Performance analysis of two-degree of freedom fractional order PID controllers for robotic manipulator with payload

A new hybrid learning control system for robots based on spiking neural networks

This paper presents a new hybrid learning and control method that can tune their parameters based on reinforcement learning. In the new proposed method, nonlinear controllers are considered multi-input multi-output functions and then the functions are replaced with SNNs with reinforcement learning algorithms. Dopamine-modulated spike-timing-dependent plasticity (STDP) is used for reinforcement learning and manipulating the synaptic weights between the input and output of neuronal groups (for parameter adjustment). Details of the method are presented and some case studies are done on nonlinear controllers such as Fractional Order PID (FOPID) and Feedback Linearization. The structure and the dynamic equations for learning are presented, and the proposed algorithm is tested on robots and results are compared with other works. Moreover, to demonstrate the effectiveness of SNNFOPID, we conducted rigorous testing on a variety of systems including a two-wheel mobile robot, a double inverted pendulum, and a four-link manipulator robot. The results revealed impressively low errors of 0.01 m, 0.03 rad, and 0.03 rad for each system, respectively. The method is tested on another controller named Feedback Linearization, which provides acceptable results. Results show that the new method has better performance in terms of Integral Absolute Error (IAE) and is highly useful in hardware implementation due to its low energy consumption, high speed, and accuracy. The duration necessary for achieving full and stable proficiency in the control of various robotic systems using SNNFOPD, and SNNFL on an Asus Core i5 system within Simulink's Simscape environment is as follows: - Two-link robot manipulator with SNNFOPID: 19.85656 hours - Two-link robot manipulator with SNNFL: 0.45828 hours - Double inverted pendulum with SNNFOPID: 3.455 hours - Mobile robot with SNNFOPID: 3.71948 hours - Four-link robot manipulator with SNNFOPID: 16.6789 hours. This method can be generalized to other controllers and systems like robots.

Hybrid controller with neural network PID/FOPID operations for two-link rigid robot manipulator based on the zebra optimization algorithm

The performance of the robotic manipulator is negatively impacted by outside disturbances and uncertain parameters. The system's variables are also highly coupled, complex, and nonlinear, indicating that it is a multi-input, multi-output system. Therefore, it is necessary to develop a controller that can control the variables in the system in order to handle these complications. This work proposes six control structures based on neural networks (NNs) with proportional integral derivative (PID) and fractional-order PID (FOPID) controllers to operate a 2-link rigid robot manipulator (2-LRRM) for trajectory tracking. These are named as set-point-weighted PID (W-PID), set-point weighted FOPID (W-FOPID), recurrent neural network (RNN)-like PID (RNNPID), RNN-like FOPID (RNN-FOPID), NN+PID, and NN+FOPID controllers. The zebra optimization algorithm (ZOA) was used to adjust the parameters of the proposed controllers while reducing the integral-time-square error (ITSE). A new objective function was proposed for tuning to generate controllers with minimal chattering in the control signal. After implementing the proposed controller designs, a comparative robustness study was conducted among these controllers by altering the initial conditions, disturbances, and model uncertainties. The simulation results demonstrate that the NN+FOPID controller has the best trajectory tracking performance with the minimum ITSE and best robustness against changes in the initial states, external disturbances, and parameter uncertainties compared to the other controllers.

Adaptive sliding-mode trajectory tracking control for state constraint master-slave manipulator systems

This study aims to propose an adaptive state-dependent gain finite-time convergent controller (using the fundamentals of the sliding mode theory) that solves the trajectory tracking for a class of state constraint master-slave robotic system (M-SRS) formed by two manipulators with the same number of articulations. The control design considers the effect of state constraints by implementing a state dependent adaptive gain. A Lyapunov-stability analysis leads to design the gain variation laws yielding proving the finite-time convergence of the sliding surface as well as the asymptotic convergence of the tracking error. The state constraints of the slave system motivate the characterization of the convergence-time as a function of the bounded uncertainties affecting the M-SRS dynamics. The forward-complete setting of the M-SRS justified the application of a robust and exact differentiator which estimated the articulation velocities for the slave robot. The estimated velocities are used as part of the realization of the output feedback controller. Numerical simulations demonstrate that the proposed control scheme provides a smaller quadratic norm of the tracking error compared with the obtained with other controllers (proportional-derivative and conventional sliding modes). The proposed control approach satisfies the state constraints while the sliding manifold converges to the origin in finite-time as justified by the theoretical stability analysis.

