Multi-model direct adaptive decoupling control with application to the wind tunnel system

In this paper, a new multi-model direct adaptive decoupling controller is presented for multivariable processes, which includes multiple fixed optimal controllers, one free-running adaptive controller, and one re-initialized adaptive controller. The fixed controllers provide initial control to the process if its model lies in the corresponding region. For each controller selected, the re-initialized adaptive controller uses the values of this particular controller to improve the adaptation speed. This controller may replace the fixed controller at a later stage according to the switching criterion which is to select the best one among all controllers. A free-running adaptive controller is also added to guarantee the overall system stability. Different from the multiple models adaptive control structure proposed in Narendra, Balakrishnan, and Ciliz [Adaptation and learning using multiple models, switching, and tuning. IEEE Control Syst. Mag. 15, 37-51 (1995)], the method not only is applicable to the multi-input multi-output processes but also identifies the decoupling controller parameters directly, which reduces both the computational burden and the chances of a singular matrix during the process of determining controller parameters. Several examples for a wind tunnel process are given to demonstrate the effectiveness and practicality of the proposed method.     

采用电磁驱动配气机构的汽油机换挡过程控制

针对采用电磁驱动配气机构（EMVT）的汽油机,建立了面向控制的无凸轮发动机平均值模型。设计了EMVT的控制模块,实现了直接通过控制进气门运动来调节进气量,进而控制发动机转速和转矩输出。在此基础上,针对电控机械式自动变速器（AMT）的换挡过程,提出了一种基于离合器传递转矩的发动机转速和转矩控制策略,以缩短换挡时间和提高换挡品质。在MATLAB/Simulink环境中进行了仿真,验证了EMVT控制模块和发动机换挡过程控制策略的有效性。     

Centralized PI controllers for interacting multivariable processes by synthesis method

In this article, two methods of designing a centralized control system for multi-input, multi-output (MIMO) processes are presented. Centralized proportional-integral (PI) controllers are designed based on a direct synthesis method. The inverse of the process transfer function matrix in the direct synthesis method is approximated based on the relative gain array concept. The method is further improved by using a relative normalized gain array, and an equivalent transfer function for each element in the process transfer function matrix is derived for the closed-loop control system. The transpose of the effective transfer function is used to approximate the inverse of the process transfer function matrix. The simulation studies demonstrate the effectiveness of this method. The proposed centralized controllers reduce the interactions better than recently reported decentralized controllers do. A centralized controller designed based on a relative normalized gain array (RNGA) gives a better performance than a centralized controller designed based on a relative gain array (RGA).     

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.     

Calculation and tuning of controllers for nonlinear systems with different-rate processes

A method for calculating the parameters of controllers for nonlinear nonstationary dynamic systems is proposed. The structure of the controller is a generalization of the structure of proportional-integral and proportional-integral-differential controllers. The method is applicable to unstable nonlinear systems with incomplete information on the plant model. The method is based on the deliberate formation of different-rate processes in a control system in which the stability of fast processes is provided by choosing the controller parameters, and the slow processes formed correspond to the reference model of the desired behavior of a nonlinear system. An example of the results of numerical simulation is given.     

烧结混合料加水的模糊自适应分数阶PI~λD~u控制

烧结混合料加水系统具有大滞后、模型复杂的特性,且客观环境中存在干扰因素,传统的控制方法很难取得理想的控制效果。分数阶PIλDu控制器比常规PID控制器多了两个可调参数,具有更好的控制效果。在分析分数阶微积分的基础上,给出了分数阶微积分的数字实现,用分数阶PIλDu控制代替常规PID控制,结合模糊控制,首次提出了一种针对烧结混合料加水系统的模糊自适应分数阶PIλDu控制方法,利用模糊逻辑实现分数阶PIλDu控制参数的在线调整。并用MATLAB/simulink进行建模仿真。仿真结果验证该控制算法的有效性,能取得较好的控制效果。     

Computation of stabilizing PI and PID controllers for processes with time delay

In this paper, a new method for the computation of all stabilizing PI controllers for processes with time delay is given. The proposed method is based on plotting the stability boundary locus in the (kp, ki) plane and then computing the stabilizing values of the parameters of a PI controller for a given time delay system. The technique presented does not need to use Pade approximation and does not require sweeping over the parameters and also does not use linear programming to solve a set of inequalities. Thus it offers several important advantages over existing results obtained in this direction. Beyond stabilization, the method is used to compute stabilizing PI controllers which achieve user specified gain and phase margins. The proposed method is also used to design PID controllers for control systems with time delay. The limiting values of a PID controller which stabilize a given system with time delay are obtained in the (kp, ki) plane, (kp, kd) plane, and (ki, kd) plane. Examples are given to show the benefits of the method presented.     

Simple method of designing centralized PI controllers for multivariable systems based on SSGM

A method is given to design multivariable PI/PID controllers for stable and unstable multivariable systems. The method needs only the steady state gain matrix (SSGM). The method is based on the static decoupler design followed by SISO PI/PID controllers design and combining the resulted decoupler and the diagonal PI(D) controllers as the centralized controllers. The result of the present method is shown to be equivalent to the empirical method proposed by Davison EJ. Multivariable tuning regulators: the feed-forward and robust control of general servo-mechanism problem. IEEE Trans Autom Control 1976;21:35–41. Three simulation examples are given. The performance of the controllers is compared with that of the reported centralized controller based on the multivariable transfer function matrix.     

