Generalized Proportional Integral Controller Research Articles

Generalized PI control for robust stabilization of dynamical systems

This paper presents a generalization of existing control methods. The proposal stands for a novel control structure that enforces the robust stabilization of a large class of physical and engineering systems, which are subject to the effect of nonlinearities, disturbances and uncertainties. The proposed scheme results as a state feedback plus a generalized proportional–integral (PI) controller. The state feedback compensates vanishing uncertainties, while the generalized PI control term gets rid of the effect of matched uncertainties, where the assumption on the regularity of the disturbance is relaxed. The proposed contribution is the generalization of conventional PI structures to account for the case of more variate closed-loop responses. Although the usefulness of the studied generalization in real applications deserves further investigation, some numerical simulations show the pertinence of the proposed scheme.

A Robust Controller for Upper Limb Rehabilitation Exoskeleton

In this paper, a portable exoskeleton for the rehabilitation of upper extremities of three degrees of freedom (DOF) is proposed. With these degrees of freedom, the exoskeleton provides the movements of flexion–extension and abduction–adduction of the arm and flexion–extension of the forearm. A robust generalized proportional integral (GPI) controller for trajectory tracking to provide smooth movements for rehabilitation with the exoskeleton is proposed. This controller only requires output measurements and is robust against different types of disturbances. Simulation results are presented in the MSC Adams® software environment in co-simulation with Matlab-Simulink® to show the controller’s performance against different types of disturbances. The results of a PID type controller are also contrasted with the results of the GPI controller.

Integration of CNN in a Dynamic Model-Based Controller for Control of a 2DOF Helicopter With Tail Rotor Perturbations

This paper shows a proposal for a control scheme for the trajectory tracking problem in a Two Degree of Freedom Helicopter (2DOFH). For this purpose, a control scheme based on a feedback linearization combined with a Generalized Proportional Integral (GPI) controller is used. In order to implement linearization by feedback, it is required to know and have access to all the physical 2DOFH parameters, however, angular velocity and viscous friction are often not available. Commonly, state observers are used to know the angular velocity, however, estimating friction results out to be more complex. Therefore, we propose the use of a Convolutional Neural Network (CNN) to estimate viscous friction and angular velocity. The variables estimated by the CNN are entered into both the GPI and feedforward controllers. Thus, the system is brought to a linear representation that directly relates the GPI control to the dynamics of perturbations and non-model parameters. Finally, results of numerical simulations are shown that validate the robustness of our scheme in the presence of disturbances in the tail rotor, as well as the advantages of using a feedforward control based on a CNN.

Controlling the PVTOL Aircraft System with an Inverted Pendular Load by means of Nested Saturation Functions and GPI Controller

This paper presents a control scheme that allows height position regulation and stabilization for an unmanned planar vertical takeoff and landing aircraft system with an inverted pendular load. The proposed controller consists of nested saturations and a generalized proportional integral (GPI). The GPI controls the aircraft height and the roll attitude; the latter is used as the fictitious input control. Next, the system is reduced through linear transformations, expressing it as an integrator chain with a nonlinear perturbation. Finally, the nested saturation function-based controller stabilizes the aircraft’s horizontal position and the pendulum’s angle. Obtaining the control approach was a challenging task due to the underactuated nature of the aircraft, particularly ensuring the pendulum’s upright position. The stability analysis was based on the second method of Lyapunov using a simple candidate function. The numerical simulation confirmed the control strategy’s effectiveness and performance. Additionally, the numerical simulation included a comparison against a PD controller, where its corresponding performance indexes were estimated, revealing that our controller had a better response in the presence of unknown disturbances.

Regulation of Nonlinear Chemical Processes with Variable Dead Time: a Generalized Proportional Integral Controller Proposal

This work shows the development and application of a Generalized Proportional Integral (GPI) Controller based on a First Order Plus Dead Time (FOPDT) approximation for an industrial chemical process. GPI control is a relatively recent advancement in automatic control. Nowadays, several enhancements with the GPI technique come from integral reconstructions of the system states. Chemical engineering processes present numerous challenging control problems, including nonlinear dynamic behavior. GPI can become a new option to consider in industrial applications since, along with the arrival of Industry 4.0, there are many improvements in computers and automation architecture to implement controller algorithms. The new controller's functionality shows significant accessibility of mathematical and logical potential. A comparison between the GPI and a PID controller is made under the same conditions to evaluate their performance. After carrying out some tests, the GPI shows better performance and a smoother controller action when applied to the mixing tank with a variable delay than the PID. Performance indexes as Integral Square Error (ISE) for evaluating the Output Variable and Control Effort Total Variation (TVu) for evaluating the control action are used to measure performance. Finally, designing an appropriate controller like the GPI that recognizes and incorporates nonlinearities is required for chemical processes. Simulations were developed using Simulink-MATLAB.

