Modified Relay Feedback Test Research Articles

Autotuning of PID controller using the modified relay feedback test and optimization under uncertainty principle for robotic manipulators

AbstractThe development of an autotuning mechanism for robotic manipulators, inspired by the success of autotuners in industrial systems, aims to reduce the time and cost of tuning robotic manipulators. This paper introduces an auto‐tuning method for PID controllers in robotic manipulators using the Modified Relay Feedback Test (MRFT) and the Optimization Under Uncertainty (OUU) principle. The mechanism is versatile, suitable for manipulators of varying scales and motor power capacities. It incorporates actuator dynamics and a combined model of Brushless DC motors with an n‐link manipulator for TR development. Various manipulator models, including commercial and open‐source types were used to refine and test the TR. An algorithm is also proposed for tuning commercial manipulators' controllers without changing the existing closed‐loop system structure. Experimental and simulation tests demonstrate the method's effectiveness, showing better performance than traditional approaches, particularly in reducing overshoot and settling time.

Design of auto‐tuning‐based adaptive controllers for voltage source converters with inductive loads

AbstractThis paper presents an auto‐tuning method for dc‐ac voltage source converters (VSCs) with an inductive load that is based on the modified relay feedback test (MRFT). Controllers tuned by the proposed method can produce near‐optimal dynamic performance for dc–ac VSCs without requiring knowledge of the plant's parameters. The controller consists of a PID cascaded with a digital notch filter. The tuning involves two steps. In the first step, the MRFT is used to tune the digital notch filter to compensate for the LCL resonance resulting from the LC filter's interaction with the inductive load. In the second step, one more MRFT is used to tune the PID controller using optimal tuning rules that are derived in advance (offline). The proposed optimal for the class of the dc–ac VSCs tuning rules can guarantee a specified phase margin and near optimal transient performance for any randomly picked VSC. The performance of the proposed tuning of the PID + notch filter is verified by simulations and experiments. The dynamic response of the auto‐tuned controller compares well to the response of a theoretically optimal but non‐auto‐tuned PID + notch filter designed using the full knowledge of the LC filter and the load.

Noise-Tolerant Identification and Tuning Approach Using Deep Neural Networks for Visual Servoing Applications

Vision-based control of unmanned aerial vehicles (UAVs) has been adopted in a wide range of applications due to the availability of low-cost onboard sensors and computers. Tuning such systems to work properly requires extensive domain-specific experience, which limits the growth of emerging applications. Moreover, obtaining performance limits for UAVs performing visual servoing is difficult due to the complexity of the models used. In this article, we propose a novel noise-tolerant approach for real-time identification and tuning of visual servoing systems. This is based on the deep neural networks (DNNs) classification of the system response generated by the modified relay feedback test (MRFT). The proposed method, called DNN with noise-protected MRFT (DNN-NP-MRFT), can be used with a multitude of vision sensors and estimation algorithms despite high levels of sensor noise. The response of DNN-NP-MRFT to noise perturbations is investigated and its effect on identification and tuning performance is analyzed. The proposed DNN-NP-MRFT is able to detect performance changes induced by the use of high latency vision sensors or by integrating an inertial measurement unit sensor into the UAV states estimation pipeline. Experimental identification closely matches simulation results, which can be used to explain the system behavior and predict the closed-loop performance limits for a given hardware and software setup. We also demonstrate the ability of DNN-NP-MRFT-tuned UAVs to reject external disturbances like wind or human push and pull. Finally, we discuss the advantages of the proposed DNN-NP-MRFT visual servoing design approach compared with other approaches in the literature.

