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.     

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.     

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.     

采用内模控制理论的双馈感应风机鲁棒控制器设计

针对工程中双馈感应电机转子电流控制器参数整定的问题,提出一种利用内模控制理论设计转子电流控制器的鲁棒控制方法。首先定义内模控制的灵敏度函数和互补灵敏度函数,并推导双馈感应电机转子电流控制系统传递函数,建立了转子电流内环的内模数学模型。IMC控制器的设计以平方积分误差值和鲁棒稳定M值为准则,并与传统比例积分控制器进行比较。通过对1.5 MW双馈感应电机的MATLAB/SIMULINK仿真表明,本文方法稳态跟踪精度高、动态响应快、对模型误差和外界干扰具有较好的鲁棒性。最后在11 k W的双馈风机实验平台上验证了所提方法的有效性。     

Design of PID controllers in double feedback loops for SISO systems with set-point filters

A PID controller is widely used to control industrial processes that are mostly open loop stable or unstable. Selection of proper feedback structure and controller tuning helps to improve the performance of the loop. In this paper a double-feedback loop/method is used to achieve stability and better performance of the process. The internal feedback is used for stabilizing the process and the outer loop is used for good setpoint tracking. An internal model controller (IMC) based PID method is used for tuning the outer loop controller. Autotuning based on relay feedback or the Ziegler-Nichols method can be used for tuning an inner loop controller. A tuning parameter (λ) that is used to tune IMC-PID is used as a time constant of a setpoint filter that is used for reducing the peak overshoot. The method has been tested successfully on many low order processes.     

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.     

A fast converging robust controller using adaptive second order sliding mode

This paper proposes an adaptive second order sliding mode (SOSM) controller with a nonlinear sliding surface. The nonlinear sliding surface consists of a gain matrix having a variable damping ratio. Initially the sliding surface uses a low value of damping ratio to get a quick system response. As the closed loop system approaches the desired reference, the value of the damping ratio gets increased with an aim to reducing the overshoot and the settling time. The time derivative of the control signal is used to design the controller. The actual control input obtained by integrating the derivative control signal is smooth and chattering free. The adaptive tuning law used by the proposed controller eliminates the need of prior knowledge about the upper bound of system uncertainties. Simulation results demonstrate the effectiveness of the proposed control strategy.     

直线电机精密定位平台轨迹跟踪控制器设计

为了实现直线电机精密定位平台的位置和速度的轨迹跟踪控制,本文基于内模控制（IMC）的基本原理,在直线电机精密定位平台参数辨识的基础上,设计了定位平台速度环的模型状态反馈（MSF）控制器和基于位置环PID和速度环MSF的级联控制器。将PID/MSF级联控制器与速度/加速度前馈控制（VFC/AFC）相结合,构成了PID/MSF+VFC/AFC的复合轨迹跟踪控制器。该复合轨迹跟踪控制器通过整定速度前馈的增益来改善位置环偏差控制的跟踪滞后现象和动态响应,增加控制系统的稳定性和伺服精度;通过整定加速度前馈的增益在不减小级联控制器位置环增益的前提下,减小速度前馈带来的超调量,提高轨迹跟踪精度。基于MATLAB/dSPACE实时仿真控制平台,实现了某直线电机平台的轨迹跟踪控制。仿真和实验结果表明,该轨迹跟踪控制器的轨迹跟踪精度为±0.028 mm,定位精度为±4 μm,满足直线电机精密定位平台轨迹跟踪控制的要求。     

Model Based Tuning of a Non Linear Spherical Tank Process with Time Delay

Abstract

A 40 liter spherical tank with varying time delay was subjected to open loop analysis using a step response technique with sodium chloride solution as tracer. The experimental data was adequately represented by a first order plus dead time (FOPDT) model with an error of less than five percent. These model parameters were used to generate Smith Predictor controller, IMC controller, and IMC PID controller using MATLAB. For closed loop control of the process based on rise time, settling time, overshoot, peaktime, decay ratio, and ISE, it was found that the IMCPID controller is better suited for this process.     

Simple robust autotuning rules for 2-DoF PI controllers

This paper addresses the problem of providing simple tuning rules for a Two-Degree-of-Freedom (2-DoF) PI controller (PI(2)) with robustness considerations. The introduction of robustness as a matter of primary concern is by now well established among the control community. Among the different ways of introducing a robustness constraint into the design stage, the purpose of this paper is to use the maximum sensitivity value as the design parameter. In order to deal with the well known performance/robustness tradeoff, an analysis is conducted first that allows the determination of the lowest closed-loop time constant that guarantees a desired robustness. From that point, an analytical design is conducted for the assignment of the load-disturbance dynamics followed by the tuning of the set-point weight factor in order to match, as much as possible, the set-point-to-output dynamics according to a first-order-plus-dead-time dynamics. Simple tuning rules are generated by considering specific values for the maximum sensitivity value. These tuning rules, provide all the controller parameters parameterized in terms of the open-loop normalized dead-time allowing the user to select a high/medium/low robust closed-loop control system. The proposed autotuning expressions are therefore compared with other well known tuning rules also conceived by using the same robustness measure, showing that the proposed approach is able to guarantee the same robustness level and improve the system time performance.     

