PID control system analysis, design, and technology

Designing and tuning a proportional-integral-derivative (PID) controller appears to be conceptually intuitive, but can be hard in practice, if multiple (and often conflicting) objectives such as short transient and high stability are to be achieved. Usually, initial designs obtained by all means need to be adjusted repeatedly through computer simulations until the closed-loop system performs or compromises as desired. This stimulates the development of "intelligent" tools that can assist engineers to achieve the best overall PID control for the entire operating envelope. This development has further led to the incorporation of some advanced tuning algorithms into PID hardware modules. Corresponding to these developments, this paper presents a modern overview of functionalities and tuning methods in patents, software packages and commercial hardware modules. It is seen that many PID variants have been developed in order to improve transient performance, but standardising and modularising PID control are desired, although challenging. The inclusion of system identification and "intelligent" techniques in software based PID systems helps automate the entire design and tuning process to a useful degree. This should also assist future development of "plug-and-play" PID controllers that are widely applicable and can be set up easily and operate optimally for enhanced productivity, improved quality and reduced maintenance requirements

Mathematical Model of the Simplest Fuzzy PID Controller with Asymmetric Fuzzy Sets

This paper deals with the simplest fuzzy PID controllers which employ two fuzzy sets for each of the three input variables and four fuzzy sets for the output variable. Mathematical model for a fuzzy PID controller is derived by using asymmetric Γ-function type and L-function type membership functions for each input, asymmetric trapezoidal membership functions for output, algebraic product triangular norm, bounded sum triangular conorm, Mamdani minimum inference, nonlinear control rules, and center-of-sums (COS) defuzzification. The effectiveness of the simplest fuzzy PID controller is demonstrated by means of a numerical example along with its simulation results

Fuzzy practical exponential tracking of an electrohydraulic servosystem

Cilj ovog rada je da doprinese teorijskoj i praktičnoj primeni fazi logičkog upravljanja korišćenjem koncepta praktičnog praćenja. Predlaže se novi fazi upravljački algoritam za ostvarivanje željenog kvaliteta praćenja jednog elektrohidrauličkog pozicionog servosistema, koji se može naći u mnogim industrijskim uređajima. Fazi logički kontroler je jedan od najjednostavnijih. On koristi samo jednu ulaznu veličinu, sa linearnom metodom zaključivanja. Fazi prateći algoritam upravljanja je zasnovan na principu samoprilagodljivosti. Strukturna karakteristika takvog sistema upravljanja je postojanje dve povratne sprege: globalne, negativne po izlaznoj veličini i lokalne, pozitivne po upravljačkoj veličini. Takva struktura obezbeđuje sintezu upravljanja bez poznavanja unutrašnje dinamike objekta i bez merenja poremećajnih veličina. Predloženi fazi prateći algoritam upravljanja obezbeđuje promenu greške izlazne veličine po unapred definisanom eksponencijalnom zakonu. Prezentuju se rezultati simulacije nelinearnog matematičkog modela hidrauličkog servosistema.The aim of this paper is to contribute to the theoretical and practical applications of fuzzy logic control using practical tracking concept. A new fuzzy control algorithm is proposed to achieve the desired tracking performance of a nonlinear electrohydraulic position servo system, which can be found in many manufacturing devices. The fuzzy logic controller is one of the simplest. It employs only one input, with linear fuzzy inference method. The practical tracking control algorithm is based on the selfadjustment principle. The structural characteristic of such a control system is the existence of two feedback sources: the global negative of the output value and the local positive of the control value. Such a structure ensures the synthesis of the control without the internal dynamics knowledge and without measurements of disturbance values. The proposed fuzzy practical control algorithm ensures the change of the output error value according to a prespecified exponential law. The simulation results of the nonlinear mathematical model of the hydraulic servo system are presented