Real-Time Adaptive Dynamics Based State Estimation Scheme for Unmanned Aircrafts

In this paper we present a state estimation scheme for Unmanned Aircrafts (UAs) utilizing dynamics based models and multi-sensor data fusion. Employing the UA dynamics in estimation can substantially enhance the estimator performance, but obtaining accurate dynamics parameters for each UA is computationally costly and complex. To eliminate these issues, we propose two decoupled Extended Kalman Filters (EKFs), namely the Rotational Decoupled Extended Kalman Filter (RDEKF) and the Translational Decoupled Extended Kalman Filter (TDEKF). The dynamics parameters in these filters are identified in real-time using the Deep Neural Network and the Modified Relay Feedback Test (DNN-MRFT) approach. This approach doesn’t demand prior knowledge of the UA physical parameters, requiring only an Inertial Measurement Unit (IMU) and a positioning system for model classification. Our estimation scheme provides position, velocity and attitude estimates, in addition to smooth lag-free inertial acceleration estimates. We show experimentally the advantages of our approach on trajectory tracking problems that uses low rate position sensors. We also demonstrate how utilizing the estimated acceleration in feedback control can reduce the tracking error of an optimally tuned system by 43%. Moreover, the proposed estimator produces smooth estimates that leads to a reduction of controller action by 6.6%, when compared to kinematic based estimators. We compare the achieved results against other methods that require full prior knowledge of the UA parameters or the noise models, and show advantages in performance and real-time capability.

Multirotors From Takeoff to Real-Time Full Identification Using the Modified Relay Feedback Test and Deep Neural Networks

Low-cost real-time identification of multirotor unmanned aerial vehicle (UAV) dynamics is an active area of research supported by the surge in demand and emerging application domains. Such real-time identification capabilities shorten development time and cost, making UAVs’ technology more accessible, and enable a wide variety of advanced applications. In this article, we present a novel comprehensive approach, called DNN-MRFT, for real-time identification and tuning of multirotor UAVs using the modified relay feedback test (MRFT) and deep neural networks (DNNs). The main contribution is the development of a generalized framework for the application of DNN-MRFT to higher order systems. One of the notable advantages of DNN-MRFT is the exact estimation of identified process gain, which mitigates the inaccuracies introduced due to the use of the describing function method in approximating the response of Lure’s systems. A secondary contribution is a generalized controller based on DNN-MRFT that takes off a UAV with unknown dynamics and identifies the inner loops dynamics in-flight. Using the developed framework, DNN-MRFT is sequentially applied to the outer translational loops of the UAV utilizing in-flight results obtained for the inner attitude loops. DNN-MRFT takes on average 15 s to get the full knowledge of multirotor UAV dynamics, and without any further tuning or calibration, the UAV would be able to pass through a vertical window and accurately follow trajectories achieving state-of-the-art performance. Such demonstrated accuracy, speed, and robustness of identification pushes the limits of state of the art in real-time identification of UAVs.

Systematic Online Tuning of Multirotor UAVs for Accurate Trajectory Tracking Under Wind Disturbances and In-Flight Dynamics Changes

The demand for accurate and fast trajectory tracking for multirotor Unmanned Aerial Vehicles (UAVs) have grown recently due to advances in UAV avionics technology and application domains. In many applications, the multirotor UAV is required to accurately perform aggressive maneuvers in challenging scenarios like the presence of external wind disturbances or in-flight payload changes. In this paper, we propose a systematic controller tuning approach based on identification results obtained by a recently developed Deep Neural Networks with the Modified Relay Feedback Test (DNN-MRFT) algorithm. We formulate a linear equivalent representation suitable for DNN-MRFT using feedback linearization. This representation enables the analytical investigation of different controller structures and tuning settings, and captures the non-linearity trends of the system. With this approach, the trade-off between performance and robustness in design was made possible which is convenient for the design of controllers of UAVs operating in uncertain environments. We demonstrate that our approach is adaptive and robust through a set of experiments, where accurate trajectory tracking is maintained despite significant changes to the UAV aerodynamic characteristics and the application of wind disturbance. Due to the model-based system design, it was possible to obtain low discrepancy between simulation and experimental results which is beneficial for potential use of the proposed approach for real-time model-based planning and fault detection tasks. We obtained RMSE of 3.59 cm when tracking aggressive trajectories in the presence of strong wind, which is on par with state-of-the-art.

