an Indigenous and Efficient Powertrains for EV, HEV & FCEV’s

Rise in greenhouse gas emissions which is resulting into ozone layer depletion and global warming effect is alarming to control CO2 emissions by drastically reducing fossil fuel consumption from the vehicles. This need has already started trend towards extreme downsizing and down speeding of Internal Combustion Engines (ICE) for making them highly efficient. In addition to this use of after treatment devices viz. Diesel Oxidation Catalyst (DOC), Diesel Particulate Filter (DPF), Lean NOx Catalyst (LNT), Selective Catalytic Reduction (SCR) are helping to a great extent for meeting emission norms till Euro - VI for automotive sector, Tier–IV F and Stage V for Off Highway Power sector. However, to address present greenhouse effect along with exponential decay of fossil fuels, there is need to achieve CO2 emissions less than 100 g/km or to achieve practically zero carbon footprint using an alternate powertrain. Electrification is one of the promising solutions and which is three-fold in present situation. The first level of electrification comes in the form of Hybrid Electric Vehicle (HEV) technology followed by Battery Electric Vehicles and Fuel Cell Electric Vehicles as second and third level of electrification respectively. In all these technologies a common thread is running in the form of an efficient electric drive train. Several efforts have been taken to improve torque per unit ampere by use of efficient motor and motor control algorithms viz PMSM powered with FOC, by developing controls which take care of parametric variations and external force disturbances by use of back stepping techniques which are based on rotor resistance estimation by fuzzy logic, FOC techniques based on adaptive input-output feedback linearization, by shifting towards high voltage systems, by going for higher switching frequencies for inverters which uses silicon carbide based MOSFET switches, by exploring use of multilevel inverters for Total Harmonic Distortion (THD) control etc. Use of E Axle based powertrains in EV, HEV and FCEV offers additional complimentary benefits apart from technology options described above. E Axle based powertrains offers flexibility in generating three variants of vehicle using one electric drive train architecture viz. making EV, HEV & FCEV. Compactness, modularity, scalability, flexibility along with efficient cooling system management and control over active current losses due to use of bus bars are the implicit advantages of E Axle based powertrains. These advantages further get multiplies if we go for 3 in 1 (gearbox + Stator housing + Inverter) architectures which are predominantly used in independent suspension-based vehicles. Lot of efforts are going on to inherit this technology for rigid axle suspension based commercial vehicles. Research in this area is getting further extended to make 5 in 1 E Axles where there will addition of DC - DC converter and On-Board Charger (OBC) apart from components present in 3 in 1 configuration. Two major challenges need to be addressed and to be resolved while designing E Axle based powertrains by doing concurrent vehicle engineering. This is mainly due to increased unsprang weight that need to be handled by suspension system and exposed electric drive components to excitation loads coming from roads. Fig: Indigenously Developed E Axle Based Powertrain for Small Commercial VehiclesBy proper lay outing for effective vehicle mass distribution and required CG location which is essential from overall vehicle dynamics, more space can be offered by E Axle based powertrains for increasing battery energy density for getting more electric range in case of BEV’s. This add on space benefit extend help in packaging of hydrogen fuel cell integrated with power cells in case of FCEV’s. Thus, E Axle based powertrains proves to be modern and most efficient way of making EV, HEV & FCEV’s.

Optimal IOFL-based economic model predictive control technique for boiler-turbine system

The optimal control design of the boiler-turbine system is vital to ensure feasibility and high responsiveness over desired load variations. Using the traditional linear control techniques realization of this task is difficult, as the boiler-turbine mechanism has strong nonlinearities. Besides, environmental and economic concerns have replaced existing tracking control ones as the primary concerns of advanced power plants. Thus, this study proposes an optimal economic model predictive controller (EMPC) scheme for this unit on the basis of the input/output feedback linearization (IOFL) method. By employing the IOFL method, this unit is decoupled into a new linearized model that is utilized for developing the suggested optimal IOFL EMPC technique. The proposed control scheme is formulated in an economic quadratic programming form that considers the input-rate and input limits of the unit for optimal economic performance. In addition, an adaptive iterative algorithm is utilized for constraints mapping with guaranteeing a feasible solution in a finite number of steps without violation of original constraints over the entire predictive horizon. The outcomes of the simulation show that the suggested optimal IOFL EMPC scheme offers an improved dynamic and economic output performance over fuzzy hierarchical MPC, fuzzy EMPC, and nonlinear EMPC techniques during various load variations.

