Improved model reduction and tuning of fractional-order PI(λ)D(μ) controllers for analytical rule extraction with genetic programming

Genetic algorithm (GA) has been used in this study for a new approach of suboptimal model reduction in the Nyquist plane and optimal time domain tuning of proportional-integral-derivative (PID) and fractional-order (FO) PI(λ)D(μ) controllers. Simulation studies show that the new Nyquist-based model reduction technique outperforms the conventional H(2)-norm-based reduced parameter modeling technique. With the tuned controller parameters and reduced-order model parameter dataset, optimum tuning rules have been developed with a test-bench of higher-order processes via genetic programming (GP). The GP performs a symbolic regression on the reduced process parameters to evolve a tuning rule which provides the best analytical expression to map the data. The tuning rules are developed for a minimum time domain integral performance index described by a weighted sum of error index and controller effort. From the reported Pareto optimal front of the GP-based optimal rule extraction technique, a trade-off can be made between the complexity of the tuning formulae and the control performance. The efficacy of the single-gene and multi-gene GP-based tuning rules has been compared with the original GA-based control performance for the PID and PI(λ)D(μ) controllers, handling four different classes of representative higher-order processes. These rules are very useful for process control engineers, as they inherit the power of the GA-based tuning methodology, but can be easily calculated without the requirement for running the computationally intensive GA every time. Three-dimensional plots of the required variation in PID/fractional-order PID (FOPID) controller parameters with reduced process parameters have been shown as a guideline for the operator. Parametric robustness of the reported GP-based tuning rules has also been shown with credible simulation examples.     

Measurement and Control of Process using Soft Computing

Abstract

Control of process parameters is considered to be a critical problem in the process industry. The process considered for modeling is a liquid level system. The model identification and parameter selection are approximated to a First Order Plus Dead Time (FOPDT). Here, the controller design is based on a conventional Proportional–Integral (PI) controller and intelligent controller like Fuzzy Logic Controller (FLC). The objective of the current study is to design control strategies in real time using MATLAB software interfaced with Adam's data acquisition module. A comparative analysis based on FLC with a conventional controller is presented, with various time domain specifications. It is found that, under servo and regulatory changes, FLC shows an improved performance over its conventional techniques based on performance measures like peak time, settling time, overshoot, Integral Square Error (ISE) and Integral Absolute Error (IAE).     

Control System Design for a Neutralization Process using Block Oriented Models

Abstract

This paper focuses on the development of a non‐linear controller for a neutralization process. Block oriented models, namely the Wiener and Hammerstein model structures, are used for the controller design. A neural network architecture that has the capability to model the steady state behavior of a complex non‐linear process is developed. The dynamic behavior is modeled with a linear model. The pH process considered in this study exhibits drastic changes in the gain, even over a small operating range. In this study, the performance of controllers designed using Weiner and Hammerstein models are compared with a PI controller for servo and regulatory changes. The comparison results based on integral square error (ISE) values shows that the Weiner model based controller is suitable for a pH process.     

Identification and Control of Bioreactor using Recurrent Networks

Abstract

A nonlinear model predictive control (NMPC) strategy based on recurrent neural networks (RNN) is proposed for a single‐input single‐output system (SISO) to control the uncertain nonlinear process. The automatic configuration and modeling of the networks is carried out using a recurrent Elman network using back propagation through time (BPTT) with MATLAB. Identification of the process is performed with a RNN based nonlinear autoregressive with exogenous input (NARX) model and the incorporation of the developed model in the formulation of NMPC is presented. Further, the results of the NMPC is compared with a well tuned IMC based PI controller, which shows a better performance based on the rise time and settling time of the proposed NMPC scheme for the control of an unstable bioreactor.     

Extension of IMC tuning correlations for non-self regulating (integrating) processes

The filter term of a PID with Filter controller reduces the impact of measurement noise on the derivative action of the controller. This impact is quantified by the controller output travel defined as the total movement of the controller output per unit time. Decreasing controller output travel is important to reduce wear in the final control element. Internal Model Control (IMC) tuning correlations are widely published for PI, PID, and PID with Filter controllers for self regulating processes. For non-self regulating (or integrating) processes, IMC tuning correlations are published for PI and PID controllers but not for PID with Filter controllers. The important contribution of this work is that it completes the set of IMC tuning correlations with an extension to the PID with Filter controller for non-self regulating processes. Other published correlations (not based upon the IMC framework) for PID with Filter controllers fix the filter time constant at one-tenth the derivative time regardless of the model of the process. In contrast, the novel IMC correlations presented in this paper calculate a filter time constant based upon the model of the process and the user's choice for the closed-loop time constant. The set point tracking and disturbance rejection performance of the proposed IMC tunings is demonstrated using simulation studies and a bench-scale experimental system. The proposed IMC tunings are shown to perform as well as various PID correlations (with and without a filter term) while requiring considerably less controller action.     