Non-parametric tuning of PID Controllers: Evolution of ideas

Non-parametric tuning was introduces by J. Ziegler and N. Nichols with the step test and continuous cycling tests and the respective tuning rules. Whereas the step test based tuning had some feature of parametric tuning, the continuous cycling test based tuning was purely non-parametric. The latter test involves bringing the system under proportional control into a sustained oscillation and measuring the frequency of these oscillations and fixing the gain value, that are called the ultimate frequency and ultimate gain. The test was intended for manual tuning of PID controllers. It is relatively hard to automate, and it is not used in auto-tuners. Another test, called relay feedback test (RFT), was proposed by K. Astrom and T. Hagglund to excite self-oscillations through the inclusion of a nonlinear element (relay) in the control loop. This test is easier to automate, and it found applications in industrial auto-tuners. In both these tests ultimate frequency coincides with the phase cross-over frequency of the process/plant. Yet, both the original continuous cycling test and the RFT suffer from such a drawback as the change of the phase cross-over frequency after PID controller introduction. A new test, the modified relay feedback test (MRFT), which can ensure that the test oscillations are excited at he frequency that becomes the phase cross-over frequency after introduction of a controller in the loop, was recently introduced. This property is attained through coordinated test and tuning, which is considered in the book chapter. Moreover, the tuning rules are optimized for a selected class of processes, which offers the paradigm of optimal non-parametric tuning.

Auto-Tuning of DC-DC Buck Converters Through the Modified Relay Feedback Test

This paper presents the design and application of the modified relay feedback test (MRFT) auto-tuning method to the PID voltage-mode control of dc-dc buck converters. The proposed method, which also includes a set of tuning rules, does not require knowledge of the converter or load parameters, and produces a controller with near-optimal dynamic performance for virtually any dc-dc buck converter. The proposed MRFT auto-tuning also guarantees a specified phase margin. An important feature of the MRFT auto-tuning is that it is non-complex and thus practical, consisting of a simple test stage and a quick tuning stage. In the test stage oscillations are excited using the MRFT algorithm, and the frequency and amplitude of these oscillations are measured. In the tuning stage, these measurements are used with the pre-designed tuning rules to calculate PID controller parameters. The designed MRFT auto-tuning is evaluated experimentally by using it to auto-tune four different dc-dc buck converter designs, where in each case parameters of the converter are unknown to the auto-tuning algorithm. The experimental results show good performance of the MRFT auto-tuned controller in all cases. A mathematical proof that the MRFT auto-tuning guarantees a specified phase margin is also provided.

Optimal non-parametric tuning of PID controllers based on classification of shapes of oscillations in modified relay feedback test

In this work, tuning rules of the PID controller have been developed by categorizing a system's response into distinct classes. The classes are formed using the shapes of the test oscillations induced by the system under the Modified Relay Feedback Test (MRFT) produced by specific system models. It is proposed that a physical system can be categorized into one of the proposed classes and thus the tuning rules for a particular class can apply to any kind of system from this class. The idea of producing tuning rules that are based on the shape of the oscillations induced in the loop containing the process comes from the observations that oscillatory responses of physical systems reveal just a few different shapes depending on system dynamics. For applying the developed optimal tuning rules for an arbitrary system, first, certain system characteristics are determined using a priori knowledge of the class model. Then the system's response with the application of the MRFT is examined to classify the oscillation waveform/shape. In this work, such classification is carried out using a cross-correlation algorithm. Finally, a class tuning rules are applied.

Auto-Tuning of PID Controller with Gain Margin Specification for Digital Voltage-Mode Buck Converter

This paper investigates application of an auto-tuning of a digital PID controller for a DC-DC buck converter, based on the modified relay feedback test (MRFT). Amplitude and frequency of the MRFT oscillations are used as input to PID controller tuning rules that are proposed in this paper. These rules are coordinated with the MRFT through a certain parameter in order to allow for the specification of gain margin - for which a mathematical proof is provided in the paper. Another contribution of this work is the development of the implementation of the MRFT auto-tuning method on a digitally-controlled DC-DC buck converter. A PID controller is auto-tuned and tested on a digitally-controlled buck converter prototype, and its performance is compared to that of an optimal but non-auto-tunable controller. Results show good performance of the proposed method. A final contribution is the discussion of important practical considerations regarding the application of the MRFT-based auto-tuning to switching converters.

