Discrete-time PID Research Articles

LMI designmethod for networked-based PID control

ABSTRACTIn this paper, we propose a methodology for the design of networked PID controllers for second-order delayed processes using linear matrix inequalities. The proposed procedure takes into account time-varying delay on the plant, time-varying delays induced by the network and packed dropouts. The design is carried on entirely using a continuous-time model of the closed-loop system where time-varying delays are used to represent sampling and holding occurring in a discrete-time digital PID controller.

Discrete-time PID observer design for state and unknown input estimations in noisy measurements

In response to MIMO discrete-time linear systems with unknown inputs and sensor noises, an observer algorithm which is capable of performing estimated system state and input disturbance is proposed in this paper. To effectively remove the effect of sensor noise, we transform the original model considered here into the descriptor form system. To effectively remove the effect of sensor noise, the original system is transformed into the descriptor system. Provided the variation of disturbance in the two consecutive sampling instances is not changed significantly and the system matrices satisfy the certain conditions, both the system state and the unknown input can be simultaneously estimated by the proposed proportional-integral-derivative observer algorithm. The estimation error can be constrained in a small bounded region of the order of O(T) where T is the sampling rate. Finally, a numerical example is presented to demonstrate the applicability of the proposed observer scheme.

Identification and control of nonlinear dynamics of a mobile robot in discrete time using an adaptive technique based on neural PID

In this work, original results, concerning the application of a discrete-time adaptive PID neural controller in mobile robots for trajectory tracking control, are reported. In this control strategy, the exact dynamical model of the robot does not need to be known, but a neural network is used to identify the dynamic model. To implement this strategy, two controllers are implemented separately: a kinematic controller and an adaptive neural PID controller. The uncertainty and variations in the robot dynamics are compensated by an adaptive neural PID controller. It is efficient and robust in order to achieve a good tracking performance. The stability of the proposed technique, based on the discrete-time Lyapunov's theory, is proven. Finally, experiments on the mobile robot have been developed to show the performance of the proposed technique, including the comparison with a classical PID.

Discrete-time fractional-order PID controller: Definition, tuning, digital realization and some applications

In some of the complicated control problems we have to use the controllers that apply nonlocal operators to the error signal to generate the control. Currently, the most famous controller with nonlocal operators is the fractional-order PID (FOPID). Commonly, after tuning the parameters of FOPID controller, its transfer function is discretized (for realization purposes) using the so-called generating function. This discretization is the origin of some errors and unexpected results in feedback systems. It may even happen that the controller obtained by discretizing a FOPID controller works worse than a directly-tuned discrete-time classical PID controller. Moreover, FOPID controllers cannot directly be applied to the processes modeled by, e.g., the ARMA or ARMAX model. The aim of this paper is to propose a discrete-time version of the FOPID controller and discuss on its properties and applications. Similar to the FOPID controller, the proposed structure applies nonlocal operators (with adjustable memory length) to the error signal. Two methods for tuning the parameters of the proposed controller are developed and it is shown that the proposed controller has the capacity of solving complicated control problems.

Energy minimization for 3-RRR fully planar parallel manipulator using particle swarm optimization

This paper presents an optimization problem for the 3-degrees-of-freedom RRR fully planar parallel manipulator (3-RRR) based on the actuator power consumption. The optimization purposes to determine the optimal link and platform masses in order to minimize the electrical energy consumed by the actuators subject to the kinematic, geometric and dynamic constraints. The Particle Swarm Optimization (PSO), increasingly being used in various engineering applications, has been considered as the optimization tool. A discrete-time PID control scheme is designed for demonstrating the energy saving by means of the mass optimization. Finally the optimization results for the eight working modes of 3-RRR have been compared to each other and given in tables.

Discretization algorithm for fractional order integral by Haar wavelet approximation

A discretization algorithm is proposed by Haar wavelet approximation theory for the fractional order integral. In this paper, the integration time is divided into two parts, one presents the effect of the past sampled data, calculated by the iterative method, and the other presents the effect of the recent sampled data at a fixed time interval, calculated by the Haar wavelet. This method can reduce the amount of the stored data effectively and be applied to the design of discrete-time fractional order PID controllers. Finally, several numerical examples and simulation results are given to illustrate the validity of this discretization algorithm.

Design of discrete-time adaptive PID controllers for a class of linear integrator systems

AbstractProportional, Integral and Derivative (PID) controllers are widely employed in control applications. The Ziegler-Nichols method is one of the most widely used PID parameter tuning methods, even though it is known to have some drawbacks. Automatic or self-tuning of PID controllers has been extensively studied. However, the stability of the resulting system with the PID controller is not considered in most PID auto-tuning methods and the tuned PID parameters may not guarantee the stability of the control system after changes in the system. This paper presents a new method to design discrete-time stabilizing PID controllers with time varying (or adaptive) gains for a special class of MIMO linear systems. The technique, based on appropriate choices of control Lyapunov functions (CLF), determines the optimal values of the parameters, with respect to the CLF choice, which guarantee the asymptotic stability of the equilibrium of the considered system.

