3D Control Research Articles

Robust DOF control for uncertain polynomial fuzzy systems in finite frequency domain

This study addresses the issue of robust dynamic output feedback control (DOF) for polynomial Takagi–Sugeno (T–S) fuzzy systems in the Finite Frequency (FF) domain. Sufficient conditions for designing the robust DOF control are derived in terms of the sum of squares (SOS). The proposed strategy is built in the FF domain to reduce conservation-generated by the techniques established in the whole frequency domain. In addition, there are no transformation matrices or equality constraints under these conditions, which simplifies the numerical solution. To show the validity of the suggested technique, several numerical examples are presented.

Investigation of 2DOF PID Controller for Physio-Therapeutic Application for Elbow Rehabilitation

The aim of this work is to evaluate the output of a two-degree of freedom (DOF) proportional integral derivative (PID) controller for controlling elbow flexion and extension on an upper limb rehabilitation robot of an existing model. Since the usage of upper limb rehabilitation is increasing dramatically because of human impairment, 2DOF has been proposed in this work as a suitable controller. The 2DOF PID controller offers set-point-weight features and, hence, is fast in removing disturbance from the system and ensuring system stability. Importantly, as the system parameters are unknown in this work, the black-box model approach has been taken into consideration, using the MATLAB System identification toolbox to estimate a model. The best-fitted estimated model is then coupled with the proposed controller in the MATLAB/Simulink environment that, upon successful simulation works, leads, finally, to the hardware implementation. Three different amplitudes of sinusoidal current signals, such as 0.3 amps, 0.2 amps, and 0.1 amps, are applied for hardware measurements. Considering patients’ physical conditions. In this work, the 2DOF controller offers a fast transient response, settling time, negligible tracking error and 0% overshoot and undershoot.

Two-Degree-of-Freedom based Model Reference Adaptive Control of Non-minimum Phase System

This paper presents the design of the Two-Degree-of-Freedom (2DOF) based Model Reference Adaptive Control (MRAC) as a tracking control system for the Non-minimum Phase (NMP) system. Perfect set point tracking is possible by using a cascade-connected inverse and non-inverse transfer function model of the dynamic system. But this method is restricted to the minimum phase system only, whereas, NMP system produces unbounded output response using this inverse model technique. Though, adaptive inverse feed-forward control technique is an effective tracking control system, it also requires an inverse model of the system. To overcome this problem, a novel feed-forward MRAC scheme for the inverse NMP model and the State feedback controller of the non-inverse model has been proposed, and both the controller are decoupled in a 2DOF framework. The feed-forward control technique guaranteed the tracking performance using the Lyapunov stability theory, and the feedback counterpart enhances the steady-state performance of the NMP plant. The robustness of the asymptotic stability as well as tracking performance of the closed-loop NMP system has been ensured by the proposed 2DOF control based MRAC technique. The effectiveness of the proposed control structure initially has been verified by the MATLAB Simulink toolbox and, then the demand has been strengthened by the implementation of the same control logic in the real-time environment using analog simulation with Op-amp based hardware model.

Anti-swing control of a hydraulic loader crane with a hanging load

In this paper, anti-swing control for a hydraulic loader crane is presented. The difference between hydraulic and electric cranes are discussed to show the challenges associated with hydraulic actuation. The hanging load dynamics and relevant kinematics of the crane are derived to create the 2-DOF anti-swing controller. The anti-swing controller is added to the electro-hydraulic motion controller via feedforward. A dynamic simulation model of the crane is made, and the control system is evaluated in simulations with a path controller in actuator space. Simulation results show significant reduction in the load swing angle during motion. Experiments are carried out to verify the performance of the anti-swing controller, showing good suppression of the payload angle in practice.

Robust structured controller synthesis for interleaved boost converters using an H∞ control method

The regulation of output voltage and equivalent distribution of phase currents of multi-phase converters which have non-minimum phase characteristic are still challenges, especially in the presence of uncertainties in real parameters, duty cycle, input voltage, and load disturbances. However, in classical third-order integral-lead (Type-III) controller design methodologies, the controller is synthesized considering only the nominal performance conditions. This paper proposes a structured [Formula: see text] synthesis framework based on an optimization methodology to the design of a robust Type-III controller for interleaved boost converters. The structured [Formula: see text] control approach is adapted for optimization of Type-III feedback and feedforward controllers in two-degree-of-freedom (2-DOF) control system configuration. The robust stability of the closed-loop interleaved boost converter system against model uncertainties is ensured via the classical [Formula: see text]-analysis technique. Numerical comparisons are made among the classical, i.e. unstructured or full order, [Formula: see text]-based controller design method, a dual-loop PI controller, and proposed 1-DOF and 2-DOF structured controller synthesis approaches on an interleaved boost converter model. Simulation results verify the effectiveness and advantages of the proposed approach from the viewpoint of the output voltage regulation under different disturbance points.

