Classification of dynamic processes and PID controller tuning in a parameter plane

A quadruplet, defined by the ultimate frequency ω_u, the ultimate gain k_u, the angle φ of the tangent to the Nyquist curve at the ultimate frequency and the gain G_p(0), is sufficient for classification of a large class of stable processes, processes with oscillatory dynamics, integrating and unstable processes G_p(s). From the model defined by the above quadruplet, a two parameter model G_n(s_n) is obtained by the time and amplitude normalizations. Two parameters of G_n(s_n), the normalized gain ρ and the angle φ, are coordinates of the classification ρ-φ parameter plane. Model G_n(s_n) is used to obtain the desired closed-loop system performance/robustness tradeoff in the desired region of the classification plane. Tuning procedures and tuning formulae are derived guaranteeing almost the same performance/robustness tradeoff as obtained by the optimal PID controller, applied to G_p(s) classified to the same region of the classification plane. Validity of the proposed method is demonstrated on a test batch consisting of stable processes, processes with oscillatory dynamics, integrating and unstable processes, including dead-time.     

Optimization of PID controller with higher-order noise filter

The proposed PID controller optimization is based on the frequency response of a process G_p(s) and maximization of the proportional gain, under constraints on the desired sensitivity to measurement noise, desired maximum sensitivity and desired maximum complementary sensitivity. The set-point and load disturbance step responses with negligible overshoot are obtained for stable processes, processes with oscillatory dynamics, integrating and unstable processes. Simulations, with a band-limited white noise added to the controlled variable, and experimental results, on a laboratory thermal plant with noisy measurements, are used to demonstrate the effectiveness of the proposed PID optimization method.     

基于衰减频率特性的PID参数优化整定研究

用衰减频率特性法整定PID控制器可使闭环系统获得要求的衰减比,但是求得的整定参数的解是不确定的,因而难以确定最佳整定参数。就此,将基于衰减频率特性的PID控制器整定问题转换成带衰减比约束的控制器参数优化问题,首先用Matlab计算出整定参数的解曲线或解曲面,然后利用Simulink在仿真环境下寻优,获得期望性能下的最佳整定参数。仿真结果表明所提出的整定方法有效,且控制器具有良好的抗干扰能力。     

A direct synthesis tuning method of unstable first-order-plus-time-delay processes

A direct synthesis tuning method is proposed for the PI controller settings of unstable first-order-plus-time-delay processes. Unlike hitherto-known PI setting rules which often result in overshoots in time response or require the modification of the feedback control structure, this method ensures the overdamped response as desired while retaining the conventional PI control structure. This enhanced performance is possible by introducing a first-order set-point filter and applying simple rules for setting the values of the controller parameters without having any tuning parameters. The comparison with both conventional PI controllers and two-stage IMC method reveals that the proposed method produces not only smooth overdamped closed-loop response for set-point changes, but also fast regulatory control response for load changes. These responses are also shown to be quite robust against the uncertainties of the parameters as well as against the noise in the signal. The stability conditions for the processes having a large time delay or different ratios of time delay/time constant have been investigated as well. ©     

PID controller design of TITO system based on ideal decoupler

The proposed method for designing multivariable controller is based on ideal decoupler D(s) and PID controller optimization under constraints on the robustness and sensitivity to measurement noise. The high closed-loop system performance and robustness are obtained using the same controller in all loops. The method is effective despite the values and positions of the right half plane zeros and dead-times in the process transfer function matrix G_p(s). The validity of the proposed multivariable control system design and tuning method is confirmed using a test batch consisting of Two-Input Two-Output (TITO) stable, integrating and unstable processes, and one Three-Input Three-Output (TITO) stable process.     

