A 2-Dof LQR based PID controller for integrating processes considering robustness/performance tradeoff

This paper focuses on the analytical design of a Proportional Integral and Derivative (PID) controller together with a unique set point filter that makes the overall Two-Degree of-Freedom (2-Dof) control system for integrating processes with time delay. The PID controller tuning is based on the Linear Quadratic Regulator (LQR) using dominant pole placement approach to obtain good regulatory response. The set point filter is designed with the calculated PID parameters and using a single filter time constant (λ) to precisely control the servo response. The effectiveness of the proposed methodology is demonstrated through a series of illustrative examples using real industrial integrated process models. The whole range of PID parameters is obtained for each case in a tradeoff between the robustness of the closed loop system measured in terms of Maximum Sensitivity (M_s) and the load disturbance measured in terms of Integral of Absolute Errors (IAE). Results show improved closed loop response in terms of regulatory and servo responses with less control efforts when compared with the latest PID tuning methods of integrating systems.     

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.     

A simple nonlinear PD controller for integrating processes

Many industrial processes are found to be integrating in nature, for which widely used Ziegler–Nichols tuned PID controllers usually fail to provide satisfactory performance due to excessive overshoot with large settling time. Although, IMC (Internal Model Control) based PID controllers are capable to reduce the overshoot, but little improvement is found in the load disturbance response. Here, we propose an auto-tuning proportional-derivative controller (APD) where a nonlinear gain updating factor α continuously adjusts the proportional and derivative gains to achieve an overall improved performance during set point change as well as load disturbance. The value of α is obtained by a simple relation based on the instantaneous values of normalized error (e_N) and change of error (Δe_N) of the controlled variable. Performance of the proposed nonlinear PD controller (APD) is tested and compared with other PD and PID tuning rules for pure integrating plus delay (IPD) and first-order integrating plus delay (FOIPD) processes. Effectiveness of the proposed scheme is verified on a laboratory scale servo position control system.     

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.     

Design of a Drilling Torque Controller for a Machining Center

In the drilling process, cutting torque control through feedrate manipulation has significant benefits in prevention of tool breakage and reduction of machine tool vibration and tool wear. In this paper, a PID torque controller was designed for real time drilling torque control in a machining centre. The drilling torque was estimated from the spindle motor current and regulated by feedrate control. The plant including the feed drive system, cutting process, and spindle system was modelled for controller design. For a certain cutting condition, the Ziegler-Nichols method was used to determine the proportional gain and derivative and integral control action times of the controller. Also, the root locus plot was used to tune the proportional gain of the controller. A simple method was also suggested to obtain the tuned controller gain instead of the Ziegler-Nichols method and the root locus plot for an arbitrary cutting condition. Experimental works have been performed to verify the performance of the proposed controller. It is shown that the gain tuning is essential for enhancement of the controller performance and the designed controller can regulate the drilling torque well at a given reference level.Nomenclature G_fc(s) transfer function of combined system of feed drive and cutting process - G_s(s) transfer function of spindle system - G_p(s) transfer function of plant - G_CL(s) transfer function of closed loop system - G_con(s) transfer function of controller - _fc1, _fc2 time constants of combined system of feed drive and cutting process - _s time constant of spindle system - K controller gain - K_c cutting process gain - K_s spindle motor current gain - K_plant plant gain - K_cr critical gain - K_p proportional gain of controller - K_{p_tune} tuned proportional gain of controller - I_s spindle motor current - I_u,v,w u, v, and w phase current of spindle motor - I_idle idling current of spindle motor - damping ratio - T oscillation period of system response - T_c cutting torque - T_m motor torque - T_idle idling torque of spindle motor - T_i integral control action time - T_d derivative control action time     

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.     

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.     

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.     

Variable-order fuzzy fractional PID controller

In this paper, a new tuning method of variable-order fractional fuzzy PID controller (VOFFLC) is proposed for a class of fractional-order and integer-order control plants. Fuzzy logic control (FLC) could easily deal with parameter variations of control system, but the fractional-order parameters are unable to change through this way and it has confined the effectiveness of FLC. Therefore, an attempt is made in this paper to allow all the five parameters of fractional-order PID controller vary along with the transformation of system structure as the outputs of FLC, and the influence of fractional orders λ and μ on control systems has been investigated to make the fuzzy rules for VOFFLC. Four simulation results of different plants are shown to verify the availability of the proposed control strategy.     

C pm MPPAC for manufacturing quality control applied to precision voltage reference process

A multiprocess performance analysis chart (MPPAC), based on the process capability index C _pm , called C _pm MPPAC, is developed to analyse the manufacturing quality of a group of processes in a multiple process environment. The C _pm MPPAC conveys critical information about multiple processes regarding the departure of the process and process variability on one single chart. Existing research on MPPAC has been restricted to obtaining quality information from one single sample of each process, ignoring sampling errors. The information provided from the existing MPPAC chart, therefore, is unreliable and misleading, resulting in incorrect decisions. In this paper, the natural estimator of C _pm is considered based on multiple samples. Based on the natural estimator of C _pm , sampling errors are considered by providing an explicit formula with Matlab to obtain the estimation accuracy of the C _pm . The sampling accuracy of C _pm is tablulated for sample size determination so that engineers/practitioners can use it for in-plant applications. An example of multiple PVR processes is presented to illustrate the applicability of C _pm MPPAC for manufacturing quality control.     

PID controller auto-tuning based on process step response and damping optimum criterion

This paper presents a novel method of PID controller tuning suitable for higher-order aperiodic processes and aimed at step response-based auto-tuning applications. The PID controller tuning is based on the identification of so-called n-th order lag (PTn) process model and application of damping optimum criterion, thus facilitating straightforward algebraic rules for the adjustment of both the closed-loop response speed and damping. The PTn model identification is based on the process step response, wherein the PTn model parameters are evaluated in a novel manner from the process step response equivalent dead-time and lag time constant. The effectiveness of the proposed PTn model parameter estimation procedure and the related damping optimum-based PID controller auto-tuning have been verified by means of extensive computer simulations.     