LPV Control Synthesis for Sensor Senescence in Feedback Control System

The senescence of system sensor(s) probably causing degenerate system behavior or systembreakdown. Motivated by that, this work considers the synthesis of a gain scheduling controlfor linear parameter varying (LPV) system via linear matrix inequalities (LMIs) techniquessuch that sensors senescence information incorporated in the design of the controller. That is,the degradation of sensor effectiveness due to senescence is modeled by the variation of sensormeasurements’ noise co-variance. The sensors’ senescence information is incorporated as apart of the scheduling parameters for the LPV controller. The synthesis control matrices via linearmatrix inequalities have been re-structured and re-formalized in a way that they incorporatethe sensors senescence information to synthesize a gain scheduling dynamic output feedback(GS - DOF) control. That is, the existing GS - DOF control design LMIs have been modifiedto include the noise co-variance matrix. The significant achievement is the control design conditionsdescription of GS - DOF control in a way that ensures the desired integrated H2&H1 performances in the presence of sensors senescence, where sensors’ senescence information isincorporated as a part of the scheduling parameters for the LPV controller. In addition, two setsof controllers have been synthesized and studied. The simulation expresses the benefits of theproposed controllers, and closed loop system H1 and H2 performances are also studied. Thesynthesized controller ensures the performance associate with a closed loop, the closed loopsystem stability, and the scheme of control is simple enough for real time implementations.

Stable, simultaneous and proportional 4-DoF prosthetic hand control via synergy-inspired linear interpolation: a case series

BackgroundCurrent commercial prosthetic hand controllers limit patients’ ability to fully engage high Degree-of-Freedom (DoF) prosthetic hands. Available feedforward controllers rely on large training data sets for controller setup and a need for recalibration upon prosthesis donning. Recently, an intuitive, proportional, simultaneous, regression-based 3-DoF controller remained stable for several months without retraining by combining chronically implanted electromyography (ciEMG) electrodes with a K-Nearest-Neighbor (KNN) mapping technique. The training dataset requirements for simultaneous KNN controllers increase exponentially with DoF, limiting the realistic development of KNN controllers in more than three DoF. We hypothesize that a controller combining linear interpolation, the muscle synergy framework, and a sufficient number of ciEMG channels (at least two per DoF), can allow stable, high-DoF control.MethodsTwo trans-radial amputee subjects, S6 and S8, were implanted with percutaneously interfaced bipolar intramuscular electrodes. At the time of the study, S6 and S8 had 6 and 8 bipolar EMG electrodes, respectively. A Virtual Reality (VR) system guided users through single and paired training movements in one 3-DoF and four different 4-DoF cases. A linear model of user activity was built by partitioning EMG feature space into regions bounded by vectors of steady state movement EMG patterns. The controller evaluated online EMG signals by linearly interpolating the movement class labels for surrounding trained EMG movements. This yields a simultaneous, continuous, intuitive, and proportional controller. Controllers were evaluated in 3-DoF and 4-DoF through a target-matching task in which subjects controlled a virtual hand to match 80 targets spanning the available movement space. Match Percentage, Time-To-Target, and Path Efficiency were evaluated over a 10-month period based on subject availability.Results and conclusionsIn 3-DoF, S6 and S8 matched most targets and demonstrated stable control after 8 and 10 months, respectively. In 4-DoF, both subjects initially found two of four 4-DoF controllers usable, matching most targets. S8 4-DoF controllers were stable, and showed improving trends over 7–9 months without retraining or at-home practice. S6 4-DoF controllers were unstable after 7 months without retraining. These results indicate that the performance of the controller proposed in this study may remain stable, or even improve, provided initial viability and a sufficient number of EMG channels. Overall, this study demonstrates a controller capable of stable, simultaneous, proportional, intuitive, and continuous control in 3-DoF for up to ten months and in 4-DoF for up to nine months without retraining or at-home use with minimal training times.