Velocity control of servo systems using an integral retarded algorithm

This paper presents a design technique for the delay-based controller called Integral Retarded (IR), and its applications to velocity control of servo systems. Using spectral analysis, the technique yields a tuning strategy for the IR by assigning a triple real dominant root for the closed-loop system. This result ultimately guarantees a desired exponential decay rate σ_d while achieving the IR tuning as explicit function of σ_d and system parameters. The intentional introduction of delay allows using noisy velocity measurements without additional filtering. The structure of the controller is also able to avoid velocity measurements by using instead position information. The IR is compared to a classical PI, both tested in a laboratory prototype.     

Relay-enhanced multi-loop PI controllers

In this paper, the development of relay-enhanced multi-loop PI controllers is described for multivariable processes. The control system employs a relay in series with the controller. The relay can ensure a satisfactory level of closed-loop performance and it also yields oscillations for tuning of the PI controller based on an equivalent process model for each loop. A simulation example [on a two-inputs-two-outputs (TITO) process] is provided to illustrate the effectiveness of the proposed method and to compare its performance to an existing method.     

Parameters identification and trajectory control for a hydraulic system

In order to improve the tracking accuracy of a hydraulic system, an improved ant colony optimization algorithm (IACO) is proposed to optimize the values of proportional–integral–derivative (PID) controller. In addition, this paper presents an experimental study on the parameters identification to deduce accurate numerical values of the hydraulic system, which also determines the relationship between control signal and output displacement. Firstly, the basic principle of the hydraulic system and the mathematical model of the electro-hydraulic proportional control system are analyzed. Based on the theoretical models, the transfer function of the control system is obtained by recursive least square identification method (RLS). Then, the key parameters of the control system model are obtained. Some improvements are proposed to avoid premature convergence and slow convergence rate of ACO: the transition probability is revised based adjacent search mechanism, dynamic pheromone evaporation coefficient adjustment strategy is adopted, pheromone update rule and parameters optimization range are also improved. Then the proposed IACO tuning based PID controller and the identification parameters are modeled and simulated using MATLAB/Simulink and AMESim co-simulation platform. Comparisons of IACO, standard ACO and Ziegler–Nichols (Z–N)PID controllers are carried out with different references as step signal and sinusoidal wave using the co-simulation platform. The simulation results of the bucket system using the proposed controller demonstrates improved settling time, rise time and the convergence speed with a new objective function J. Finally, experiments with leveling operations are performed on a 23 ton robotic excavator. The experimental results show that the proposed controller improves the trajectory accuracy of the leveling operation by 28% in comparison to the standard ACO-PID controller.     

Simple PID parameter tuning method based on outputs of the closed loop system

Most of the existing PID parameters tuning methods are only effective with pre-known accurate system models, which often require some strict identification experiments and thus infeasible for many complicated systems. Actually, in most practical engineering applications, it is desirable for the PID tuning scheme to be directly based on the input-output response of the closed-loop system. Thus, a new parameter tuning scheme for PID controllers without explicit mathematical model is developed in this paper. The paper begins with a new frequency domain properties analysis of the PID controller. After that, the definition of characteristic frequency for the PID controller is given in order to study the mathematical relationship between the PID parameters and the open-loop frequency properties of the controlled system. Then, the concepts of M-field and θ-field are introduced, which are then used to explain how the PID control parameters influence the closed-loop frequency-magnitude property and its time responses. Subsequently, the new PID parameter tuning scheme, i.e., a group of tuning rules, is proposed based on the preceding analysis. Finally, both simulations and experiments are conducted, and the results verify the feasibility and validity of the proposed methods. This research proposes a PID parameter tuning method based on outputs of the closed loop system.     