PID tuning rules for SOPDT systems: review and some new results

PID controllers are widely used in industries and so many tuning rules have been proposed over the past 50 years that users are often lost in the jungle of tuning formulas. Moreover, unlike PI control, different control laws and structures of implementation further complicate the use of the PID controller. In this work, five different tuning rules are taken for study to control second-order plus dead time systems with wide ranges of damping coefficients and dead time to time constant ratios (D/tau). Four of them are based on IMC design with different types of approximations on dead time and the other on desired closed-loop specifications (i.e., specified forward transfer function). The method of handling dead time in the IMC type of design is important especially for systems with large D/tau ratios. A systematic approach was followed to evaluate the performance of controllers. The regions of applicability of suitable tuning rules are highlighted and recommendations are also given. It turns out that IMC designed with the Maclaurin series expansion type PID is a better choice for both set point and load changes for systems with D/tau greater than 1. For systems with D/tau less than 1, the desired closed-loop specification approach is favored.     

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.     

RTDS implementation of an improved sliding mode based inverter controller for PV system

This paper proposes a novel approach for testing dynamics and control aspects of a large scale photovoltaic (PV) system in real time along with resolving design hindrances of controller parameters using Real Time Digital Simulator (RTDS). In general, the harmonic profile of a fast controller has wide distribution due to the large bandwidth of the controller. The major contribution of this paper is that the proposed control strategy gives an improved voltage harmonic profile and distribute it more around the switching frequency along with fast transient response; filter design, thus, becomes easier. The implementation of a control strategy with high bandwidth in small time steps of Real Time Digital Simulator (RTDS) is not straight forward. This paper shows a good methodology for the practitioners to implement such control scheme in RTDS. As a part of the industrial process, the controller parameters are optimized using particle swarm optimization (PSO) technique to improve the low voltage ride through (LVRT) performance under network disturbance. The response surface methodology (RSM) is well adapted to build analytical models for recovery time (R_t), maximum percentage overshoot (MPOS), settling time (T_s), and steady state error (E_ss) of the voltage profile immediate after inverter under disturbance. A systematic approach of controller parameter optimization is detailed. The transient performance of the PSO based optimization method applied to the proposed sliding mode controlled PV inverter is compared with the results from genetic algorithm (GA) based optimization technique. The reported real time implementation challenges and controller optimization procedure are applicable to other control applications in the field of renewable and distributed generation systems.     

基于模糊神经网络PID的液位串级控制的研究

利用PID算法对液位串级系统进行控制虽然是一种有效的控制方法,但由于它的精确数学模型难以确定,使得参数整定困难、控制效果不理想。该文将PID算法、模糊控制算法以及神经网络算法相结合,形成了一种智能控制算法——模糊神经网络PID算法。将该算法运用到液位串级控制系统中,实现了PID参数的自整定,并且提高了控制质量。实验结果表明,模糊神经网络PID算法与PID算法的控制效果相比,在鲁棒性和响应时间等方面有了较大的提高,具有一定的应用前景。     

模糊参数自整定PID控制器的设计与仿真研究

为实现PID参数的自动整定,在PID控制和模糊控制的基础上,设计了一种用于某型热像仪分子筛激活机中恒温炉温控系统的模糊参数自整定PID控制器,它基于PID参数的优化规律利用模糊控制规则对PID参数进行在线的自动整定.与常规PID温控系统比较,该控制器的系统超调量明显减小,控制系统的动静态性能均得到改善,升温速度和目标温度控制精度超过了设计指标,且结构简单、计算量小.系统仿真验证了该设计的有效性与实用价值.     

Optimal controller synthesis for second order time delay systems with at least one RHP pole

An optimal H₂ minimization framework is proposed in this paper for devising a controller of PID in nature, based on a refined IMC filter configuration. The tuning strategy is for controlling time delay system with at least one pole which falls on the right half of the s-plane. An underdamped model based filter is used in place of the unity damping ratio (critically damped) filter available in the literature to improve the reset action. The method has a single adjustable closed loop tuning parameter. Guidelines have been provided for choosing the pertinent tuning parameter based on the sensitivity function. Simulation work has been executed on diverse unstable models to support the advantages of the proposed scheme. The proposed controller yields improved performances over other recently reported tuning techniques in the literature. Experimental implementation is carried out on an inverted pendulum for demonstrating the practical applicability of the present method. The efficacy of the intended controller design is quantitatively analyzed using the time integral performance index.     

Drilling torque control using spindle motor current and its effect on tool wear

Drilling torque was estimated using the spindle motor current and controlled through feedrate manipulation for the reduction of drill wear. A PID controller was used to control the cutting torque measured indirectly from the spindle motor current. The effect of cutting torque control on drill flank wear was also investigated. Experimental results showed that the drilling torque was well-regulated at a given reference level and the risk of drill failure and drill flank wear were reduced remarkably through cutting torque control. Moreover, the suggested cutting torque control system does not disturb the cutting process and is practical in an industrial environment.Nomenclature I _rms Root mean square value of spindle motor current (ampere) - I _u,v,w U, V, and W phase current of the spindle motor (ampere) - I _rms,c Spindle motor current due to cutting (ampere) - I _rms,t Tare current of the spindle motor (ampere) - T _c Cutting torque (Nm) - T _s Sampling rate (Hz) - N _r Number of revolution - N _d Number of data per revolution - K _I Spindle motor current gain (ampere N^–1m^–1) - _d Time constant of the spindle system (sec)     

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.