典型工业过程鲁棒PID控制器的整定

提出一阶迟延过程、积分迟延过程、不稳定迟延过程和二阶迟延过程等典型工业过程的鲁棒PID整定公式.本文从抗干扰性能和鲁棒性能两方面综合考虑,把鲁棒PID控制器的设计问题转化为求解一个带鲁棒性能约束的绝对误差积分指标(IAE)优化问题.鉴于该问题是非凸的,本文采用遗传算法来求解,并通过曲线拟合得到典型工业过程的PID控制器的整定公式.仿真结果表明本文的PID整定公式有效,且控制器具有良好的抗干扰能力和频域鲁棒性.     

A dead-time compensating PID controller structure and robust tuning

In the present paper a dead-time compensating proportional-integral-derivative (DTC–PID) controller with anti-windup action is derived. The proposed controller also can be configured as a PID controller or as a dead-time compensating PI (DTC–PI) controller. For stable, integrating and unstable processes, approximated with the first-order plus dead-time (FOPDT) model, robust tuning procedure is derived for the DTC–PI controller. Optimization of the regulatory performance of the DTC–PID controller is based on the frequency response of higher-order models, under constraints on the robustness and sensitivity to measurement noise. Excellent performance/robustness trade-off is obtained for stable, integrating and unstable processes, including dead-time, as confirmed by simulations and by experimental results obtained on a laboratory thermal process.     

Analytical method of PID controller design for parallel cascade control

An analytical method of PID controller design is proposed for parallel cascade control. Firstly, a general structure for parallel cascade control is proposed that takes both setpoint and load disturbance responses into account. Analytical tuning rules for the PID controllers are then derived for the general process model by employing the IMC design procedure. The proposed method offers a simple and effective way to obtain the PID controller rules for parallel cascade control system which takes into account the interaction between primary and secondary control loops. The simulation results illustrate the application of the proposed method and demonstrate its superiority compared to several alternatives.     

Comparing 2DOF PI and predictive disturbance observer based filtered PI control

This paper analyses the optimal nominal tuning of a new modification of predictive disturbance observer (PDO) based filtered PI control (PDO FPI) applied to a first order plus dead time (FOPDT) plant with exactly known parameters.The impacts of applied filters on optimal controller tuning and on achievable closed loop performance are evaluated first of all. The limits of achievable performance are compared with those of traditional two degree of freedom (2DOF) PI control, with both controllers tuned by the multiple real dominant pole method. This comparison shows the potential of PDO FPI control to improve tracking and regulatory dynamics significantly, permitting the Pareto-like servo/regulator trade-off of 2DOF PI control to be removed.Two PDO FPI tuning approaches are proposed, allowing optimal filter degree and time constants to be evaluated.The first tuning scenario considers optimization of closed loop performance expressed in terms of the Integral of the Absolute Error (IAE) weighted alternatively by the relative total variance TV₁ of the control signal. This is carried out by changing the filter order n under the constraint that a constant position of the dominant closed loop pole is maintained. This keeps the dynamics of the setpoint step responses almost unchanged. In the second tuning scenario the optimization is carried out under a constraint on constant speed of disturbance step responses.All the main results are then numerically checked for the integral first order plant with dead time by the performance portrait (PP) method.The analysis presented here shows that the new PDO FPI structure substantially enriches the spectrum of controllers applicable to simple control tasks.     

Tuning PI/PID controllers for integrating processes with deadtime and inverse response by simple calculations

A simple calculation method of a practical PI/PID controller tuning for integrating processes with deadtime and inverse response based on a model is presented in this study. First, analytical expressions for PI/PID controller settings based on the model using a direct synthesis method for disturbance rejection (DS-d) are employed. Next, optimum tuning parameter (λ) for DS-d based on the model and minimum IAE criterion are obtained via the golden-section searching technique. These optimum λ data are then empirically correlated into two equations. Thus, PI/PID controller settings for the model can easily be obtained from the parameter λ using DS-d formulas. The advantage of the proposed method is that DS-d PI/PID settings could be expediently sought by simple calculations using these equations without any tedious design. Simulation results have demonstrated that the proposed tuning technique can perform better for load/disturbance changes than other available methods in the literature.     