Improved Low Voltage Ride-Through Capability of DFIG with ESO Controller under Unbalanced Network Conditions

Under unbalanced grid condition, in a Doubly-Fed Induction Generator (DFIG), voltage, current, and flux of the stator become asymmetric. Therefore, active-reactive power and torque will be oscillating. In DFIG controlling Rotor Side Converter (RSC) aims to eliminate power and torque oscillations. However, simultaneous elimination of the power and torque oscillations is not possible. Also, Grid Side Converter (GSC) aims to regulate DC-Link voltage. In this paper, in order to regulate DC-Link voltage, an Extended State Observer (ESO) based on a Generalized Proportional-Integral (GPI) controller, is employed. In this controlling method, DC-Link voltage is controlled without measuring the GSC current, and due to using the GPI controller, the improved dynamic response is resistant against voltage changes, and the settling time is reduced. To improve the transient stability and Low Voltage Fault Ride Through (LVRT) capability of DFIG, Statistic Fault Current Limiter (S-FCL) and Magnetic Energy Storage Fault Current Limiter (MES-FCL) are proposed in this paper. The proposed FCL does not only limit the fault current but also fasten voltage recovery. The simulations are implemented by MATLAB software in the synchronous positive and negative sequence reference (d-q).

Control of Doubly-fed Induction Generator with Extended State Observer under Unbalanced Grid Conditions

Under unbalanced grid condition, in a doubly-fed induction generator (DFIG), voltage, current, and flux of the stator become asymmetric. Therefore, active-reactive power and torque will be oscillating. In DFIG controlling rotor side converter (RSC) aims to eliminate power and torque oscillations. However, simultaneous elimination of the power and torque oscillations is not possible. Also, grid side converter (GSC) aims to regulate DC-Link voltage. In this paper, in order to regulate DC-Link voltage, an extended state observer (ESO) based on a generalized proportional-integral (GPI) controller, is employed. In this controlling method, DC-Link voltage is controlled without measuring the GSC current, and due to using the GPI controller, the improved dynamic response is resistant against voltage changes, and the settling time is reduced. A versatile rotor position computation algorithm (RPCA) is utilized to measure the rotor speed. This algorithm is simple, yet it is accurate and is resistant to changes in the resistance of the rotor and stator. The simulations are implemented by MATLAB software in the synchronous positive and negative sequence reference (d-q).

A Generalized Interpretation of Three Types of Disturbance-Based Controllers for Perturbed Integral Systems in Frequency Domain

It is well recognized that two-degree-of-freedom controllers are more proficient than one-degree-of-freedom controllers in overcoming uncertainty and large parameter variation. Establishing the equivalence analysis criterion among different classes of two-degree-of-freedom controllers to evaluate or compare the performance of controllers can stimulate more advanced two-degree-of-freedom controllers. We establish the equivalence analysis criterion by exploring the equivalence among proportional (P) with full-order extended state observer (FESO), P with reduced-order extended state observer (RESO) and proportional-integral (PI) with reduced-order proportional-integral observer (RPIO) in the context of a class of second-order, cascade integral systems. The equivalence analysis results are also suitable for high-order cascade integral systems. Moreover, P with FESO, P with RESO and PI with RPIO can be interpreted as a class of the generalized PI controllers, which can provide parameter tuning guidelines for the traditional PI controllers. Furthermore, the parameters of PI with RPIO cascade control can be entirely applied to tune the parameters of P with FESO cascade control and P with RESO cascade control and vice versa. Lastly, simulations in high speed permanent magnetic synchronous machine starter are provided to illustrate the theoretical results in this brief.

Robust compound control of dynamic bipedal robots

This paper presents a robust compound control strategy to produce a stable gait in dynamic bipedal robots under random perturbations. The proposed control strategy consists of two interactive loops: an adaptive trajectory generator and a robust trajectory tracking controller. The adaptive trajectory generator produces references for the robot controlled joints without a-priori knowledge of the terrain features and minimizes the effects of disturbances and model uncertainties during the gait, particularly during the support-leg exchange. The trajectory tracking controller is a non-switching robust multivariable generalized proportional integral (GPI) controller. The GPI controller rejects external disturbances and uncertainties faced by the robot during the swing walking phase. The proposed control strategy was evaluated on the numerical model of a five-link planar bipedal robot with one degree of under-actuation, four actuators, and point feet. The results showed robust performance and stability under external disturbances and model parameter uncertainties on uneven terrain with uphills and downhills. The stability of the gait was proven through the computation of a Poincaré return map for a hybrid zero dynamics with uncertainties (HZDU) model, which shows convergence to a bounded neighborhood of a nominal orbital periodic behavior.

