15 - The PID controller

Chapter 13 - The PID Controller

In the paper recent design and tuning methods of PID controllers are summarized briefly. Several decades have seen the widely application of PID controllers and the design and tuning methods have been of considerable development. Process model identification, PID controller structure design, PID parameters tuning methods and the use and expansions of PID are described in turn. PID parameter tuning methods are highlighted.

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.

Adaptive Design of PID Controllers Based on an Alternative Method to Root Locus ⋆

Using the PID algorithm to control electrical elements is a practical industrial application that have been studied for decades. This paper constructs a study on the difference between BLDC motor control and applying traditional PID and fuzzy PID. The simulation is done through Falstad and Matlab/Simulink. The math model of the transfer function of a BLDC motor is constructed by analyzing voltage and torque equilibrium. The parameters are determined approximately by looking up the datasheet of 2338 0006s. Then, Falstad establishes the operational amplifier model of the BLDC motor and traditional PID controller. The parameters are determined through both root locus and step response presented by Falstad’s scope. Next, Simulink is used to realize the fuzzy PID controller. The comparison study of traditional PID controller and fuzzy PID controller is constructed by looking at the scope and export data. After that, it is concluded that fuzzy PID controller performs better than traditional PID controller, it is robust and the influence of the input parameter is small. Finally, a lead lag compensator is applied to the whole system to improve the performance in the frequency domain.

In the present day, transportation plays an important role in any country’s economy and sustenance. Even though electric vehicles have started market intrusion, at present, main commuting vehicles such as cars, ships and planes work on internal combustion engines (ICEs). In line with any complex system, an ICE exhibits poor time domain characteristics when not controlled properly. Generally, PID controller is used to control the ICE to give better time domain characteristics. There are various conventional methods available to tune the PID controller such as OLTR methods and ultimate cycle methods. Generally, these offline controller tuning methods cannot address non-linear disturbances effectively. So, to overcome these drawbacks, there is a need for using artificial intelligence-based tuning methods. Hence, this paper implements an artificial neural network-based PID controller and compares it with a conventional method and track the rate of change of PID parameters with the injection of disturbances. This paper concludes that the response of the ICE system tuned with ANN-PID gives a better output when compared to the key conventional PID tuning methods.KeywordsSpeed controlIC enginePID controllerANN-PID controller

Windup effect in a PID controller is the condition of cumulative error in the integral action. It saturates the system actuators, letting the system out of control with a higher controller action. Putting a saturator for the controller action, it is limited into a linear range of operating values. However, it does not eliminate the cumulative error of the integral term. This paper presents the speed control of a motor generator system using a digital PID controller with antiwindup scheme to eliminate the cumulative error of the integral term of controller action. Initially, a linear model of the motor generator system was identified. From the linear model of the system, a PID controller was designed using pole placement technique. Controller discrete implementation was perform using the backward difference discretization methodology. PID controller consider the antiwindup scheme. PID controller practical implementation employed Matlab Stateflow and a data acquisition card. Obtained results showed that discrete implementation of the PID controller has a good performance against external disturbances and random noise.

An analytical approach for tuning fractional PID controllers based on the frequency response of the system is addressed in this paper. Fractional PID controller inherits all advantages of conventional PID controllers and also has additional degrees of freedom. Based on their frequency response a new method of tuning is proposed in this paper, which is inspired from the previous works associated with this topic. Then the same method is validated by applying for attitude control of Reusable launch vehicle. The robustness study of the whole system is also carried out.

The purpose of this research is to design PID control on BLDC motors using 2 tuning methods, namely Cohen-Coon and Trial &amp; Error. PID control of formula calculations with calculations in Simulink Matlab. From the simulation results shown in graphical form, the use of the PID control gives a better effect than the use of the P and PI controls. This can be seen in the comparison curve which shows the speed of the initial start process when using the PID control. In the Trial &amp; Error method, the response value of the system to controller P is obtained, namely, rise time = 0.0151 s, settling time = 0.6 s, overshoot = 75.9%, peak time = 1.74 s, and time delay = 0.424 s. on the PI controller namely, rise time = 0.0148 s, settling time = 0.591 s, overshoot = 76.3%, peak time = 1.74 s, and time delay = 0.0416 s. on the PID controller namely, rise time = 0.0496 s, settling time = 0.55 s, overshoot = 44 %, peak time = 1.31 s, and time delay = 0.128 s. In the Cohen-Coon method, the response value of the system to controller P is obtained, namely, rise time = 0.0168 s, settling time = 0.575 s, overshoot = 73.3%, peak time = 1.71 s, and time delay = 0.0469 s. on the PI controller namely, rise time = 0.0573 s, settling time = 0.603 s, overshoot = 39.3%, peak time = 1.23 s, and time delay = 0.142 s. on the PID controller namely, rise time = 0.276 s, settling time = 0.658 s, overshoot = 2.42 %, peak time = 0.159 s, and time delay = 0.576 s. From the simulation results it is shown that the value for the Cohen-Coon tuning method is better than the Trial &amp; Error method, perhaps because the input value for the Trial &amp; Error method is larger.