Model Based Controller and Linear Cascade Controller Applied to Fed Batch pH Process

Abstract

The present study aims at bringing out the best features of model‐based control, linear cascade control when applied to highly non‐linear systems like pH‐controlled fed‐batch processes. For these processes, control of pH by conventional Proportional‐Integral‐Derivative controller fails to provide satisfactory performance, because of the extreme non‐linearity in the pH dynamics. In the present study, for a fed‐batch neutralization process, a non‐linear control law has been derived for the model‐based Proportional Integral controller. Typical problems in process control like sampling, delay and perturbations in model parameters are addressed in this study using model‐based control. The simulation results show the superior performance and robustness of the model‐based controller and linear cascade controller over that of the conventional Proportional Integral controller.     

Track velocity control of crawler type underwater mining robot through shallow-water test

The concept of continuous mining for manganese nodules suggests three sub-operations in total mining: collecting, lifting, onboard treatment. The combination of three components could be shaped by self-propelled seafloor mining robot, flexible conduit and buffer, lifting pumps and pipe, and mining platform. Particularly, the self-propelled robot tracking the mining paths on the seafloor is the key to accomplish the continuous mining. This paper discusses track velocity control of remotely operated mining robot, which is a basic and indispensable requirement for path tracking. The track velocity control is realized by PI controller from gain tuning formulas based on the model identification. First, to investigate the nature of the tracking system, a laboratory test is executed with the robot hung in air by overhead crane. Next, the transfer function of the tracking system is identified by the open-loop response and the closed-loop response. Through familiar tuning formulas based on the identified system parameters, PI gains are tuned. Finally, among the tuned PI gains, the one of best performance is set as the track velocity controller.     

Particle Swarm Optimization Technique Based Design of Pi Controller for a Real-Time Non-Linear Process

Abstract

The increasing complexity of modern control systems has emphasized the idea of applying new approaches in order to solve design problems for different control engineering applications. Proportional-Integral-Derivative (PID) control schemes have been widely used in most of process control systems represented by chemical processes for a long time. However, a very important problem is how to determine or tune the PID parameters, because these parameters have a great influence on the stability and the performance of the control system. Computational intelligence (CI), which has caught the eyes of researchers due to its simplicity, low computational cost, and good performance, makes it a possible choice for tuning of PID controllers, to increase their performance. This paper discusses, in detail, the Particle Swarm Optimization (PSO) algorithm, a CI technique, and its implementation in PID tuning for a controller of a real time process. Compared to other conventional PID tuning methods, the result shows that better performance can be achieved with the proposed method. The ability of the designed controller, in terms of tracking set point, is also compared and simulation results are shown.     

Model Based Tuning of Controller for Non‐Linear Hemispherical Tank Processes

Abstract

A non linear liquid level process represented by a 5 liter hemispherical tank was subjected to dynamic analysis using a step response technique. The data fitted a first order plus dead time model with an error of less than 3 percent. The level was measured using an on‐line Honeywell capacitance sensor. From the model parameters, PI and fuzzy tuned PI controllers were designed using MATLAB. The closed loop performance was studied for both the servo and regulator problems. Based on the overshoot, rise time, settling time, and ISE, it is found that the Fuzzy tuned PI controller is better suited for this process.     

Explicit analytical tuning rules for digital PID controllers via the magnitude optimum criterion

Analytical tuning rules for digital PID type–I controllers are presented regardless of the process complexity. This explicit solution allows control engineers 1) to make an accurate examination of the effect of the controller's sampling time to the control loop's performance both in the time and frequency domain 2) to decide when the control has to be I, PI and when the derivative, D, term has to be added or omitted 3) apply this control action to a series of stable benchmark processes regardless of their complexity. The former advantages are considered critical in industry applications, since 1) most of the times the choice of the digital controller's sampling time is based on heuristics and past criteria, 2) there is little a–priori knowledge of the controlled process making the choice of the type of the controller a trial and error exercise 3) model parameters change often depending on the control loop's operating point making in this way, the problem of retuning the controller's parameter a much challenging issue. Basis of the proposed control law is the principle of the PID tuning via the Magnitude Optimum criterion. The final control law involves the controller's sampling time T_s within the explicit solution of the controller's parameters. Finally, the potential of the proposed method is justified by comparing its performance with the conventional PID tuning when controlling the same process. Further investigation regarding the choice of the controller's sampling time T_s is also presented and useful conclusions for control engineers are derived.     

Autotuning positive feedback time delay controller for dead time processes

Biased relay feedback tests are applied to dead time processes to obtain their ultimate gains and ultimate frequencies. First-order process with dead time models are then fitted to the estimated gains and frequencies. A time delay controller that incorporates a simple compensator with a delay element in positive feedback can be derived from the fitted model. The time delay controller gives better performance comparing with classical Ziegler and Nichols tuned PID controller. Experimental study is included to demonstrate the effectiveness of the proposed tuning scheme and the time delay control algorithm.     

