Metaheuristic Optimization of PD and PID Controllers for Robotic Manipulators

In this paper, the Particle Swarm Optimization algorithm (PSO) is combined with Proportional-Derivative (PD) and Proportional-Integral-Derivative (PID) to design more efficient PD and PID controllers for robotic manipulators. PSO is used to optimize the controller parameters Kp (proportional gain), Ki (integral gain) and Kd (derivative gain) to achieve better performances. The proposed algorithm is performed in two steps: (1) First, PD and PID parameters are offline optimized by the PSO algorithm. (2) Second, the obtained optimal parameters are fed in the online control loop. Stability of the proposed scheme is established using Lyapunov stability theorem, where we guarantee the global stability of the resulting closed-loop system, in the sense that all signals involved are uniformly bounded. Computer simulations of a two-link robotic manipulator have been performed to study the efficiency of the proposed method. Simulations and comparisons with genetic algorithms show that the results are very encouraging and achieve good performances.

Impact of the Sampling Period on the Design of Digital PID Controllers

The impact of the sampling period on the parameterization of a digital PID controller in the frequency domain is attempted using three different digital approximations of the integral action. The controller is implemented in the industrial process of regulation of the cement sulphates in the cement mill outlet. The maximum sensitivity, Ms, has been utilized as a main robustness criterion. For the same Ms, proportional and differential gain, a rise of the sampling period leads to a decrease of the integral gain ki for all the three approximations. For the same sampling period, the function between proportional and integral gain differs for the three approximations studied. If the design satisfies two criteria simultaneously, maximum sensitivity and phase margin in the current study, then the permissible PID gains zone becomes narrower.

PD Control Compensation Based on a Cascade Neural Network Applied to a Robot Manipulator

A Proportional Integral Derivative (PID) controller is commonly used to carry out tasks like position tracking in the industrial robot manipulator controller; however, over time, the PID integral gain generates degradation within the controller, which then produces reduced stability and bandwidth. A proportional derivative (PD) controller has been proposed to deal with the increase in integral gain but is limited if gravity is not compensated for. In practice, the dynamic system non-linearities frequently are unknown or hard to obtain. Adaptive controllers are online schemes that are used to deal with systems that present non-linear and uncertainties dynamics. Adaptive controller use measured data of system trajectory in order to learn and compensate the uncertainties and external disturbances. However, these techniques can adopt more efficient learning methods in order to improve their performance. In this work, a nominal control law is used to achieve a sub-optimal performance, and a scheme based on a cascade neural network is implemented to act as a non-linear compensation whose task is to improve upon the performance of the nominal controller. The main contributions of this work are neural compensation based on a cascade neural networks and the function to update the weights of neural network used. The algorithm is implemented using radial basis function neural networks and a recompense function that leads longer traces for an identification problem. A two-degree-of-freedom robot manipulator is proposed to validate the proposed scheme and compare it with conventional PD control compensation.

A Novel Fast MPPT Strategy for High Efficiency PV Battery Chargers

The paper presents a new maximum power point tracking (MPPT) method for photovoltaic (PV) battery chargers. It consists of adding a low frequency modulation to the duty-cycle and then multiplying the ac components of the panel voltage and power. The obtained parameter, proportional to the conductance error, is used as a gain for the integral action in the charging current control. The resulting maximum power point (MPP) is very still, since the integral gain tends to zero at the MPP, yielding PV efficiencies above 99%. Nevertheless, when the operating point is not the MPP, the integral gain is large enough to provide a fast convergence to the MPP. Furthermore, a fast power regulation on the right side of the MPP is achieved in case the demanded power is lower than the available maximum PV power. In addition, the MPPT is compatible with the control of a parallel arrangement of converters by means of a droop law. The MPPT algorithm gives an averaged duty-cycle, and the droop compensation allows duty-cycles to be distributed to all active converters to control their currents individually. Moreover, the droop strategy allows activation and deactivation of converters without affecting the MPP and battery charging operation. The proposed control has been assayed in a battery charger formed by three step-down converters in parallel using synchronous rectification, and is solved in a microcontroller at a sampling frequency of 4 kHz. Experimental results show that, in the worst case, the MPPT converges in 50 ms against irradiance changes and in 100 ms in case of power reference changes.

The usage of Lambert W function for identification and speed control of a DC motor

The paper proposes a new method of identifying the linear model of a DC motor. The parameter estimation is based on the closed-loop step response of the DC motor under a proportional controller. For the application of the method, a deliberate delay of the measured speed was introduced. The paper considers the speed regulation of the direct current motor with negligible inductance by applying 1-DOF and 2-DOF, proportional integral retarded controllers. The proportional and integral gain of the PI retarded controllers was received by using a pole placement method on the identified model. The Lambert W function was applied for the identification and in designing the controller with the purpose of finding the rightmost poles of the closed-loop as well as the boundary conditions for selecting the gain of the PI controller. The robustness of the calculated controllers was considered under the effect of an disturbance, uncertainty in each of the DC motor parameters as well as perturbations in time delay.

Robust PID controller design for rigid uncertain spacecraft using Kharitonov theorem and vectored particle swarm optimization

This paper presents a robust Proportional Integral Derivative controller design methodology for three axis attitude control of a rigid spacecraft with parametric uncertainty using a combination of Kharitonov theorem and vectored particle swarm optimization based approaches. A controller is designed for each of the three axes using a systematic graphical approach. Here, a plot of the stability boundary loci in the integral gain versus proportional gain parameter plane, for the specified gain and phase margins for each of the Kharitonov interval plants is used to determine the region representing the set of all PID controllers that satisfy the desired performance and stability requirements. Vectored particle swarm optimization technique is used to determine the optimized proportional and integral gain values. The spacecraft attitude control system is simulated using Matlab-Simulink tool which shows that the designed controller provides stability, robustness, good reference pointing and disturbance rejection for perturbations within the specific bounds.

Stabilising an Inverted Pendulum with PID Controller

Inverted pendulum is a system in which the centre of the mass is above the pivot point, where the mass can freely rotate. The inverted pendulum has a unique trait; it is unpredictable, non-linear and consists of multiple variables. Balancing by PID controller is a continuous process where it corrects the feedback system error from the difference between the measured value and the desired value. This research mainly focusses on balancing an inverted pendulum with reaction wheel. The research objectives are to construct a self-balanced inverted pendulum and using PID controller to control the stability of the pendulum. The PID configuration is then evaluated based on the response of the system. The idea is to use the reaction torque generated by the motor to counter balance the inverted pendulum. The factor which governs the amount of torque generated is the height of the pendulum and the mass of the wheel. To balance the pendulum, tuning the PID gain is essential. Proportional gain is tuned first to get oscillation, next is to tune the integral and derivative gain to get a smoother and quicker response. Idea is to get short settling time, and minimum overshoot percentage. Hypothesis is that higher proportional gain will give a faster response rate and the acceleration of the motor is the key on generating torque. A simulation of the pendulum falling is simulated and the results are recorded in term of the response of the pendulum against time. At initial point, proportional gain, integral gain and derivative gain are set to zero to validate the simulation. The finding in this research is that torque is generated by the acceleration of the reaction wheel. Higher acceleration gives a high torque. Others findings is the PID parameter; Proportional gain increases the response rate; Integral gain is used to eliminate steady state error; Derivative gain is used to lessen the overshoot.