A Modified 2-DOF Control Framework and GA Based Intelligent Tuning of PID Controllers

Although a controller is well-tuned for set-point tracking, it shows poor control results for load disturbance rejection and vice versa. In this paper, a modified two-degree-of-freedom (2-DOF) control framework to solve this problem is proposed, and an optimal tuning method for the pa-rameters of each proportional integral derivative (PID) controller is discussed. The unique feature of the proposed scheme is that a feedforward controller is embedded in the parallel control structure to improve set-point tracking performance. This feedforward controller and the standard PID con-troller are combined to create a new set-point weighted PID controller with a set-point weighting function. Therefore, in this study, two controllers are used: a set-point weighted PID controller for set-point tracking and a conventional PID controller for load disturbance rejection. The parameters included in the two controllers are tuned separately to improve set-point tracking and load dis-turbance rejection performances, respectively. Each controller is optimally tuned by genetic algo-rithm (GA) in terms of minimizing the IAE performance index, and what is special at this time is that it also tunes the set-point weighting parameter simultaneously. The simulation results performed on four virtual processes verify that the proposed method shows better performance in set-point tracking and load disturbance rejection than those of the other methods.

Cuckoo optimised 2DOF controllers for stabilising the frequency changes in restructured power system with wind-hydro units

This paper introduces an innovative approach for automatic generation control (AGC) of multi-area diverse-sources of the interconnected systems under a restructured scenario. In this work, proportional-integral (PI), proportional-integral derivative (PID), and 2-degree of freedom PID (2-DOF-PID) controllers are proposed to stabilise the variations in the system parameters at distinct loading conditions. Different types of metaheuristic optimisation methods like teaching–learning-based optimisation (TLBO) and cuckoo search algorithms are suggested to acquire the optimal gain values of the proposed controllers. To alleviate the frequency and inter-area power line deviations, the cuckoo tuned 2-DOF-PID controller has rendered better dynamic performances in terms of overshoot, settling time, and undershoot over other control approaches. Further, the robustness of the system has been ascertained while varying the loading circumstances and system specifications up to ±25% from their prescribed values which helped to exhibit the ability of the proposed method.

Tuning of the two degrees of freedom FOIMC based on the Smith predictor

This paper proposes a novel two degrees of freedom (2-DOF) fractional order internal model controller (FOIMC) for the height control of a coupled tank system. Coupled tank systems find applications in the process control industries. The level control of the coupled tank system is a challenging problem in the control systems because of its nonlinearity and time delay involved. The level control of the coupled tank system has variable servo tracking and disturbance rejection requirements. 2-DOF controller achieves better servo tracking and disturbance rejection than a one degree of freedom (1-DOF) controller. The proposed servo tracking controller is designed using the Bode’s ideal loop transfer function and direct synthesis approach. The parameters of the Servo tracking controller are tuned using peak overshoot and settling time specifications. The disturbance rejection controller is designed analytically. A detailed study of the effect of the fractional order on the disturbance rejection property and stability. Robust stability of the proposed controller is analysed using $$H_{\infty }$$ norm of the uncertainty bound. Comparison of the simulation results of the proposed controller with the state of the art showed better performance of the proposed controller. Frequency domain analysis also indicates the superior performance of the proposed 2-DOF FOIMC.

Model Predictive Feedforward Control for High-Dynamic Speed Control of Combustion Engine Test Beds

Hardware-in-the-Loop tests have become a key factor in decreasing development time of various drive systems. In this context, high performance test beds, where feedback control plays a major role, are necessary to meet the demanding requirements such as real driving emissions in the automotive industry. Particularly for combustion engine test beds, periodic combustion strokes cause large oscillations in different measurement signals on engine test beds, which causes severe problems since conventional controllers try to compensate for these periodic disturbances. The control settings are a trade-off between fast reference tracking and undesirably strong disturbance rejection, which may compromise test results. An ordinary two-degree-of-freedom (2-DOF) control with flatness-based feedforward control produces relief in separating reference and disturbance behavior but cannot handle input constraints. Thus, a model predictive feedforward controller (MPFFC) in combination with the 2-DOF strategy is introduced for high-dynamic speed control in this contribution. The MPFFC generates optimal input and output trajectories, which respect constraints of the system. Fast reference tracking is achieved without the risk of falsification by high feedback. Comparisons between the proposed method, a simple feedback and a standard 2-DOF controller with a conventional flatness-based feedforward control are performed on a state-of-the-art 4-cylinder engine test bed. The experiments constitute a rare implementation of a MPFFC on a real system and demonstrate its capabilities of separating reference and disturbance response as well as taking advantage of certain situations to even further improve reference tracking speed.