From flatness, GPI observers, GPI control and flat filters to observer-based ADRC

In this article, we establish the route taken by the author, and his research group, to bring differential flatness to the realm of active disturbance rejection control (ADRC). This avenue entitled: 1) generalized proportional integral observers (GPIO), as natural state and disturbance observers for flat systems, 2) generalized proportional integral (GPI) control, provided with extra integrations, to produce a modular controller known as flat filters (FF’s) and, finally, 3) the establishing of an equivalence of observer based ADRC with FF’s. The context is that of pure integration systems. The obtained controllers depend only on the order of the flat system and they are to be directly used on the basis of the available flat output signal in a universal, modular, fashion. The map is complemented with the relevant references where the intermediate techniques were illustrated and developed, over the years, in connection with laboratory experimental implementations.

Robust GPI Control of a New Parallel Rehabilitation Robot of Lower Extremities

In this paper, we propose a new robot for lower limbs rehabilitation by using a parallel structure. The goal of this robot is not only to produce smooth and precise motions for ankle, knee, and hip, but also to support trajectory tracking. Its parallel configuration was based on the four-bar mechanism in order to have a more stable and robust structure. For the kinematic analysis, the length of one bar was considered variable. For the dynamic analysis, the Euler-Lagrange method was used to define the equations of motion. For the robot control, the robust generalized proportional integral (GPI) controller was proposed to guarantee safe rehabilitation movements. This parallel robot not only showed good results, but also showed various movement possibilities for lower limbs rehabilitation.

Robust flat filtering DSP based control of the boost converter

The article deals with the design and implementation of a flat filter tracking digital controller for a boost DC-DC power converter. A highly perturbed switched boost converter circuit is shown to be efficiently controlled, in a trajectory tracking task for its non-minimum phase output, by means of a suitable linear filter, here addressed as a flat filter. Flat filtering is a natural robust version of generalized proportional integral control (GPIC) by which the effects of arbitrary time varying exogenous disturbances, unknown endogenous nonlinearities and un-modeled dynamics can be jointly attenuated in a conceptually similar fashion to observer-based active disturbance rejection control (ADRC) and algebraic identification based model free control (MFC) but: a) without using extended state observers and b) respecting the original system order in a time-varying simplified model while avoiding algebraic estimation techniques. The proposed control technique based on the TMS320F28335 digital signal processor chip is tested by means of realistic simulations and experimental setup.

Generalized Proportional Integral Control for an Unmanned Quadrotor System

In this article, a generalized proportional integral (GPI) control approach is presented for regulation and trajectory tracking problems in a nonlinear, multivariable quadrotor system model. In the feedback control law, no asymptotic observers or time discretizations are needed in the feedback loop. The GPI controller guarantees the asymptotically and exponentially stable behaviour of the controlled quadrotor position and orientation, as well as the possibilities of carrying out trajectory tracking tasks. The simulation results presented in the paper show that the proposed method exhibits very good stabilization and tracking performance in the presence of atmospheric disturbances and noise measurements.

Speed synchronization control for integrated automotive motor–transmission powertrain system with random delays

This paper presents a robust speed synchronization controller design for an integrated motor–transmission powertrain system in which the driving motor and multi-gearbox are directly coupled. As the controller area network (CAN) is commonly used in the vehicle powertrain system, the possible network-induced random delays in both feedback and forward channel are considered and modeled by using two Markov chains in the controller design process. For the application perspective, the control law adopted here is a generalized proportional–integral (PI) control. By employing the system-augmentation technique, a delay-free stochastic closed-loop system is obtained and the generalized PI controller design problem is converted to a static output feedback (SOF) controller design problem. Since there are external disturbances involved in the closed-loop system, the energy-to-peak performance is considered to guarantee the robustness of the controller. And the controlled output is chosen as the speed synchronization error. To further improve the transient response of the closed-loop system, the pole placement is also employed in the energy-to-peak performance based speed synchronization control. The mode-dependent control gains are obtained by using an iterative linear matrix inequality (LMI) algorithm. Simulation results show the effectiveness of the proposed control approach.

