Derivative Kick Research Articles

PID control: Resilience with respect to controller implementation

One of the major drawbacks of the basic parallel formulations of a PID controller is the effects of proportional and derivative kick. In order to minimize these effects, modified forms of parallel controller structures such as PI-D and I-PD are usually considered in practice. In addition, there is a usual servo/regulation tradeoff regarding closed-loop control system operation. Appropriate tuning is needed for each situation. One way of focusing explicitly on load disturbance is by the appropriate selection of a controller equation. A gap is generated here between the conception of a tuning rule and its final application that may need deployment on different controller equations. There is no danger when we go from PI-D to I-PD as we just change reference processing. However, there will be a loss of performance. The potential loss of performance, depending on the final controller equations used, motivates the authors to introduce the idea of resilient PID tuning: minimize the effects of changing the controller equation on the achieved performance/robustness. Today, this can be seen as a complement to the well-known controller fragility concept. On the basis of this scenario, this paper motivates the analysis of a tuning rule from such a point of view and also emphasizes the benefits that a better process model may provide from such an aspect.

Mitigation of Derivative Kick Using Time-Varying Fractional-Order PID Control

In this paper, a novel approach for the design of a fractional order proportional integral derivative (FOPID) controller is proposed. This design introduces a new time-varying FOPID controller to mitigate a voltage spike at the controller output whenever a sudden change to the setpoint occurs. The voltage spike exists at the output of the proportional integral derivative (PID) and FOPID controllers when a derivative control element is involved. Such a voltage spike may cause a serious damage to the plant if it is left uncontrolled. The proposed new FOPID controller applies a time function to force the derivative gain to take effect gradually, leading to a time-varying derivative FOPID (TVD-FOPID) controller, which maintains a fast system response and significantly reduces the voltage spike at the controller output. The time-varying FOPID controller is optimally designed using the particle swarm optimization (PSO) or genetic algorithm (GA) to find the optimum constants and time-varying parameters. The improved control performance is validated through controlling the closed-loop DC motor speed via comparisons between the TVD-FOPID controller, traditional FOPID controller, and time-varying FOPID (TV-FOPID) controller which is created for comparison with all three PID gain constants replaced by the optimized time functions. The simulation results demonstrate that the proposed TVD-FOPID controller not only can achieve 80% reduction of voltage spike at the controller output but also is also able to keep approximately the same characteristics of the system response in comparison with the regular FOPID controller. The TVD-FOPID controller using a saturation block between the controller output and the plant still performs best according to system overshoot, rise time, and settling time.

Design of gain-scheduling PID controllers for Z-source inverter using iterative reduction-based heuristic algorithms

This paper presents gain-scheduling control strategy for Z-source inverter used in traction motors. An iterative reduction-based heuristic algorithms (IRHA) is introduced for optimization of controller parameters. Since it is difficult to implement a stabilizable optimization with the conventional heuristic algorithm, optimum design can be achieved via creating stable sets by employing IRHA. In this optimization method, a new reduced subset is created at the end of each iteration, thereby reducing computation complexity. The proposed scheme adjusts proportional, integral, differential and derivative kick coefficients (Kp, Ki, Kd and Td). In this study, various PID controllers are designed using IRHA and H∞ norm-based optimization methods. Furthermore, in order to overcome non-linearity which exists in the nature of ZSI, gain scheduling is resorted to. The effectiveness of the proposed gain-scheduled controller structure is demonstrated over different input values and voltage fluctuations.

LMI-based design of an I-PD+PD type LPV state feedback controller for a gantry crane

In this paper, an alternative gain-scheduled PID tuning procedure is proposed for gantry crane control systems. In order to avoid excessive overshoot and aggressive control action due to the proportional kick and/or derivative kick effects, an I-PD+PD type control law is considered. The scheduling parameter is considered the cable length due to the payload lifting and lowering movements. A linear parameter-varying (LPV) gantry crane model is constructed to enable gain-scheduled controller design with a linear matrix inequalities (LMIs) framework. Based on the LPV model, a convex optimization problem is formulized to minimize L2 gain under regional pole location constraints. Then, a fixed gain L2 gain state feedback I-PD+PD type controller and a conventional pole placement state feedback I-PD+PD controller are designed to investigate the efficiency of the proposed controller. A pole placement controller is tuned to minimize the very common ITAE (integral of time multiplied by absolute error) performance index. Simulation results show that the proposed controller has superior tracking performance under time-varying cable length, when compared with nominal fixed gain controllers.