Robust PID controller tuning based on the constrained particle swarm optimization

This paper proposes a novel tuning strategy for robust proportional-integral-derivative (PID) controllers based on the augmented Lagrangian particle swarm optimization (ALPSO). First, the problem of PID controller tuning satisfying multiple H_∞ performance criteria is considered, which is known to suffer from computational intractability and conservatism when any existing method is adopted. In order to give some remedy to such a design problem without using any complicated manipulations, the ALPSO based robust gain tuning scheme for PID controllers is introduced. It does not need any conservative assumption unlike the conventional methods, and often enables us to find the desired PID gains just by solving the constrained optimization problem in a straightforward way. However, it is difficult to guarantee its effectiveness in a theoretical way, because PSO is essentially a stochastic approach. Therefore, it is evaluated by several simulation examples, which demonstrate that the proposed approach works well to obtain PID controller parameters satisfying the multiple H_∞ performance criteria.     

Dimensional analysis approach to dominant three-pole placement in delayed PID control loops

PID control loops with time delay are characterized by infinite number of poles but the pole assignment technique for adjusting the controller parameters can be applied to placing three poles only. The dominance of these poles is therefore an essential condition for this application. A novel approach to this problem involves applying dimensional analysis theory to obtain a generalized model of the control loop and then to perform a parameter tuning for its dimensionless representation. A one-row dimensional matrix results from the assumption of the usual dimensionless interpretation of both control error and actuating signals of the controller. Dimensionless similarity numbers of the so-called swingability and laggardness are introduced to specify the plant dynamics in the controller synthesis. A trio of numbers is assigned to become the dominant zeros of the characteristic quasi-polynomial of the control loop and the corresponding PID parameter adjustment is derived in the form of uniform formulae. The tuning of the proper damping and the real pole position ratios is provided by means of an IAE optimization technique. A dominance degree notion is introduced and an argument increment criterion is proposed to check the dominance of any of the pole placement cases. The quality of the disturbance rejection response is taken as the general criterion in the design of the time delay plant control.     

PID参数整定法的仿真

PID调节器的控制品质,主要取决于调节器的参数整定.计算量大是用理论计算方法整定PID调节器参数要解决的难题之一.针对PID调节器参数整定过程中计算复杂、计算量大的问题,提出了一种基于Matlab的调节器参数衰减频率特性整定法.该方法以Matlab为工具,将理论计算与仿真分析结合起来,根据控制要求计算并绘制出控制器整定参数关系曲线,对计算结果进行仿真,分析整定参数在解平面上变化时闭环系统的响应,从而确定出最佳的调节器整定参数.结果表明,对于不同的被控对象参数或不同的整定要求,该方法都能方便地求得最佳的调节器整定参数,使得采用理论计算法整定调节器参数具有了工程实用价值.     

Control quality enhancement using fractional PIλDμ controller

The proportional–integral–derivative (PID) controllers have remained, by far, the most commonly and practically used in all industrial feedback control applications; therefore, there is a continuous effort to improve the system control quality performances. More recently Podlubny has proposed the fractional PI^λD^μ controller, a generalisation of the classical PID controller, involving an integration action of order λ and differentiation action of order μ. Since then, many researchers have been interested in the use and tuning of this type of controller. In this article, a new conception method of this fractional PI^λD^μ controller is considered. The basic ideas of this new tuning method are based, in the first place, on the classical Ziegler–Nichols tuning method for setting the parameters of the fractional PI^λD^μ controller for λ = μ = 1, which means setting the parameters of the classical PID controller, and on the minimum integral squared error criterion by using the Hall–Sartorius method for setting the fractional integration action order λ and the fractional differentiation action order μ. Illustrative examples and simulation results are presented to show the control quality enhancement of this proposed fractional PI^λD^μ controller conception method compared to the PID controller conception using Ziegler–Nichols tuning method.     