Discretized PID Control and Robust Stabilization for Continuous Plants

This paper describes discrete-time and discrete-value (discretized/quantized) PID control and robust stabilization for continuous plants. Although all control systems are currently realized using discretized signals, the analysis and design of such nonlinear discrete-time control systems has not been elucidated. In this paper, the robust stability analysis of discrete-time and discrete-value (digital) control systems that accompany discretizing units at the input and output sides of a nonlinear element is performed in the frequency domain, and a method for achieving PID control and robust stabilization for nonlinear discretized systems on a grid pattern in the time and control variables space is presented. In the design procedure, a modified Nichols diagram and parameter specifications are applied. Numerical examples are provided to verify the validity of the designing method.

All-electronic droplet generation on-chip with real-time feedback control for EWOD digital microfluidics

Electrowetting-on-dielectric (EWOD) actuation enables digital (or droplet) microfluidics where small packets of liquids are manipulated on a two-dimensional surface. Due to its mechanical simplicity and low energy consumption, EWOD holds particular promise for portable systems. To improve volume precision of the droplets, which is desired for quantitative applications such as biochemical assays, existing practices would require near-perfect device fabrication and operation conditions unless the droplets are generated under feedback control by an extra pump setup off of the chip. In this paper, we develop an all-electronic (i.e., no ancillary pumping) real-time feedback control of on-chip droplet generation. A fast voltage modulation, capacitance sensing, and discrete-time PID feedback controller are integrated on the operating electronic board. A significant improvement is obtained in the droplet volume uniformity, compared with an open loop control as well as the previous feedback control employing an external pump. Furthermore, this new capability empowers users to prescribe the droplet volume even below the previously considered minimum, allowing, for example, 1 : x (x < 1) mixing, in comparison to the previously considered n : m mixing (i.e., n and m unit droplets).

Intelligent adaptive nonlinear flight control for a high performance aircraft with neural networks

This paper describes the development of a neural network (NN) based adaptive flight control system for a high performance aircraft. The main contribution of this work is that the proposed control system is able to compensate the system uncertainties, adapt to the changes in flight conditions, and accommodate the system failures. The underlying study can be considered in two phases. The objective of the first phase is to model the dynamic behavior of a nonlinear F-16 model using NNs. Therefore a NN-based adaptive identification model is developed for three angular rates of the aircraft. An on-line training procedure is developed to adapt the changes in the system dynamics and improve the identification accuracy. In this procedure, a first-in first-out stack is used to store a certain history of the input-output data. The training is performed over the whole data in the stack at every stage. To speed up the convergence rate and enhance the accuracy for achieving the on-line learning, the Levenberg-Marquardt optimization method with a trust region approach is adapted to train the NNs. The objective of the second phase is to develop intelligent flight controllers. A NN-based adaptive PID control scheme that is composed of an emulator NN, an estimator NN, and a discrete time PID controller is developed. The emulator NN is used to calculate the system Jacobian required to train the estimator NN. The estimator NN, which is trained on-line by propagating the output error through the emulator, is used to adjust the PID gains. The NN-based adaptive PID control system is applied to control three angular rates of the nonlinear F-16 model. The body-axis pitch, roll, and yaw rates are fed back via the PID controllers to the elevator, aileron, and rudder actuators, respectively. The resulting control system has learning, adaptation, and fault-tolerant abilities. It avoids the storage and interpolation requirements for the too many controller parameters of a typical flight control system. Performance of the control system is successfully tested by performing several six-degrees-of-freedom nonlinear simulations.

Performance Improvement of Discrete Time PID Controller using Neural Networks

Performance Improvement of Discrete Time PID Controller using Neural Networks

Solution to the Shell standard control problem using genetically tuned PID controllers

A solution to the Shell standard control problem is presented in this paper, based on genetic algorithms (GAs). The proposed scheme includes two discrete-time PID controllers with integral anti-windup and a multivariable Smith predictor to provide the required process output regulation, while the process input minimisation problem is analytically solved on-line, by estimating the unmeasured disturbances entering the process and solving the associated linear programming problem. This, as well as the presence of constraints in the process manipulated variables, results in a complex, non-linear closed-loop system and hence, the manual tuning of the PID controllers according to some given performance specifications becomes a difficult task. GAs are successfully applied to the automatic tuning of the PID controllers according to the given specifications, using a specially formulated objective function which quantifies the controller performance in terms of time-domain bounds on the closed-loop system responses. Simulation results are presented to demonstrate the effectiveness of the proposed control scheme.