Robust Output Feedback Stabilization and Tracking for an Uncertain Nonholonomic Systems with Application to a Mobile Robot.

This paper presents a novel robust output feedback control that simultaneously performs both stabilization and trajectory tracking for a class of underactuated nonholonomic systems despite model uncertainties, external disturbance, and the absence of velocity measurement. To solve this challenging problem, a generalized normal form has been successfully created by employing an input-output feedback linearization approach and a change in coordinates (diffeomorphism). This research mainly focuses on the stabilization problem of nonholonomic systems that can be transformed to a normal form and pose several challenges, including (i) a nontriangular normal form, (ii) the internal dynamics of the system are non-affine in control, and (iii) the zero dynamics of the system are not in minimum phase. The proposed scheme utilizes combined backstepping and sliding mode control (SMC) techniques. Furthermore, the full-order high gain observer (HGO) has been developed to estimate the derivative of output functions and internal dynamics. Then, full-order HGO and the backstepping SMC have been integrated to synthesize a robust output feedback controller. A differential-drive type (2,0) the wheeled mobile robot has been considered as an example to support the theoretical results. The simulation results demonstrate that the backstepping SMC exhibits robustness against bounded uncertainties.

Model Simplification for Asymmetric Marine Vehicles in Horizontal Motion—Verification of Selected Tracking Control Algorithms

This paper addresses a trajectory tracking control algorithm for underactuated marine vehicles moving horizontally in which the current in the North–East–Down frame is constant. This algorithm is a modification of a control scheme based on the input-output feedback linearization method, for which the application condition was that the vehicle was symmetric with respect to the left and right sides. The proposed control scheme can be applied to a fully asymmetric model, and, therefore, the geometric center can be different from the center of mass in both the longitudinal and lateral directions. A velocity transformation to generalized vehicle equations of motion was used to develop a suitable controller. Theoretical considerations were supported by simulation tests performed for a model with 3 degrees of freedom, in which the performance of the proposed algorithm was compared with that of the original algorithm and the selected control scheme based on a combination of backstepping and integral sliding mode control approaches.

Adaptive PMSM Control of Ship Electric Propulsion with Energy-Saving Features

Electric ship propulsion is considered one of the most promising alternatives to conventional combustion systems. Its goal is to reduce the carbon footprint and increase a ship’s maneuverability, operational safety, and reliability. The high requirements for ship propulsion make permanent magnet synchronous motors (PMSMs) an attractive solution due to their characteristics. This paper discusses the control problem of a PMSM based on the input–output feedback linearization method combined with the optimal and adaptive control techniques. The method presented here integrates the parameter tuning process with the optimal design of the baseline controller. Since the load disturbances are treated as an additional unknown parameter, there is no need to introduce an integral action to deal with the resulting steady-state error. An important feature of the designed controller is the so-called energetic optimization of the system; i.e., in addition to the aforementioned adaptive and optimal controller, it has a feature of ensuring zero reactive power consumed by the system. The performed simulations of the machine speed stabilization process confirmed the high efficiency of the proposed controller despite the assumed uncertainty of the system parameters and environmental (load) disturbances. Besides achieving high-quality control, an essential feature of this approach is the elimination of the tuning problem.

Design of a feedback linearizing controller for a CSTR reactor

The design of a controller for a chemical reactor was studied. Based on the input-output feedback linearization, the controller was designed for a situation where the output of the system is the concentration. The reaction in the reactor is of the first-order type. First, the reactor is modeled and presented, and then a controller for this system is designed. The control system was implemented in Simulink MATLAB. The simulation results show that the designed controller is able to control the concentration in a wide range and its performance is desirable for changing either the disturbances or the set point.