基于PID参数整定的无模型自适应控制器参数整定方法

本文针对一阶线性时不变(FOLTI)系统, 将常用的比例–积分–微分(PID)控制器参数整定方法推广到无模型自适应控制(MFAC)参数整定中, 利用PID控制参数整定方法整定直接型MFAC方案的伪梯度初值, 以期改变MFAC控制律初始参数的试凑式选取, 提升MFAC应用的方便性和可接受性. 通过仿真, 验证了所提伪梯度初值整定方法的有效性, 并对比了FOLTI系统的系统参数和系统结构发生变化后, 应用MFAC与PID控制的性能差异.     

Series PID controller tuning based on the SIMC rule and signal filtering

The SIMC (Simple control) rule, proposed by Skogestad, is ineffective for a class of processes with oscillatory dynamics and processes defined by transfer functions obtained as a result of ideal decoupling of multiple-input multiple-output systems. For this class of stable processes it is proposed to apply a higher-order filtering to the open-loop process step response and to approximate the filtered step response with stable SOPDT models. These models are used to obtain a high performance/robustness tradeoff by the ideal series PID controllers, tuned by the SIMC rule, with the higher-order filter in the feedback loop. Parallel PID controllers, with higher-order noise filters, tuned by applying exact process frequency response and optimization under constraints on the robustness and sensitivity to measurement noise, are used to demonstrate merits of the proposed simple design and tuning of the series PID controller. Experimental results on a mechanical laboratory plant are presented in Appendix.     

基于Maclaurin 展开的PID 设计与无模型自整定

针对自衡对象,提出一种基于期望模型的PID自整定方法,该方法无需被控对象的数学模型.利用Maclaurin展开技术,给出了PID控制器的整定公式;并通过开环阶跃响应,实现了PID控制器的无模型自整定.仿真结果表明,利用该自整定方法所得的PID能有效地提高高阶被控对象的系统性能;即使在噪声环境下,该方法仍具有很好的鲁棒性.     

一种改进的针对线性时不变单输入单输出系统的PID控制器

本文提出了一种提高PID控制器的稳定范围和控制精度的改进方法，即通过改变PID控制器的积分项结构，并给出了二阶系统控制对象达到渐进稳定时的相关参数方程。最后采用Ziegler-Nichols参数整定法对改进后的PID控制器和常规PID控制器进行了仿真，仿真结果表明控制效果明显提高。     

An alternative structure for next generation regulatory controllers: Part I: Basic theory for design, development and implementation

Even though employed widely in industrial practice, the popular PID controller has weaknesses that limit its achievable performance, and an intrinsic structure that makes tuning not only more complex than necessary, but also less transparent with respect to the key attributes of the overall controller performance, namely: robustness, set-point tracking, and disturbance rejection. In this paper, we propose an alternative control scheme that combines the simplicity of the PID controller with the versatility of model predictive control (MPC) while avoiding the tuning problems associated with both. The tuning parameters of the proposed control scheme are related directly to the controller performance attributes; they are normalized to lie between 0 and 1; and they arise naturally from the formulation in a manner that makes it possible to tune the controller directly for each performance attribute independently. The result is a controller that can be designed and implemented much more directly and transparently, and one that outperforms the classical PID controller both in set-point tracking and disturbance rejection while using precisely the same process reaction curve information required to tune PID controllers. The design, implementation and performance of the controller are demonstrated via simulation on a nonlinear polymerization process.     

Domains of PID controller coefficients which guarantee stability and performance for LTI time-delay systems

In this work, the computation of the regions in the space of coefficients of a PID controller, inside which the controller stabilizes an LTI time-delay plant and guarantees a performance specification for the closed-loop system, is addressed. To ascertain the sensor noise attenuation, as a sample performance requirement, the H_∞-norm of the weighted complementary sensitivity function is kept below a desired bound. The problem of minimization of the H_∞-norm is transformed into the simultaneous stabilization of a family of quasipolynomials. Then, the stable domains of the PID coefficients are computed for these quasipolynomials using the parameter space approach. This work extends the previous results on the computation of the stability domains of a PID controller to ensure the desired performance specification for the closed-loop system.