Modeling and Fuzzy FOPID Controller Tuned by PSO for Pneumatic Positioning System

A pneumatic cylinder system is believed to be extremely nonlinear and sensitive to nonlinearities, which makes it challenging to establish precise position control of the actuator. The current research is aimed at reducing the overshoot in the response of a double-acting pneumatic actuator, namely, the IPA positioning system’s reaction time. The pneumatic system was modeled using an autoregressive with exogenous input (ARX) model structure, and the control strategy was implemented using a fuzzy fractional order proportional integral derivative (fuzzy FOPID) employing the particle swarm optimization (PSO) algorithm. This approach was used to determine the optimal controller parameters. A comparison study has been conducted to prove the advantages of utilizing a PSO fuzzy FOPID controller over PSO fuzzy PID. The controller tuning algorithm was validated and tested using a pneumatic actuator system in both simulation and real environments. From the standpoint of time-domain performance metrics, such as rising time (tr), settling time (ts), and overshoot (OS%), the PSO fuzzy FOPID controller outperforms the PSO Fuzzy PID controller in terms of dynamic performance.

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.

A Critical Review of Control Techniques for Flexible and Rigid Link Manipulators

There is a high demand for developing effective controllers to perform fast and accurate operations for either flexible link manipulators (FLMs) or rigid link manipulators (RLMs). Thus, this paper is beneficial for such vast field, and it is also advantageous and indispensable for researchers who are interested in robotics to have sufficient knowledge about various controllers of FLMs and RLMs as the controllers’ concepts are elaborated in detail. The paper concentrates in critically reviewing classical controllers, intelligent controllers, robust controllers, and hybrid controllers for both FLMs and RLMs. The advantages and disadvantages of the aforementioned control methods are summarized in this paper; it also has a detailed comparison for the controllers in terms of the design difficulty, performance, and the suitability for controlling FLMs or RLMs.

Design of a Complex fractional Order PID controller for a First Order Plus Time Delay system

Complex fractional Order PID (COPID) controller is an extension to the Real fractional Order PID (ROPID) controller by extending the orders of differentiation and integration to include complex numbers, i.e., two extra parameters (the imaginary parts of the orders of the differentiator and the integrator) are introduced into the formula of the controller. The purpose is to overcome the limitation stemmed from restricting the parameters of the ROPID controller to belong to certain intervals, where this limitation results in a control system that does not satisfy the required design specification accurately. In this paper, analysis and design of COPID controller is presented, and for comparison purposes, both ROPID and COPID controllers are designed for a low pressure flowing water circuit, which is a First Order Plus Time Delay (FOPTD) system. The design specifications are given in frequency domain, which are gain crossover frequency, phase margin, and robustness against gain variation. The design specifications are taken as two cases, simple an rigorous, where the latter is considered to demonstrate the superiority of the COPID controller over the ROPID controller to achieve hard specifications. Although the design of the COPID controller is more complex than that of the ROPID controller, the first achieves the required design specification more accurately.

An optimal interval type-2 fuzzy logic control based closed-loop drug administration to regulate the mean arterial blood pressure

BACKGROUND AND OBJECTIVE

The main aim of this work is to present an optimal and robust controller design in order to improve the drug infusion to the automatic control of mean arterial blood pressure in conditions like critically-ill or post-operative or anaesthesia administration. The physiological systems also have uncertainty issues such as parameter variations with time or external disturbances and noise. Therefore, a controlled drug administration is necessary to regulate the mean arterial blood pressure of a person during surgery/observation. Over the years, the proportional-integral-derivative (PID) controller is the most commonly used controller in industries due to its easy structure and simplicity. However, this controller does not meet the desired performance with the complex and uncertain plants. Therefore, a robust controller is required to regulate the physiological variables that are uncertain in nature and can affect the human life.

METHODS

In this work, a hybrid control scheme consisting of an interval type-2-fuzzy logic controller which acts as pre-compensator to the traditional PID controller is presented, to regulate the mean arterial blood pressure of a patient by administering the drug sodium nitroprusside in a controlled manner. An effective and well-established nature-inspired optimization technique namely cuckoo search algorithm is employed for obtaining the optimal parameters for the presented scheme.

RESULTS

Simulation results are presented to show the effectiveness and robustness of proposed interval type-2-fuzzy logic controller based PID controller scheme, for maintaining the mean arterial pressure to 100 mmHg within considerable limit through SNP infusion. The results are further compared with other two controllers namely type-1 fuzzy logic based PID and traditional PID controllers for the parameter variations and external noise.

CONCLUSION

In this study, the proposed interval type-2-fuzzy logic controller pre-compensator based PID controller provides an effective control than traditional type-1 fuzzy logic based control scheme and PID controller in terms of overshoot, settling-time and error which are the prime performance objectives of the closed-loop controlled drug delivery of human blood pressure. The presented study provides a firm base for initial design considerations for development of a low-cost closed-loop drug delivery system for blood pressure regulation.