An Active Disturbance Rejection Approach to Leader‐Follower Controlled Formation

AbstractThis article describes the design of a linearizing, observer‐based, robust dynamic feedback control scheme for output reference trajectory tracking tasks in a leader‐follower non‐holonomic car formation problem. The approach is based on the cars' kinematic models. A radical simplification in the form of a global ultra‐model is proposed on the follower's exact open loop position tracking error dynamics obtained via flatness considerations. This results in a system described by an additively disturbed set of two, second order integrators with non‐linear velocity dependent control input gain matrix. The unknown additive disturbances are modeled as absolutely uniformly bounded time signals which may be locally approximated by arbitrary elements of a sufficiently high degree family of Taylor polynomials. Linear high‐gain Luenberger observers of the generalized proportional integral (GPI) type may be readily designed. These observers include the self updating internal model of the unknown disturbance input vector components in the form of generic, instantaneous, time‐polynomial models. The proposed (GPI) observers, which are the dual counterpart of GPI controllers [17], achieve a simultaneous disturbance estimation and tracking error phase variables estimation. This on‐line gathered information is used to advantage on the follower's feedback controller thus allowing for a simple, yet efficient, disturbance and control input gain cancelation effort. The results are applied to have the follower track a time‐delayed version of the actual leader's trajectory. Experimental results are presented which illustrate the robustness and viability of the proposed approach.

A Robust Nonlinear Control Scheme for a Sag Compensator Active Multilevel Rectifier Without Sag Detection Algorithm

In this paper, a robust nonlinear control scheme is proposed for the single-phase active multilevel rectifier (SPAMR) subject to voltage input sags. The scheme is based on the input-output model of the rectifier system combined with exact linearization achieved via generalized proportional-integral (GPI) control. The GPI controller provides enhanced robustness for the SPAMR against unexpected voltage sags and load changes. The main contribution of this paper resides on avoiding the need for voltage sags detection algorithms while improving the dynamic response of the SPAMR. Simulation and experimental results obtained on a 1-kVA SPAMR laboratory prototype are presented.

A Comparison Between the GPI and PID Controllers for the Stabilization of a DC–DC “Buck” Converter: A Field Programmable Gate Array Implementation

This paper presents a comparison between two stabilizing average output feedback controllers implemented on a field programmable gate array (FPGA) facility. A generalized proportional integral (GPI) controller and a proportional integral derivative (PID) controller are implemented using an FPGA, and their respective performances are duly compared. The GPI controller is found to present a better dynamic response than the PID controller in terms of the settling time while exhibiting a greater degree of robustness regarding disturbance rejection represented by severe changes in static and dynamic loads. The average controllers and their corresponding pulsewidth modulation actuators are implemented using a Spartan 3E1600 FPGA.

Nonlinear Control for Magnetic Levitation Systems Based on Fast Online Algebraic Identification of the Input Gain

The control of the popular magnetic levitation system is addressed from the viewpoint of adaptive control based on fast, on line, algebraic parameter estimation, exact linearization and generalized proportional integral (GPI) output feedback control. The GPI controller guarantees an asymptotically exponentially stable behavior of the controlled ball position and the possibilities of carrying out rest-to-rest trajectory tracking tasks. The online algebraic parameter estimation approach estimates, quite accurately, and in a very short period of time, the unknown parameter or the magnetic levitation system. The proposed adaptive controller is actually implemented on a laboratory prototype with excellent experimental results for, both, stabilization and trajectory tracking tasks.

Adaptive Controller for Single-Link Flexible Manipulators Based on Algebraic Identification and Generalized Proportional Integral Control

In this paper, we propose a fast online closed-loop identification method combined with an output-feedback controller of the generalized proportional integral (GPI) type for the control of an uncertain flexible robotic arm with unknown mass at the tip, including a Coulomb friction term in the motor dynamics. A fast nonasymptotic algebraic identification method developed in continuous time is used to identify the unknown system parameter and update the designed certainty equivalence GPI controller. In order to verify this method, several informative simulations and experiments are shown.

Sliding Mode-Delta Modulation GPI Control of a DC Motor through a Buck Converter

In this article, one Generalized Proportional Integral (GPI) feedback control scheme is proposed for a smooth “ starter” for a DC motor based on a switch controlled DC-to-DC power converter of the “buck” type. The dynamic feedback controller is based on a suitable combination of GPI based control, flatness and a Σ – Δ modulator implementation of the average designed controller. The scheme proposes a direct regulation of the motor shaft speed. As a consequence, the proposed feedback controller, which are not based on asymptotic observers nor calculations based on samplings, use only an optical velocity sensor. The effectiveness of the proposed controller was verified by computer simulations using the P-Spice circuit simulation program.