Model Based Tuning of Humidifying Processes with Transportation Lag

Abstract

A humidifying system with varying transportation lag was studied experimentally. Various models were tried and the system fitted a first order plus dead time model with an error of ±5%. The humidity was measured using an on‐line Yokogawa hygrometer. From the model parameters, various controllers, such as PI, Smith predictor, IMC, and IMC PID were analyzed using Matlab. The closed loop performance was studied for both regulator and servo problems. Based on rise time, settling time, and overshoot, the present study concludes that the IMC controller is best suited for this process.     

Robust controller for uncertain parameters systems

In this paper, we present the synthesis of a robust controller for Linear Time Invariant (LTI) uncertain systems. A linear parametric uncertainties model is used to describe the system dynamic behavior. The main purpose of this controller is to guarantee some step response performances such as the settling time and the overshoot. The controller synthesis is formulated as a min-max optimization problem which takes in account the desired closed-loop performances and the uncertainties on the model parameters. Then the controller parameters represent the best solution for the worst case of all possible models. In order to emphasize its performances and its efficiency, a real time implementation of the proposed controller on a laboratory pilot plant has been presented.     

Optimal solution,quantitative performance estimation,and robust tuning of the simplifying controller

Recently, a simplifying controller has been proposed based on the principal of simplification of the control system transfer functions, which offers improved control for processes with a large time delay. It is the purpose of this complementary paper to give a comprehensive analysis on the scheme. First, the relationship among the simplifying controller, the Smith predictor, and the internal model control are discussed. Second, an analytical design procedure is developed based on internal model control (IMC) and optimal solution is derived. Third, the problem of estimating the time domain performance of the closed loop system, quantitatively, is discussed. Fourth, a simple robust tuning procedure is presented. Numerical examples are provided to illustrate the proposed method.     

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.     

基于限幅的最优PID控制器

本文提出了一种允许PID控制器输出达到限幅的非线性控制策略，探讨了寻求PID最优参数的搜索算法，并对搜索算法进行了改进。仿真表明，本文所提出的基于限幅的PID控制策略与传统的线性PID控制策略相比，能使系统的调节时间、超调量、鲁棒性等性能指标有着显著的提高。     

一类切换模糊PID控制器设计及其仿真

提出了一类高动态性能切换模糊PID控制器设计方法.通过对传统PID控制中比例控制和微分控制作用的分析,结合模糊PID控制器鲁棒性能和自适应性好的优点,设计了一类新的模糊控制器.由于该类控制器先后经历比例控制,微分控制和模糊PID控制的切换,使被控系统不仅具有一般模糊PID控制器的所具有的良好的鲁棒性能和自适应性,而且与一般模糊控制器相比具有更小的超调量和调节时间,是一类动态性能良好的控制器.最后将该控制器应用于一伺服系统进行仿真对比,并给出了Simulink仿真框图.仿真结果说明了该控制器的优越性.     

永磁直线伺服系统模糊PI速度控制器研究

针对永磁直线同步电机伺服系统常规PI速度调节器动态响应慢、输出超调大等问题,提出了模糊自适应PI速度控制器,对比常规PI速度控制器进行了仿真和实验。基于永磁直线同步电机矢量速度闭环控制,分析了模糊PI速度控制器和基于模糊PI控制器的伺服矢量控制系统的结构,设计了模糊PI速度控制器,在Matlab/Simulink仿真环境下,建立了基于模糊PI速度控制器的永磁直线同步电机伺服系统仿真模型,并通过实际永磁同步直线电机伺服系统实验对仿真结果进行了实验验证。研究结果表明,模糊PI速度控制器,相对于常规PI控制器,可以明显降低超调量和调节时间。将仿真结果和试验结果对比,两者基本吻合,说明模糊PI速度控制确实可以较好地改善永磁直线同步电机伺服系统的动态性能。     

Design of an Internal Model Control strategy for single-phase grid-connected PWM inverters and its performance analysis with a non-linear local load and weak grid

This paper presents the design of a controller based on Internal Model Control (IMC) applied to a grid-connected single-phase PWM inverter. The mathematical modeling of the inverter and the LCL output filter, used to project the 1-DOF IMC controller, is presented and the decoupling of grid voltage by a Feedforward strategy is analyzed. A Proportional – Resonant Controller (P+Res) was used for the control of the same plant in the running of experimental results, thus moving towards the discussion of differences regarding IMC and P+Res performances, which arrived at the evaluation of the proposed control strategy. The results are presented for typical conditions, for weak-grid and for non-linear local load, in order to verify the behavior of the controller against such situations.     

Control of a permanent magnet synchronous motor with a fuzzy sliding-mode controller

This paper is concerned with the topics in the speed control of a permanent magnet synchronous motor (PMSM). First, the vector control scheme in the synchronously rotating reference frame is used to formulate the PMSM model as the system plant. Then, the modern control theory using a sliding mode with fuzzy controller is presented to design the corresponding closed-loop system and Matlab/Simulink software is used for computer simulation. The original PMSM is stable, sluggish with large overshoot deficiency. It can be shown that the proposed fuzzy sliding-mode controller not only can delete the overshoot problem and achieve very good tracking performance without zero steady-state errors, but can also obtain good robustness to system parameter uncertainty. This proposed fuzzy-sliding mode controller for PMSM can be applied to the positioning control of the robot arms to suppress unnecessary vibrations. For assembly lines, this proposed controller can be used to obtain fast tracking ability, less steady-state errors, and robustness for different velocity movements.