Fuzzy practical exponential tracking of an electrohydraulic servosystem

Cilj ovog rada je da doprinese teorijskoj i praktičnoj primeni fazi logičkog upravljanja korišćenjem koncepta praktičnog praćenja. Predlaže se novi fazi upravljački algoritam za ostvarivanje željenog kvaliteta praćenja jednog elektrohidrauličkog pozicionog servosistema, koji se može naći u mnogim industrijskim uređajima. Fazi logički kontroler je jedan od najjednostavnijih. On koristi samo jednu ulaznu veličinu, sa linearnom metodom zaključivanja. Fazi prateći algoritam upravljanja je zasnovan na principu samoprilagodljivosti. Strukturna karakteristika takvog sistema upravljanja je postojanje dve povratne sprege: globalne, negativne po izlaznoj veličini i lokalne, pozitivne po upravljačkoj veličini. Takva struktura obezbeđuje sintezu upravljanja bez poznavanja unutrašnje dinamike objekta i bez merenja poremećajnih veličina. Predloženi fazi prateći algoritam upravljanja obezbeđuje promenu greške izlazne veličine po unapred definisanom eksponencijalnom zakonu. Prezentuju se rezultati simulacije nelinearnog matematičkog modela hidrauličkog servosistema.The aim of this paper is to contribute to the theoretical and practical applications of fuzzy logic control using practical tracking concept. A new fuzzy control algorithm is proposed to achieve the desired tracking performance of a nonlinear electrohydraulic position servo system, which can be found in many manufacturing devices. The fuzzy logic controller is one of the simplest. It employs only one input, with linear fuzzy inference method. The practical tracking control algorithm is based on the selfadjustment principle. The structural characteristic of such a control system is the existence of two feedback sources: the global negative of the output value and the local positive of the control value. Such a structure ensures the synthesis of the control without the internal dynamics knowledge and without measurements of disturbance values. The proposed fuzzy practical control algorithm ensures the change of the output error value according to a prespecified exponential law. The simulation results of the nonlinear mathematical model of the hydraulic servo system are presented

Performance comparison of optimal fractional order hybrid fuzzy PID controllers for handling oscillatory fractional order processes with dead time

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.Fuzzy logic based PID controllers have been studied in this paper, considering several combinations of hybrid controllers by grouping the proportional, integral and derivative actions with fuzzy inferencing in different forms. Fractional order (FO) rate of error signal and FO integral of control signal have been used in the design of a family of decomposed hybrid FO fuzzy PID controllers. The input and output scaling factors (SF) along with the integro-differential operators are tuned with real coded genetic algorithm (GA) to produce optimum closed loop performance by simultaneous consideration of the control loop error index and the control signal. Three different classes of fractional order oscillatory processes with various levels of relative dominance between time constant and time delay have been used to test the comparative merits of the proposed family of hybrid fractional order fuzzy PID controllers. Performance comparison of the different FO fuzzy PID controller structures has been done in terms of optimal set-point tracking, load disturbance rejection and minimal variation of manipulated variable or smaller actuator requirement etc. In addition, multi-objective Non-dominated Sorting Genetic Algorithm (NSGA-II) has been used to study the Pareto optimal trade-offs between the set point tracking and control signal, and the set point tracking and load disturbance performance for each of the controller structure to handle the three different types of processes

Mathematical Models of the Simplest Fuzzy Two-Term (PI/PD) Controllers Using Algebraic Product Inference

This paper reveals mathematical models of the simplest Mamdani PI/PD controllers which employ two fuzzy sets (N: negative and P: positive) on the universe of discourse (UoD) of each of two input variables (displacement and velocity) and three fuzzy sets (N: negative, Z: zero, and P: positive) on the UoD of output variable (control output in the case of PD, and incremental control output in the case of PI). The basic constituents of these models are algebraic product/minimum AND, bounded sum/algebraic sum/maximum OR, algebraic product inference, three linear fuzzy control rules, and Center of Sums (CoS) defuzzification. Properties of all these models are investigated. It is shown that all these controllers are different nonlinear PI/PD controllers with their proportional and derivative gains changing with the inputs. The proposed models are significant and useful to control community as they are completely new and qualitatively different from those reported in the literature