A novel composite adaptive flap controller design by a high-efficient modified differential evolution identification approach

The optimal tuning of adaptive flap controller can improve adaptive flap control performance on uncertain operating environments, but the optimization process is usually time-consuming and it is difficult to design proper optimal tuning strategy for the flap control system (FCS). To solve this problem, a novel adaptive flap controller is designed based on a high-efficient differential evolution (DE) identification technique and composite adaptive internal model control (CAIMC) strategy. The optimal tuning can be easily obtained by DE identified inverse of the FCS via CAIMC structure. To achieve fast tuning, a high-efficient modified adaptive DE algorithm is proposed with new mutant operator and varying range adaptive mechanism for the FCS identification. A tradeoff between optimized adaptive flap control and low computation cost is successfully achieved by proposed controller. Simulation results show the robustness of proposed method and its superiority to conventional adaptive IMC (AIMC) flap controller and the CAIMC flap controllers using other DE algorithms on various uncertain operating conditions. The high computation efficiency of proposed controller is also verified based on the computation time on those operating cases.     

Repetitive control approach towards automatic tuning of Smith predictor controllers

This paper proposes a new method for automatic tuning of the Smith predictor controller based on a Repetitive Control (RC) approach. The method requires the input of a periodic reference signal which can be derived from a relay feedback experiment. A modified repetitive control scheme repetitively changes the control signal to achieve tracking error convergence. Once a satisfactory performance is achieved through the learning control, the parameters of the Smith predictor controller can be computed from the signals using a nonlinear least squares algorithm. The same relay feedback experiment can provide an initial parameter vector for an efficient implementation of the parameter estimation. Simulations and experimental results will be furnished to illustrate the effectiveness of the proposed tuning method.     

An analytical method for PID controller tuning with specified gain and phase margins for integral plus time delay processes

In this paper, an analytical method is proposed for proportional-integral/proportional-derivative/proportional-integral-derivative (PI/PD/PID) controller tuning with specified gain and phase margins (GPMs) for integral plus time delay (IPTD) processes. Explicit formulas are also obtained for estimating the GPMs resulting from given PI/PD/PID controllers. The proposed method indicates a general form of the PID parameters and unifies a large number of existing rules as PI/PD/PID controller tuning with various GPM specifications. The GPMs realized by existing PID tuning rules are computed and documented as a reference for control engineers to tune the PID controllers.     

Evolutionary optimization of sliding mode controller for level control system

This paper accords the level control of single-input-single-output (SISO) level control system based on the fusion of sliding mode control (SMC) and evolutionary techniques or bio-inspired techniques. The non-dominated sorting genetic algorithm II (NSGA-II) and multi-objective particle swarm optimization (MOPSO) are considered as two evolutionary techniques. Here, a comparative analysis of performances of an optimal proportional–integral (PI) controller, proportional–integral–derivative (PID) controller, conventional SMC, NSGA-II based tuned SMC and SMC parameter tuning using MOPSO algorithm has been carried out through MATLAB/SIMULINK. The objective functions, integral absolute error (IAE), integral squared error (ISE) and an integration of weighted objective function aggregated approach of the error performance indices, IAE and ISE are considered. Realistic conditions are used in a plant for testing the robustness of controller. The stability of the controller is successfully obtained which satisfies the Lyapunov stability criteria. Reduction in long settling time with tiny magnitude variations about an equilibrium point is achieved using bio-inspired techniques. The simulation as well as experimental results reveal that SMC parameter tuning based on NSGA-II algorithm gives a better performance as compared to the other design strategies.     

A fast closed-loop process dynamics characterization

Stable, integrating and unstable processes, including dead-time, are analyzed in the loop with a known PI/PID controller. The ultimate gain and frequency of an unknown process G_p(s), and the angle of tangent to the Nyquist curve G_p(iω) at the ultimate frequency, are determined from the estimated Laplace transform of the set-point step response of amplitude r₀. Gain G_p(0) is determined from the measurements of the control variable and known r₀. These estimates define a control relevant model G_m(s), making possible the use of the previously determined and memorized look-up tables to obtain PID controller guaranteeing desired maximum sensitivity and desired sensitivity to measurement noise. Simulation and experimental results, from a laboratory thermal plant, are used to demonstrate the effectiveness and merits of the proposed method.