Distributed Multiagent-Based Event-Driven Fault-Tolerant Control of Islanded Microgrids.

This article proposes an observer-based event-driven fault-tolerant (OBEDFT) secondary control strategy for AC microgrids (MGs) to achieve load voltage regulation. First, the input-output feedback linearization method transforms the voltage regulation issue into an output feedback tracking problem for linear multiagent systems (MASs) with nonlinear dynamics. This transformation provides the necessary preprocessing for load voltage regulation. Then, an OBEDFT secondary control protocol that considers full-state immeasurability is proposed. The actuators of distributed generators (DGs) may experience partial loss of effectiveness (PLOE) and bias faults, and these fault parameters may be heterogeneous and time-varying. The protocol introduces adaptive techniques to avoid information related to fault parameters while using event-driven mechanisms to achieve discrete measurements of neighboring DG. Additionally, the protocol uses boundary layers to construct smooth controllers that prevent the chattering effect caused by nonsmooth controllers. Finally, simulation results confirm the effectiveness of this load voltage regulation strategy.

Nonlinear control of permanent magnet synchronous generators (PMSG) using feedback linearization

This paper presents nonlinear control of permanent magnet synchronous generators using feedback linearization. Permanent-magnet synchronous generators (PMSGs) are commonly used for small variable-speed wind turbines to produce highefficiency, high-reliability, and low-cost wind power generation. To eliminate the effects of nonlinearity caused by magnetic saturation, an input–output feedback linearization technique is applied to design the high-performance nonlinear current controllers. With this nonlinear control scheme, output voltage responses become faster than those in cascade control structures. Thus, the size of the output filter capacitor can be much reduced since fast voltage control is feasible. As with usual PWM power converters, in addition, the input current is regulated in a sinusoidal waveform. The proposed control scheme provides the wind generation system with the maximum efficiency and high dynamic performance.

Sliding Input Output Control of Squirrel Cage Motor Based NPC Five Level Inverter

Speed squirrel cage motor control is an area of research that has been in evidence for some time now. In this paper, a nonlinear controller is presented for the squirrel cage motor drives, based on a combination between input-output feedback linearization control (IOLC) technique and sliding mode control (SMC) to create a new control which is sliding input-output linearization (SIOLC) control of squirrel cage motors which associates by an NPC five levels inverter PWM technical used for the variation of its speed, where the sliding mode control it used for controlling the speed of squirrel cage motor and the input-output linearization control applied for two input witch are flux and current. To test robustness and performance of sliding input-output linearization control (SIOLC) we created a variation of internal parameters of the motor. The simulation results show robustness the sliding input-output linearization control of squirrel cage motor responses.

An Extendable Bidirectional High-Gain DC–DC Converter for Electric Vehicle Applications Equipped With IOFL Controller

High gain bidirectional dc-dc converters are so popular in many applications such as drives, photovoltaic systems, Electric Vehicles (EV) and etc. This paper proposes an extendable bidirectional common-ground dc-dc converter suitable for high gain applications such as EVs. The proposed converter uses fewer number of switches to provide high step-up and high step-down voltage converting capabilities in both power flow directions. Since the input and output of this converter share the same ground, the electromagnetic interface (EMI) is alleviated. In order to assess the versatility of the proposed dc-dc converter and to achieve a fast response, by equipping this converter with an Input-Output Feedback Linearization (IOFL) controller, its performance is analyzed in EV applications. To this end, the steady state calculations are worked out for both charge and discharge directions, then dynamic analysis and control design is presented based on nonlinear controller by IOFL. Simulation and experimental results are provided to prove the feasibility of the proposed converter.