DISCRETE-TIME ROBUST PID AND THREE-TERM CONTROL

It has been shown, that stability regions for PID-controllers in a (κD, κI)-plane for fixed κP are convex polygons. This result allows a simple calculation of the set of all stabilizing PID controllers for a given plant. In the present paper this result is transferred to the case of discrete-time PID controllers or three-term controllers, where stability with respect to the unit circle or other circles in the 2-plane must be checked. Since the orientation of the cross section planes for polygonal stability regions does not depend on the plant, it is easy to find the set of all simultaneous stabilizers for several representative plant parameters and to select a robust discrete-time controller from this set. A mass-spring-mass system proposed in (Bernstein and Wie, 1990) as a benchmark control problem for digital robust control is used to illustrate the method.

Discrete-Time Model Reference Feedback and PID Control for Interval Plants

Abstract The physical parameters of controlled systems (plants) are uncertain and are accompanied by nonlinearity. The transfer function of the controlled system should, therefore, be expressed by interval polynomials. This paper describes the realization of robust control for that type of plant via discrete-time model reference feedback, and discusses the relationship between the feedback structure and the conventional (discrete-time) PID control system. Robust performance of the feedback control system is evaluated by using a discrimination method of characterisitic (dominant) roots area on a 2-plane. In this paper, we will present designing examples of a robust control system via model reference feedback which corresponds to a high-gain feedback and a kind of PID control.

Adaptive neural PID control case study: Tubular chemical reactor

A new simple solution of deriving adaptive PID control based on artificial neural network (ANN) policy is presented. The design problem consists of training of both, a recurrent and a feedforward neural network model. The recurrent and the feedforward neural network are respectively used as a predictor and adaptive neural feedback controller. They are trained using the back-propagation through the time and stochastic approximation algorithms, respectively. The multi-layer feedforward ANN is trained so as to achieve the control objective. The controller consists of a multi-layer feedforward ANN and a discrete-time PID algorithm. The network serves for adaptive tuning of the PID controller. To demonstrate the feasibility and the performance of this control scheme, a tubular chemical reactor is chosen as a realistic non-linear case study. Simulation results demonstrate the usefulness and the robustness of the control system proposed.

Flux and torque control of switched reluctance machines

The theory and implementation of a flux-linkage controller applied to a switched reluctance machine drive are described. Analysis of the simplified discrete time load model shows that a simple flux-linkage controller can produce a ‘dead-beat’ system response. Comparison of the response from a discrete time PID current controller, hysteresis current controller and the new flux-linkage controller, show that the flux controller has a much improved response. The experimental controller is used to control an IGBT converter, driving a commercial 7.5 kW switched reluctance motor. A method of constant torque operation is introduced. This takes account of limitations imposed by the finite DC-link voltage and rotor speed when calculating the reference values. The method is based on ‘flux ramps’, where the ramps are chosen to give constant shaft torque, and remain within the capabilities of the power converter. Correct selection of the flux ramps allows constant torque operation to be achieved over a wide speed and torque range. Measured results for the experimental drive demonstrate the low torque ripple achieved for motoring and generating operation over a range of speed and torque values.

Relationship between deadbeat and pole-placement discrete-time PID controllers

This paper considers PID control in terms of its implementation by means of an ARMA plant model. Two controller actions are considered, namely pole placement and deadbeat, both being applied via a PID structure for the adaptive real-time control of an industrial level system. As well as looking at two controller types separately, a comparison is made between the forms and it is shown how, under certain circumstances, the two forms can be seen to be identical. It is shown how the pole-placement PID form does not in fact realise an action which is equivalent to the deadbeat controller, when all closed-loop poles are chosen to be at the origin of the z-plane.

Disk Drive Actuator BIAS: Prediction and Compensation

Disk drive actuator bias, which is the average torque (current) required to maintain a set actuator position, has a profound impact on the performance of a disk drive by influencing the settle time at the hand-off from seek mode to track follow mode. With an adequate prediction of bias, the settling time of a seek can be reduced by properly selecting the initial conditions of the track follow controller at the hand-off. In this paper, a state-space prediction algorithm is derived which is based Dahl's friction model and which accounts for much of the hysteresis behavior of bias. Based on an accurate bias prediction, a method is also developed for choosing the optimal initial condition of the integrator of a discrete time PiD controller which minimizes the seek settle time.

AUTOMATIC TUNING OF PID CONTROLLERS THROUGH RESPONSE OPTIMIZATION OVER A FINITE TIME HORIZON

Abstract The input-output functional relationship of a plant is identified and expressed in explicit form over a finite time horizon. Several schemes (orthogonal expansions, ARMA and MA models) are shown to result in a similar problem formulation. The identified model is operated on the fixed structure of a discrete time PID controller, and the parameters of the latter calculated as to minimize a performance index that penalizes both the quadratic departure of the error from the desired value and large variations in the error signal therefore avoiding abrupt controller actions Results from simulation are given in terms of tuning the PID controller of a triple effect evaporator that simulates a. real equipment used at the industry to obtain juice concentrate.