A Robust Offline Precomputed Optimal Feedforward Control Action for the Real Time Feedback/Feedforward Control of Double Pendulum Gantry Cranes

This paper deals with FeedBack/ FeedForward (FB/FF) control of double pendulum gantry crane systems with payloads taking values over arbitrarily large intervals. The new proposed 2DoF control architecture is aimed at: 1) to speed up the horizontal payload transportation while minimizing the tracking error with respect to a desired trajectory, 2) to minimize the sway angles amplitude. The main features of the control design procedure are: 1) the dynamic output FB control is designed in order to ensure the robust stability of the closed loop system and the steady-state exact payload positioning; 2) the FF control action is given by the optimally weighted sum of the two contributions due to FF Plant Inversion a (FFPI) and FF Closed Loop Inversion (FFCLI) control schemes; 3) the optimal robust FF control input is obtained as the solution of a min max optimization problem that can be solved offline with numerically efficient procedures; 4) the provided analytical closed form of the FF input in terms of a linear combination of polynomial B-splines basis functions allows an easy implementation on commercial devices.

Design of 2DOF Control System for Quadrotor Control System with a PFC

Design of 2DOF Control System for Quadrotor Control System with a PFC

A 3DOF Path-Following Controller for a Non-Directionally Stable Vessel with Slow Thruster Dynamics

Abstract In this paper, a 3DOF path-following controller for an electric double-ended passenger ferry prototype is presented. The controller is formulated through a 3-step backstepping approach, taking into consideration several challenging physical properties of the vessel, such as a lack of passive damping in the vessel hull, lack of directional stability, and slow thruster dynamics compared to the vessel dynamics. The controller design also features a new thrust allocation approach that allows the thrust allocation of the over-actuated thruster system to be formulated on closed form, which enables us to include the thruster dynamics in the control law. The performance of the suggested 3DOF controller is demonstrated and compared to two other controllers through simulations with a model of the electric passenger ferry.

Affine linear parameter‐varying embedding of non‐linear models with improved accuracy and minimal overbounding

In this study, automated generation of linear parameter-varying (LPV) state-space models to embed the dynamical behaviour of non-linear systems is considered, focusing on the trade-off between scheduling complexity and model accuracy and the minimisation of the conservativeness of the resulting embedding. The LPV state-space model is synthesised with affine scheduling dependency, while the scheduling variables themselves are non-linear functions of the state and input variables of the original system. The method allows to generate complete or approximative embedding of the non-linear system model and also it can be used to minimise the complexity of existing LPV embeddings. The capabilities of the method are demonstrated on simulation examples and also in an empirical case study where the first-principle motion model of a three degrees of freedom (3DOF) control moment gyroscope is converted by the proposed method to an LPV model with low scheduling complexity. Using the resulting model, a gain-scheduled controller is designed and applied on the gyroscope, demonstrating the efficiency of the developed approach.

Performance Assessment of an Islanded Hybrid Power System with Different Storage Combinations Using an FPA-Tuned Two-Degree-of-Freedom (2DOF) Controller

During the past few decades, there has been significant growth in the renewable energy market because of increased concern over global warming and the continuous depletion of fossil fuel resources. There is a promising solar thermal technology that utilizes low-temperature heat to generate electricity. The conversion process of thermal energy to electricity is based on the principle of an organic Rankine cycle (ORC). This study investigated a novel islanded hybrid power system consisting of an ORC low temperature solar thermal system, wind (WTG), diesel generation (DEG) set, and combined application of an energy storage system (ESS), such as a battery (BESS), super magnetic energy storage (SMES), and an ultracapacitor (UC) unit. Furthermore, the hybrid system was employed with a single controller (one of proportional-integral (PI), PI with derivative (PID), two-degree-of-freedom (2DOF) PI, and 2DOF PID controllers) with proportionate gains to the DEG, and the ESS, which is another unique aspect of this work. Moreover, a comparative performance assessment of the flower pollination algorithm (FPA) to tune the PI, PID, 2DOF PI, and 2DOF PID controllers was carried out. Finally, the performance of the above hybrid system was compared with different ESS combinations, namely, (i) only BESS, (ii) BESS + UC, and (iii) BESS + SMES. The simulation results indicated that a renewable integrated isolated power system with BESS + SMES provided a better response than the other ESS combinations. In fact, the presence of comparative dynamic responses verified the superiority of an FPA-tuned 2DOF PID compared with other FPA-tuned controllers.