Adaptive Fuzzy Backstepping Sliding Mode Control for a 3-DOF Hydraulic Manipulator with Nonlinear Disturbance Observer for Large Payload Variation

The paper proposes an adaptive fuzzy position control for a 3-DOF hydraulic manipulator with large payload variation. The hydraulic manipulator uses electrohydraulic actuators as primary torque generators to enhance carrying payload of the manipulator. The proposed control combines backstepping sliding mode control, fuzzy logic system (FLS), and a nonlinear disturbance observer. The backstepping sliding mode control includes a sliding mode control for manipulator dynamics and a PI control for actuator dynamics. The fuzzy logic system is utilized to adjust the control gain and robust gain of the sliding mode control (SMC) based on the output of the nonlinear disturbance observer to compensate the payload. The Lyapunov approach and backstepping technique are used to prove the stability and robustness of the whole system. Some simulations are implemented, and the results are compared to other controllers to exhibit the effectiveness of the proposed control.

Adaptive sliding mode disturbance rejection control with prescribed performance for robotic manipulators

This study proposes an adaptive sliding mode disturbance rejection control with prescribed performance for robotic manipulators. A transformation with respect to tracking error using certain performance functions is used to ensure the transient and steady-state performances of the trajectory tracking control for robotic manipulators. Using the transformed error, a nonsingular terminal sliding mode surface is proposed. A continuous terminal sliding mode control (SMC) is presented to stabilize the system. To compensate for the uncertainty and external disturbance, a novel sliding mode disturbance observer is proposed. Considering the unknown boundary of the derivative of a lumped disturbance, an adaptive law based on the idea of equivalent control is designed. Combining the adaptive law, continuous nonsingular terminal SMC, and sliding mode disturbance observer, the adaptive sliding mode disturbance rejection control with prescribed performance is developed. Simulations are carried out to demonstrate the effectiveness of the proposed approach.

Design of interval type-2 fuzzy precompensated PID controller applied to two-DOF robotic manipulator with variable payload

The interval type-2 fuzzy logic controller (IT2-FLC), with footprint of uncertainty (FOU) in membership functions (MF), has increasingly recognized for controlling uncertainties and nonlinearities. Within the ambit of this, the efficient interval type-2 fuzzy precompensated PID (IT2FP-PID) controller is designed for trajectory tracking of 2-DOF robotic manipulator with variable payload. A systematic strategy for optimizing the controller parameters along with scaling factors and the antecedent MF parameters for minimization of performance metric integral time absolute error (ITAE) is presented. Prominently, recently proposed optimization technique hybridizing grey wolf optimizer and artificial bee colony algorithm (GWO-ABC) is utilized for solving this high-dimensional constrained optimization problem. In order to witness effectiveness, the performance is compared with type-1 fuzzy precompensated PID (T1FP-PID), fuzzy PID (FPID), and conventional PID controllers. More significantly, the robustness of IT2FP-PID is examined for payload variation, model uncertainties, external disturbance, and noise cancellation. After experimental outcome, it is inferred that IT2FP-PID controller outperforms others and can be referred as a viable alternative for controlling nonlinear complex systems with higher uncertainties.

Can fractional-order coexisting attractors undergo a rotational phenomenon?

This paper presents an interesting phenomenon unobserved so far in literature to the best of the authors' knowledge in fractional-order chaotic systems (FOCSs). It is the rotational phenomenon of fractional-order coexisting attractors. Another significant feature of the newly proposed FOCS is that two 2-wing chaotic attractors coexist in its fractional-order dynamics i.e. α<1. But once the system attains integer-order, the two attractors merge and evolve into a single 4-wing attractor. Furthermore, the authors have drawn its comparison with various well-known FOCSs to prove its superior features. In a novel attempt, the authors have utilised the property of simultaneous existence of coexisting attractors in the FOCS to carry out the synchronisation. A fractional-order circuit implementation with minimum components, has been performed using numerous audio signals with variable frequencies and amplitudes, as test signals. The objectives of the paper are finally achieved as the circuit implementation results are in perfect agreement with those of the theoretical analyses.

On the Taylor series asymptotic tracking control of robots

Achieving the asymptotic tracking control of electrically driven robot manipulators is a challenging problem due to approximation/modelling error arising from parametric and non-parametric uncertainty. Thanks to the specific property of Taylor series systems as they are universal approximators, this research outlines two robust control schemes using an adaptive Taylor series system for robot manipulators, including actuators' dynamics. First, an indirect adaptive controller is designed such as to approximate an uncertain continuous function by using a Taylor series system in the proposed control law. Second, a direct adaptive scheme is established to employ the Taylor series system as a controller. In both controllers, not only a robustifying term is constructed using the estimation of the upper bound of approximation/modelling error, but the closed-loop stability, as well as the asymptotic convergence of joint-space tracking error and its time derivative, is ensured. Due to the design of the Taylor series system in the tracking error space, our technique clearly has an advantage over fuzzy and neural network-based control methods in terms of the small number of tuning parameters and inputs. The proposed methods are simple, model free in decentralized forms, no need for uncertainty bounding functions and perfectly capable of dealing with parametric and non-parametric uncertainty and measurement noise. Finally, simulation results are introduced to confirm the efficiency of the proposed control methods.