Real-Time Control of Pressure Plant Using 2DOF Fractional-Order PID Controller

Control of real-time pressure process is quite challenging due to high nonlinearity and sensitivity. PID controllers being the most employed for industrial applications have the potential for control of such processes. This is due to the PID’s advantages of simple structure, ease of tuning and implementation. However, its performance degrades during set-point change and high external disturbances due to high sensitivity and nonlinearity of the pressure plant. Therefore, this paper proposes the two-degree-of-freedom fractional-order PID (2DOF–FOPID) controller for real-time control of pressure process in both parallel and series configurations. Furthermore, the controller parameters are obtained experimentally using Ziegler–Nichols and closed-loop set-point approaches. The controller has the advantages of improving set-point tracking and disturbance rejection performance through smoother control action over the conventional PID. From the real-time experimental results obtained, the proposed approach outperforms PID, fractional-order PID and 2DOF-PID controllers in terms of overshoot and settling time. Hence, the approach has better set-point tracking ability and disturbance rejection capability. Furthermore, the control action of the approach is less affected by undesired oscillations and derivative kick effect thereby extending the life of actuator.

Fuzzy PD Plus I Control-based Adaptive Cruise Control System in Simulation and Real-time Environment

ABSTRACT An effort is made to design the fuzzy proportional-derivative (PD) plus I controller for a nonlinear cruise control system in automobiles, which provides adaptive capability in set-point tracking performance. A cruise control system has been considered as a nonlinear first order plus delay time model to exhibit the control behaviour involved in both conventional proportional-integral-derivative (PID) control and fuzzy control. The paper demonstrates the design of fuzzy PD plus I controller including comparative investigation with control structures like PID, I – PD, and PI – D using Simulink modelling. Real-time implementation has been carried out on a robotic prototype using Arduino UNO micro-controller. Based on the performance measures such as integral absolute error (IAE) and integral squared error (ISE), the proposed fuzzy PD plus I structure shows superior performance on servo and regulatory problems in the cruise control system. This control structure avoids integral windup issues and to suppress the derivative kick in the cruise control system.

Some investigations on hybrid fuzzy IPD controllers for proportional and derivative kick suppression

Proportional and derivative kick i.e., a large change in control action of a proportional plus integral plus derivative (PID) controller due to a sudden change in reference set-point is generally undesired in process industry. Therefore, the structure of conventional parallel PID controller is modified to integral minus proportional derivative (I-PD) controller. In this paper, three hybrid fuzzy IPD controllers such as a fuzzy I-fuzzy PD (FI-FPD) controller and its hybrid combinations with its conventional counterpart such as fuzzy I-PD (FI-PD) and I-fuzzy PD (I-FPD) are presented in view of above industrial problem. These controllers are based upon the counterpart conventional I-PD controller and contains analytical formulae. Computer simulations are carried out to evaluate the performance of hybrid fuzzy controllers along with conventional I-PD and PID controllers for set-point tracking and disturbance rejection for an induction motor in closed loop using LabVIEW™ environment. The gains of conventional and hybrid fuzzy controllers are tuned using genetic algorithm (GA) for minimum overshoot and settling time. It has been observed that hybrid fuzzy controllers along with the conventional I-PD controller significantly remove the kick from the control action in reference set-point tracking. However, in disturbance rejection, I-PD and FI-PD controllers fail to eliminate the kick from the control signal. In contrast, FI-FPD and I-FPD controllers considerably reduced spikes from the control action in disturbance rejection. Among the conventional and hybrid fuzzy IPD controllers, FI-FPD demonstrates much better set-point tracking and disturbance rejection response with spike free control action.

Application of a self-tuning fuzzy PI–PD controller in an active anti-roll bar system for a passenger car

A fuzzy proportional-integral-derivative (PID) controller has not been widely investigated for active anti-roll bar (AARB) application due to its unspecific mathematical analysis and the derivative kick problem. This paper briefly explains how the derivative kick problem arises due to the nature of the PID controller as well as the conventional fuzzy PID controller in association with an AARB. There are two types of controllers proposed in this paper: self-tuning fuzzy proportional-integral–proportional-derivative (STF PI–PD) and PI–PD-type fuzzy controller. Literature reveals that the PI–PD configuration can avoid the derivative kick, unlike the standard PID configuration used in fuzzy PID controllers. STF PI–PD is a new controller proposed and presented in this paper, while the PI–PD-type fuzzy controller was developed by other researchers for robotics and automation applications. Some modifications were made on these controllers in order to make them work with an AARB system. The performances of these controllers were evaluated through a series of handling tests using a full car model simulated in MATLAB Simulink. The simulation results were compared with the performance of a passive anti-roll bar and the conventional fuzzy PID controller in order to show improvements and practicality of the proposed controllers. Roll angle signal was used as input for all the controllers. It is found that the STF PI–PD controller is able to suppress the derivative kick problem but could not reduce the roll motion as much as the conventional fuzzy PID would. However, the PI–PD-type fuzzy controller outperforms the rest by improving ride and handling of a simulated passenger car significantly.