In this paper, a decentralized PID controller in PI mode is tuned using Biggest-Log Modulus (BLT) tuning method and a stochastic optimization method i.e. Duelist Algorithm (DA) for multivariable system. A TITO system with FOPDT model is considered to examine the performance of the controller using those two different methods. In BLT method, the PID controller tuning parameters were first designed by using Ziegler-Nichols (ZN) method from S-curve, then the biggest log modulus is obtained to find the F factor and detuned the ZN value using the factor of BLT method. In DA method, the Integral Absolute Error (IAE) was utilized as objective function to determine optimal PID controller settings. The two PID controllers are simultaneously being optimized to find the optimal PID parameters. The performances of the control system are observed for both the changes of set point and disturbance value. The performance showed by the system using DA method is better than BLT method. DA method did improve the stability of the system towards the step changes and has a lower IAE value.

The paper studies the discrete event model-based PID controller. The structure of the networked controller is constructed. The structure is reduced for stability investigation. Than the automatic tuning method of PID controller and the synthesis of the model is presented. The stability theorem for a known process is formulated and proved using piecewise quadratic Lyapunov function. Finally, the numeric example of the whole process is shown.

Many control engineers try to avoid the use of derivative action in operating units. As Isaksson and Graebe have pointed out (in a presentation at Control Systems 2000, Victoria, British Columbia, May 2000), there is an “industrial myth that derivative action does not work.” They claim that some of this is due to the need to adjust the derivative filter constant, in addition to the usual three parameters of PID controllers. Modern distributed control systems offer a variety of choices for the PID algorithm, including both series (interacting) and parallel (ideal). The many PID tuning methods that have been developed over the years have used different algorithms, and some are limited to a narrow range of parameter values (dead times). Most tuning methods require setting three tuning parameters, but some propose setting four parameters. All this complexity presents a confusing picture to the practitioner who is faced with trying to tune a PID controller. This paper presents a quantitative comparison of alternative derivative algorithms and tuning methods for processes with a wide range of dead-time/lag ratios. Results show that, when the correct algorithm is used, the IMC tuning method proposed by Morari and Zafiriou (Robust Process Control; Prentice Hall: New York, 1989) gives good performance for large-dead-time processes. The correct algorithm has a four-parameter, parallel, output-filtered PID structure.

DC motor is a very popular actuator which is used in many industries like paper mill, rolling mill where precise speed control is required. There are various controllers available such as PID, state variable feedback controller but among all, PID controller is extensively used as the design of PID is simple and gives good performance characteristics. Though PID controller is simple, tuning of this controller is tedious and hence proper tuning of PID is necessary to have satisfactory performance. Most common method applied to tune the PID is using Zieglar-Nichols (Z-N) method. This method of tuning is easy to implement but the main disadvantage of this technique is that it produces high overshoot which is undesirable. Thus, this paper aims to further expand the adaptive capabilities of the PID Controller using various techniques like model reference adaptive control (MRAC), particle swarm optimization (PSO) and fuzzy logic controller. MATLAB/Simulink is used to implement PID controller design using the mentioned techniques. The closed loop step response of DC motor for various designed controllers is determined, analyzed based on performance characteristics like rise time (tr), settling time (ts), peak overshoot (OS) and the same are compared.

Essential oils are one of the main compounds in the pharmaceutical, fragrance and food industries. Essential oils are volatile and sensitive to heat. They can be extracted using various methods and including steam distillation which is regarded in this research. Consequently, the temperature during the extraction process is an important factor that influences the quality of essential oils. For decades the famous PID controller dominated the industrial control loop. Poor PID control tuning may result in poor control performance and even poor quality products. This study proposes an Internal Model Control (IMC) tuning method for a PID controller to control steam temperature during the extraction process. IMC suggested a model based tuning rules so that the closed-loop will be less sensitive to disturbance. Two types of IMCPID controller approaches were considered in this paper which are IMC-PID controller with integer-order filter (IOF) and IMC-PID controller with fractional-order filter (FOF). There is a single tuning parameter in IO filter, while the FO filter has two parameters to be tuned in order to achieve satisfactory response of the system. The simulation is done in Simulink using MATLAB R2018a and comparison studies are made for transient response (Tr, Ts, %Mp) for both controllers. The result has shown that the IMC-PID FOF controller gives a better response than IMC-PID IOF controller by having less overshoot (2.59%) and has fastest rise time and settling time by 264.7s and 447.4s respectively.

Purpose – Damage induced during drilling of polymer matrix composites depends upon torque during drilling. Modeling of torque with feed rate and its control becomes imminent for damage free drilling of composite laminates. Therefore, the purpose of this paper is to construct a transfer function between drilling torque and feed rate based upon experiments. Thereafter, the torque is controlled by using PID controller. Design/methodology/approach – This paper presents step-by-step procedure to capture complex drilling dynamics of polymer matrix composites in a mathematical model. A glass fiber reinforced plastic (GFRP) composite laminate is drilled at constant feed rate during experimentation. The corresponding time response of torque is recorded. First order, second order and third order transfer functions between torque and feed rate are identified using system identification toolbox of Matlab®. These transfer functions are then converted into state-space models. Experimental verification is performed on GFRP composite laminate. PID controller is designed using Simulink® to track a given reference torque during drilling of polymer matrix composite. The controller is then validated using different reference torque trajectories. Findings – Good match is observed between torque response from state-space models and experiments. Error analysis based on integral absolute error and integral squared error on experimental and simulated response show that third-order system represents the complex drilling dynamics in a better way than first and second-order systems. PID controller effectively tracks given reference trajectories. Originality/value – Third-order model between torque and feed rate for drilling of composites not available in literature has been presented. PID controller has previously been applied successfully for drilling of conventional materials, this paper extends implementation of PID torque control for drilling of composites.