Fractional order PIλ controller synthesis for steam turbine speed governing systems

The current state of the art of fractional order stability theory is hardly to build connection between the time domain analysis and frequency domain synthesis. The existing tuning methodologies for fractional order PI^λD^μ are not always satisfy the given gain crossover frequency and phase margin simultaneously. To overcome the drawbacks in the existing synthesis of fractional order controller, the synthesis of optimal fractional order PI^λ controller for higher-order process is proposed. According to the specified phase margin, the corresponding upper boundary of gain crossover frequency and stability surface in parameter space are obtained. Sweeping the order parameter over λ∈(0,2), the complete set of stabilizing controller which guarantees both pre-specifying phase frequency characteristic can be collected. Whereafter, the optimal fractional order PI^λ controller is applied to the speed governing systems of steam turbine generation units. The numerical simulation and hardware-in-the-loop simulation demonstrate the effectiveness and satisfactory closed-loop performance of obtained fractional order PI^λ controller.

Robust and novel two degree of freedom fractional controller based on two-loop topology for inverted pendulum

A rotary single inverted pendulum (RSIP) typically represents a space booster rocket, Segway and similar systems with unstable equilibrium. This paper proposes a novel two degree of freedom (2-DOF) fractional control strategy based on 2-loop topology for RSIP system which can be extended to control the systems with unstable equilibrium. It comprises feedback and feed-forward paths. Primary controller relates the perturbation attenuation while the secondary controller is accountable for set point tracking. To tune the parameters of proposed fractional controller a simple graphical tuning method based on frequency response is used. The study will serve the outstanding experimental results for both, stabilization and trajectory tracking tasks. The study will also serve to present a comparison of the performance of the proposed controller with the 1-DOF FOPID controller and sliding mode controller (SMC) for the RSIP system. Further to confirm the usability of the proposed controller and to avoid the random perturbations sensitivity, robustness, and stability analysis through fractional root-locus and Bode-plot is investigated.

A novel interval type-2 fractional order fuzzy PID controller: Design, performance evaluation, and its optimal time domain tuning

In this paper, a novel concept of an interval type-2 fractional order fuzzy PID (IT2FO-FPID) controller, which requires fractional order integrator and fractional order differentiator, is proposed. The incorporation of Takagi-Sugeno-Kang (TSK) type interval type-2 fuzzy logic controller (IT2FLC) with fractional controller of PID-type is investigated for time response measure due to both unit step response and unit load disturbance. The resulting IT2FO-FPID controller is examined on different delayed linear and nonlinear benchmark plants followed by robustness analysis. In order to design this controller, fractional order integrator-differentiator operators are considered as design variables including input-output scaling factors. A new hybridized algorithm named as artificial bee colony-genetic algorithm (ABC-GA) is used to optimize the parameters of the controller while minimizing weighted sum of integral of time absolute error (ITAE) and integral of square of control output (ISCO). To assess the comparative performance of the IT2FO-FPID, authors compared it against existing controllers, i.e., interval type-2 fuzzy PID (IT2-FPID), type-1 fractional order fuzzy PID (T1FO-FPID), type-1 fuzzy PID (T1-FPID), and conventional PID controllers. Furthermore, to show the effectiveness of the proposed controller, the perturbed processes along with the larger dead time are tested. Moreover, the proposed controllers are also implemented on multi input multi output (MIMO), coupled, and highly complex nonlinear two-link robot manipulator system in presence of un-modeled dynamics. Finally, the simulation results explicitly indicate that the performance of the proposed IT2FO-FPID controller is superior to its conventional counterparts in most of the cases.

Robust nonlinear PID-like fuzzy logic control of a planar parallel (2PRP-PPR) manipulator

In this paper, a robust nonlinear proportional-integral-derivative (PID)-like fuzzy control scheme is presented and applied to complex trajectory tracking control of a 2PRP-PPR (P-prismatic, R-revolute) planar parallel manipulator (motion platform) with three degrees-of-freedom (DOF) in the presence of parameter uncertainties and external disturbances. The proposed control law consists of mainly two parts: first part uses a feed forward term to enhance the control activity and estimated perturbed term to compensate for the unknown effects namely external disturbances and unmodeled dynamics, and the second part uses a PID-like fuzzy logic control as a feedback portion to enhance the overall closed-loop stability of the system. Experimental results are presented to show the effectiveness of the proposed control scheme.