Derivative backoff: The other saturation problem for PID controllers

The PID controller is by far the most common controller, and to ensure good behavior under all circumstances, a PID implementation must consider many practical aspects such as integrator windup, derivative kick, and bumpless parameter and mode changes.In this paper, an entirely new issue for the derivative part is introduced and has been named derivative backoff. It occurs when the process value measurement saturates and is a general issue that affects all PID implementations.Derivative backoff is described in detail and it is shown that it can cause considerable, undesired, effects on industrially relevant processes even when they are controlled by well-tuned PID controllers. An anti-backoff strategy for PID controllers with integral action is proposed and evaluated, and a simple patch for existing PID implementations is presented. Possible strategies for PID controllers without integral action are also discussed.

Design of Optimal Fractional-Order PID Controllers Using Particle Swarm Optimization Algorithm for Automatic Voltage Regulator (AVR) System

In practical applications, the pure derivative action is never used, due to the “derivative kick” produced in the control signal for a step input, and to the undesirable noise amplification. It is usually replaced by a first-order low-pass filter. In this paper, we use a $$\mu $$ -order fractional low-pass filter and define a practical fractional-order controller. The proposed approach with new defined fitness function has very easy implementation and the most control performance. We present a method for optimum tuning of practical fractional PID controllers for automatic voltage regulator system using particle swarm optimization (PSO) algorithm. PSO is a robust stochastic optimization technique based on the movement and intelligence of swarm, applies the concept of social interaction to problem solving. From the comparison this technique with the other methods, its influence and efficiency are illustrated. Simulations and comparisons with other FOPID/PID controllers illustrate that the proposed PSO-FOPID controller can provide good control performance with respect to reference input and also improve the system robustness with respect to model uncertainties.

Optimization of I-PD Controller for a FOLIPD Model using Particle Swarm Intelligence

this paper, I-PD controller is designed and controller parameters are optimized using particle swarm intelligence for a First Order Lag Integrating plus Time Delayed model (FOLIPD). One of the modifications of PID controller is I-PD controller, which can be used for eliminating the proportional and derivative kick occurs during set point change. The controller parameters play the major role in obtaining the desired performance of a process and that urges the importance of selecting the most suitable parameters. The simulation results show that particle swarm optimized I-PD controller gives better performance compared to traditional Ziegler Nichols tuning technique and tuning method proposed by Arvanitis. Keywords-PD controller, FOLIPD model, PSO (Particle Swarm Optimization), Settling time, Rise time, and Peak overshoot.

A Simple Multiloop Tuning Method for PID Controllers with No Proportional Kick

A simple tuning method for multiloop PID controllers will be presented in this article. The method is suited for PID algorithms with no proportional and derivative kick. This tuning method is derived from a controller synthesis method with a control performance specification of 5% overshoot on servo response. Depending on the interaction natures of the multiloop systems, tuning based on the diagonal elements of the model or further detuning may be necessary. For systems with a relative gain array [RGA(λii)] < 1, a detuning factor based on this information is proposed. The information needed for controller tuning purposes is the dynamic model parameters of the diagonal elements and the process gain information of the off-diagonal elements. The tuning method procedure is very simple and straightforward, utilizing only nth identification tests with n as the number of the interacting control loops. The tuning method can easily be applied to various industrial situations with almost no need for a priori process knowledge.

Auto-tuning of output predictive PI controller

Predictive PI (PPI) Controller was introduced in (A.B. Rad, W.L. Lo, Predictive PI controller. International Journal of Control 60 (5) (1994) 953–975. The purpose of this paper is to introduce an enhanced PPI (output predictive PI controller) which overcomes the problems of large control action and derivative kick, which may arise in some situations. The practical problem of auto-tuning of the output predictive PI controller is also considered in this paper. The performance of the new auto-tuning output predictive PI controller is demonstrated and compared with a commercial PID auto-tuner.

PID algorithms and their computer implementation

Three-term or PID regulators are deservedly popular in industrial control systems. They give satisfactory performance for a wide class of processes, they are readily understood by technical plant personnel, and they are easy to implement using analogue or digital hardware. Stable elimination of offset due to load-disturbances is a principal control requirement, as in many cases processes are operated continuously at a fixed set-point Often this is achieved by the PI terms alone, though derivative action can be added for plant with excessive phase lag. In practice, however, nonlinear behaviour such as actuator saturation is a critical component of overall performance. This report discusses various forms of the PID regulator (positional, incremental, cascade, etc) and their closed-loop properties. Practical features such as avoidance of 'integral windup' and 'derivative kick' are described. The ways in which the PID algorithm can be discretised for use in a digital computer are outlined, together with appropriate Fortran coding. The effect of choice of sample interval on the discretised performance is analysed. Often the interval is chosen to be as short as possible given the computational power available; the influence of this on quantisation noise and offset is discussed Various filters are used in a discrete PID algorithm, including the anti-aliasing filter and a filter on derivative action. The properties of these filters are investigated and some interesting nonlinear filters, such as 'spike' filters are presented .