Real-Time System Identification Using Deep Learning for Linear Processes With Application to Unmanned Aerial Vehicles

This paper proposes a novel parametric identification approach for linear systems using Deep Learning (DL) and the Modified Relay Feedback Test (MRFT). The proposed methodology utilizes MRFT to reveal distinguishing frequencies about an unknown process; which are then passed to a trained DL model to identify the underlying process parameters. The presented approach guarantees stability and performance in the identification and control phases respectively, and requires few seconds of observation data to infer the dynamic system parameters. Quadrotor Unmanned Aerial Vehicle (UAV) attitude and altitude dynamics were used in simulation and experimentation to verify the presented methodology. Results show the effectiveness and real-time capabilities of the proposed approach, which outperforms the conventional Prediction Error Method in terms of accuracy, robustness to biases, computational efficiency and data requirements.

Design of rules for in-flight non-parametric tuning of PID controllers for unmanned aerial vehicles

Designing high performance controllers for multirotors is a rigorous task that is often solved by trial and error approach. Trial and error tuning usually results in non-optimal controller parameters. Tuning controllers based on the existing quadrotor models would result in poor performance of quadrotors due to simplifications and inaccuracies in the underlying models. In this paper optimal tuning rules for quadrotor attitude dynamics are designed, which guarantees near-optimal performance and robustness. A single in-flight run of the Modified Relay Feedback Test that takes only few seconds with guaranteed stability is enough to have near-optimal tuning of the controller. The designed tuning rule is tested experimentally in-flight on a custom-built quadrotor. The results showed significant advantages in performance and robustness due to the proposed approach.

Design of gain scheduling control strategy for artificial gas lift in oil production through modified relay feedback test

Artificial gas lift technology is widely used in oil production to sustain oil flow from the well to the surface when reservoir pressure drops. Dynamic model that describes artificial gas lift system is highly nonlinear, which makes the controller design for this system not an easy task. A dynamic model of this system is further detailed with respect to the models available in the literature to account for the depth of the well. Two approaches to controller design are implemented: the first one is based on the local linearization in a number of operating (equilibrium) points that are characterized by different gas flow set points; the other approach is based on the use of the modified relay feedback test (MRFT) applied incrementally in different operating points. In both approaches, the controller is designed as a gain-scheduled PI controller.

MRFT-based design of robust and adaptive controllers for gas loop of oil–gas separator

AbstractThe modified relay feedback test (MRFT), which was recently proposed as a continuous oscillation method for identification of the process parameters and controller tuning, is used for the design of a robust and an adaptive Proportional-Integral (PI) controller for a gas loop in the oil–gas separator. The gas normally found in the separator is the natural gas (mostly methane) which is contained in crude oil coming from the reservoir. The robust and adaptive PI controllers are developed from analysis of 64 operating modes corresponding to certain ranges of the gas inflow and liquid-level values. It is shown through the developed model and simulations that these operating modes have significant effect on the dynamics of the gas loop. Dynamic properties of the process in each mode are studied through MRFT. The controllers are designed in order to maintain the pressure during the change of the operating conditions. Performance of the designed control system is studied by simulations.

Design of non-parametric process-specific optimal tuning rules for PID control of flow loops

The problem of designing optimal process-specific rules for non-parametric tuning is undertaken in the paper. It is shown that producing non-parametric process-specific optimal tuning rules for PID controllers leads to the problem that can be characterized as optimization under uncertainty. This happens due to the fact that tuning rules, unlike tuning constants, are produced not for a particular process or plant model but for a set of models from a certain domain. The novelty of the proposed approach is that the problem of obtaining optimal tuning rules for a flow process is formulated and solved as a problem of optimization of an integral performance criterion parametrized through values that define the domain of available process models. The considered non-parametric tuning assumes the use of the modified relay feedback test (MRFT) recently proposed in the literature. It allows one to tune the PID controller satisfying the requirements to gain or phase margins that is achieved through coordinated selection of tuning rules and test parameters. This approach constitutes a holistic approach to tuning. In the present paper, optimal tuning rules coupled with MRFT, for flow loops, are proposed. Final results are presented in the form of tables containing coefficients of optimal tuning rules for the PI controller, obtained for a number of specified gain margins. The produced non-parametric tuning rules well agree with the practice of loop tuning.