Robust Linear Control of Boost and Buck-Boost DC-DC Converters in Micro-Grids with Constant Power Loads

Power distribution systems nowadays are highly penetrated by renewable energy sources, and this explains the dominant role of power electronic converters in their operation. However, the presence of multiple power electronic conversion units gives rise to the so-called phenomenon of Constant Power Loads (CPLs), which poses a serious stability challenge in the overall operation of a DC micro-grid. This article addresses the problem of enhancing the stability margin of boost and buck-boost DC-DC converters employed in DC micro-grids under uncertain mixed load conditions. This is done with a recently proposed methodology that relies on a two-degree-of-freedom (2-DOF) controller, comprised by a voltage-mode Proportional Integral Derivative (PID) (Type-III) primary controller and a reference governor (RG) secondary controller. This complementary scheme adjusts the imposed voltage reference dynamically and is designed in an optimal fashion via the Model Predictive Control (MPC) methodology based on a specialized composite (current and power) estimator. The outcome is a robust linear MPC controller in an explicit form that is shown to possess interesting robustness properties in a wide operating range and under various disturbances and mixed load conditions. The robustness and performance of the proposed controller/observer pair under steady-state, line, and mixed load variations is validated through extensive Matlab/Simulink simulations.

Weighted Internal Model Control-Proportional Integral Derivative Control Scheme Via Fractional Gradient Descent Algorithm

Abstract An adaptive controller design technique based on internal model control (IMC) scheme is proposed in this paper. Multiple IMC controllers having different values of filter time constants and exhibiting widely different performance are combined via weight update rule. The weight update rule, formulated via convex combination of integral and fractional order gradient descent algorithms, assigns time varying weights to individual candidate controllers to obtain an enhanced performance over the individual candidate controllers. The beauty of the proposed technique is that it employs the simplicity of one degree-of-freedom (1DOF) IMC structure to achieve an improved performance over existing 2DOF control schemes. The efficacy of the proposed technique is demonstrated via three illustrative examples and via experimental validation on the hardware setup of dc servosystem. An extensive comparative analysis in terms of simulation plots and performance indices offers a testimony to the effectiveness of the proposed scheme.

Performance Analysis and Implementation of Fractional Order 2-DOF Control on Cart–Inverted Pendulum System

Analysis of a typical cart–inverted pendulum system is very effective to evaluate and perceive the significant control strategies including various aspects of control engineering with vast application in industrial robots. The system is nonminimum-phase highly unstable nonlinear with a single input voltage to the dc motor providing two outputs, i.e., cart position and pendulum angle. Based on its mathematical model comprising of two loops dispensing two outputs following a single reference input, the control method is proposed. Here, the inner primary loop is regulating the pendulum angle, while the outer secondary loop is steering the position of the cart on the rail. A robust control is achieved by the fractional-order (FO)-PI λ D µ controller, which allows one to have auxiliary tuning parameters compared with the classical one. Furthermore, this is extended to FO two degrees of freedom allowing improvement in the transient response with this additional flexibility in design while maintaining adequate loop robustness. The simulation and experimental results are demonstrated to quantify the performance improvement attained. This verifies the effectiveness of the approach made minimizing significantly the oscillations in the output response.

Performance analysis of distributed power flow controller with ultra-capacitor for regulating the frequency deviations in restructured power system

Abstract This paper presents a novel approach for automatic generation control (AGC) of two-area deregulated system with unequal sources for sustaining the frequency and tie-line power at perturbations. The combination of ultra-capacitor (UC) and various FACTS controllers such as Thyristor-controlled series capacitor (TCSC), Static synchronous series compensator (SSSC), Unified power flow controller (UPFC), and Distributed power flow controller (DPFC) have been investigated in AGC of interconnected system with thermal-wind and hydro-diesel generating units. An innovative metaheuristic method called bat algorithm (BA) is used to ascertain the optimal gain parameters of the two degree of freedom (2DOF) controllers using an integral squared error (ISE) criteria. Furthermore, the productive assessment of the bat tuned 2DOF controllers are also compared with teaching learning-based optimization (TLBO) and cuckoo search (CS) methods optimized 2DOF in distinct contract scenarios of the suggested restructured system. The effect of the coordinated performance of UC and DPFC has been mitigated the oscillatory response of the AGC system at various operating circumstances. The investigations disclose that the bat optimized 2DOF-PID yield the productive outcomes with coordination of DPFC and UC in all contract transactions of the restructured system.