INPUT-OUTPUT LINEARIZATION CONTROL BASED ON THE SLIDING MODE OF THE SQUIRREL CAGE MOTOR

Speed squirrel cage motor control is an area of research that has been in evidence for some time. In this paper, a nonlinear controller is presented for the squirrel cage motor drives, based on a combination between input-output feedback linearization control (IOLC) technique and sliding mode control (SMC) to create a new control which is sliding input-output linearization (SIOLC) control of squirrel cage motors, where the sliding mode control is used for controlling the speed of squirrel cage motor and the input-output linearization control applied for two input witch are flux and current. To test the robustness and performance of sliding input-output linearization control (SIOLC) we created a variety of internal and external parameters of the motor. The simulation results are done using Matlab/Simulink, which shows the robustness of the sliding input-output linearization control of squirrel cage motor responses.

Integrated Isolated AC/DC Converter Using IOFL for LED Driver Applications

Power factor correction, voltage and current ripple reduction and eradicating short-life electrolytic capacitors are challenging issues in state-of-the-art ac/dc Light-Emitting-Diode (LED) drivers. Conventional single-stage drivers need an electrolytic capacitor to ensure low output current flicker. However, electrolyte capacitors having a high failure rate, reduce the life-span of the LED driver. To cover these challenges, in this paper an integrated LED driver is proposed. The proposed driver, is combined of three dc/dc converters with only one active switch. It features high power factor, low current flicker, and due to using only one active switch its cost, volume, complexity and power loss is low. The driver is analyzed step by step to show the operation principles based on duty cycle variations. Dynamic analysis and control design of the proposed driver is presented based on nonlinear control by Input-Output Feedback Linearization (IOFL). The simulation and experimental results have been provided to verify the versatility of the proposed driver.

Disturbance Observer-Based Terminal Sliding Mode Tracking Control for a Class of Nonlinear SISO Systems with Input Saturation

This paper focuses on the trajectory tracking control for general nonlinear single-input single-output (SISO) systems in which the output is not directly related to the control input. To address the tracking problem with the consideration of possible model uncertainty, external disturbance, and control input saturation, we employ the input-output feedback linearization technique and design a finite-time disturbance observer-based terminal sliding mode controller to improve the tracking performance and enhance the robustness. The stability analysis is carried out by using the Lyapunov method. To alleviate the chattering while achieving an acceptable control performance, a boundary layer method is adopted for the trade-off between the high-frequency control actions and the bounded unavoidable nonzero steady-state error. The proposed method is evaluated on the two typical nonlinear systems, which are fully linearizable and partially linearizable, respectively, and compared to the state-of-the-art method in terms of tracking and robustness through comprehensive numerical simulations. The results show that the proposed method not only renders the estimated disturbance error tends to be zero in finite time, but also has superiority in the fast reaction to disturbance and small tracking error without high-frequency chattering.

Modification of Nonlinear Controller for Asymmetric Marine Vehicles Moving in Horizontal Plane

This paper considers a trajectory-tracking control algorithm for underactuated marine vehicles moving horizontally in which the current in the North-East-Down frame is constant. This algorithm is a modification of a control scheme based on the input-output feedback linearization method for which the application condition is that the vehicle is symmetric with respect to the left and right sides. The proposed control scheme can be applied to a fully asymmetric model, and, therefore, the geometric center can be different from the center of mass in both the longitudinal and lateral directions. A velocity transformation to generalized vehicle equations of motion was used to develop a suitable controller. Theoretical considerations were supported by simulation tests performed for a model with 3 degrees of freedom, in which the performance of the proposed algorithm was compared with that of the original algorithm and the selected control scheme based on a combination of backstepping and integral sliding mode control approaches.

Trajectory Control in Discrete-Time Nonlinear Coupling Dynamics of a Soft Exo-Digit and a Human Finger Using Input–Output Feedback Linearization

This paper presents a quasi-static model-based control algorithm for controlling the motion of a soft robotic exo-digit with three independent actuation joints physically interacting with the human finger. A quasi-static analytical model of physical interaction between the soft exo-digit and a human finger model was developed. Then, the model was presented as a nonlinear discrete-time multiple-input multiple-output (MIMO) state-space representation for the control system design. Input–output feedback linearization was utilized and a control input was designed to linearize the input–output, where the input is the actuation pressure of an individual soft actuator, and the output is the pose of the human fingertip. The asymptotic stability of the nonlinear discrete-time system for trajectory tracking control is discussed. A soft robotic exoskeleton digit (exo-digit) and a 3D-printed human-finger model integrated with IMU sensors were used for the experimental test setup. An Arduino-based electro-pneumatic control hardware was developed to control the actuation pressure of the soft exo-digit. The effectiveness of the controller was examined through simulation studies and experimental testing for following different pose trajectories corresponding to the human finger pose during the activities of daily living. The model-based controller was able to follow the desired trajectories with a very low average root-mean-square error of 2.27 mm in the x-direction, 2.75 mm in the y-direction, and 3.90 degrees in the orientation of the human finger distal link about the z-axis.

Full State Constrained Flight Tracking Control for Helicopter Systems with Disturbances

In this paper, a full state-constrained anti-disturbance dynamic surface control method is proposed for six-degree-of-freedom unmanned helicopter systems under full state constraints and disturbances. Firstly, due to the underactuated characteristics of six-degree-of-freedom unmanned helicopter systems, an input–output feedback linearization method is used to transform the complex nonlinear systems into facilitated-control nonlinear ones. Based on the transformed systems, the nonlinear disturbance-observer-based control, backstepping control and Barrier Lyapunov function methods are used to construct the flight controller via uniting the state constraint control and dynamic surface control technologies. Then, Lyapunov stability theory is adopted for analysing the closed-loop tracking error systems, which confirms that the tracking errors are bounded under the proposed flight control scheme. Finally, a simulation in the MATLAB/Simulink environment verifies that the unmanned helicopter system can constrain all states under the action of the designed controller, with good dynamic performance.

Stable feedback linearization-based economic MPC scheme for thermal power plant

The major concern of modern power plants is changing from tracking control to environmental and economic issues. The economic model predictive control (EMPC) scheme, which incorporates the boiler-turbine unit's dynamic tracking and economic optimization into one online framework, can well enhance the dynamic economic performance. Considering the strong nonlinearity that existed in the boiler-turbine system, this paper presents an advanced EMPC scheme based on the input/output feedback linearization (IOFL) approach. The boiler-turbine dynamics are converted via the IOFL method to a linear form, which can be readily used to constitute the standard EMPC scheme. A dual-mode method is adopted in this paper to guarantee the stability of the IOFL EMPC strategy for the boiler-turbine system, in which the first-mode optimizes the economic objective function while preserving the states of the system within a feasible region, and the second-mode moves the system state to the optimum operating point using an auxiliary controller. The simulations under the MATLAB environment demonstrate that the application of the IOFL-based EMPC scheme enhances the economic and dynamic output performance under load demand changes in comparison with fuzzy hierarchical MPC and fuzzy economic MPC schemes.

Adaptive Feedback Linearization Control of SynRM Drives With On-Line Inductance Estimation

This article proposes an adaptive input-output Feedback Linearization Control ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">FLC</i> ) techniques for Synchronous Reluctance Motor ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SynRM</i> ) drives, taking into consideration the iron losses. As a main original content, this work proposes a control law based on a new dynamic model of the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SynRM</i> including iron losses as well as the on-line estimation of the static inductances. The on-line estimation of the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SynRM</i> static inductances permits to inherently take into consideration the magnetic saturation phenomena occuring on both axes. As a major result, it permits a null stator current steady state tracking error even with a proportional derivative controller. The estimation law is obtained thanks to a Lyapunov-based analysis and thus the stability of the entire control system, including the estimation algorithm, is intrinsically guaranteed. The proposed adaptive <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">FLC</i> technique, has been tested experimentally on a suitably developed test set-up, and compared experimentally with its non-adaptive versions in both tuned and detuned working conditions. Moreover, a sensitivity analysis of the performance of the adaptive <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">FLC</i> to the variations of the stator resistance at low speed has been made. Finally, an analysis of the effects of the iron losses on the control performance and stability at high speed in the field weakening region at medium/high loads has been made.