Centralized PI control for high dimensional multivariable systems based on equivalent transfer function

This article presents a new scheme to design full matrix controller for high dimensional multivariable processes based on equivalent transfer function (ETF). Differing from existing ETF method, the proposed ETF is derived directly by exploiting the relationship between the equivalent closed-loop transfer function and the inverse of open-loop transfer function. Based on the obtained ETF, the full matrix controller is designed utilizing the existing PI tuning rules. The new proposed ETF model can more accurately represent the original processes. Furthermore, the full matrix centralized controller design method proposed in this paper is applicable to high dimensional multivariable systems with satisfactory performance. Comparison with other multivariable controllers shows that the designed ETF based controller is superior with respect to design-complexity and obtained performance.     

A new design method for PI–PD control of unstable processes with dead time

PID controllers are still widely practiced in the industrial systems. In the literature, many publications can be found considering PID controller design for unstable processes. However, owing to the structural limitations of PID controllers, generally, good closed loop performance cannot be achieved with a PID for controlling unstable processes and usually a step response with a high overshoot and oscillation is obtained. On the other hand, PI–PD controllers are proved to give very satisfactory closed loop performances for unstable processes. The paper presents a simple design method to tune parameters of a PI–PD controller for the control of the unstable processes with time delay. The proposed method is based on plotting the stability boundary locus, which is a locus dependent on the parameters of the controller and frequency, in the parameter plane. The method uses a new concept named centroid of the convex stability region. Simulation examples and an experimental application are given to illustrate the superiority of the proposed method over some existing ones.     

Smith predictor based-sliding mode controller for integrating processes with elevated deadtime

An approach to control integrating processes with elevated deadtime using a Smith predictor sliding mode controller is presented. A PID sliding surface and an integrating first-order plus deadtime model have been used to synthesize the controller. Since the performance of existing controllers with a Smith predictor decrease in the presence of modeling errors, this paper presents a simple approach to combining the Smith predictor with the sliding mode concept, which is a proven, simple, and robust procedure. The proposed scheme has a set of tuning equations as a function of the characteristic parameters of the model. For implementation of our proposed approach, computer based industrial controllers that execute PID algorithms can be used. The performance and robustness of the proposed controller are compared with the Matausek-Mici? scheme for linear systems using simulations.     

Data-driven model reference control of MIMO vertical tank systems with model-free VRFT and Q-Learning

This paper proposes a combined Virtual Reference Feedback Tuning–Q-learning model-free control approach, which tunes nonlinear static state feedback controllers to achieve output model reference tracking in an optimal control framework. The novel iterative Batch Fitted Q-learning strategy uses two neural networks to represent the value function (critic) and the controller (actor), and it is referred to as a mixed Virtual Reference Feedback Tuning–Batch Fitted Q-learning approach. Learning convergence of the Q-learning schemes generally depends, among other settings, on the efficient exploration of the state-action space. Handcrafting test signals for efficient exploration is difficult even for input-output stable unknown processes. Virtual Reference Feedback Tuning can ensure an initial stabilizing controller to be learned from few input-output data and it can be next used to collect substantially more input-state data in a controlled mode, in a constrained environment, by compensating the process dynamics. This data is used to learn significantly superior nonlinear state feedback neural networks controllers for model reference tracking, using the proposed Batch Fitted Q-learning iterative tuning strategy, motivating the original combination of the two techniques. The mixed Virtual Reference Feedback Tuning–Batch Fitted Q-learning approach is experimentally validated for water level control of a multi input-multi output nonlinear constrained coupled two-tank system. Discussions on the observed control behavior are offered.     

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.     

Real Time Control of pH in Fed‐Batch Process

Abstract

The objective of this work is to implement the linear, non linear model based and linear cascade controllers to control pH in a fed batch neutralisation process in real time and compare the performance with the simulation results. The control objective here is to make the process output pH to follow the given reference trajectory. This work aims at bringing out the best features of model‐based control and linear cascade control, when applied to highly non‐linear systems like pH‐controlled fed‐batch processes. For these processes, control of pH by a conventional Proportional Integral Derivative controller fails to provide satisfactory performance because of the extreme non‐linearity in the pH dynamics. Typical problems in control, e.g., uncertainty in model parameters, are addressed in this work. These controllers are implemented in real time using a lab scale setup and compared with the simulation. The results show the superior performance of the non linear model‐based and linear cascade controller over that of the conventional Proportional Integral controller.     

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.     

Fuzzy control of multivariable process by modified error decoupling

In this paper, a control concept for the squared (equal number of inputs and outputs) multivariable process systems is given. The proposed control system consists of two parts, single loop fuzzy controllers in each loop and a centralized decoupling unit. The fuzzy control system uses feedback control to minimize the error in the loop and the decoupler uses an adaptive technique to mitigate loop interactions. The decoupler predicts the interacting loop changes and modifies the input (error) of the loop controller. The controller was tested on the simulation model of "single component vaporizer" process. The results indicate that the decoupling controller shows better performance for set point and load changes.     

Set point weighted modified Smith predictor for integrating and double integrating processes with time delay

A simple method of designing the controllers for a modified form of Smith predictor is proposed for integrating and double integrating processes with time delay. The modified Smith predictor has two controllers, namely, a set point tracking controller and a load disturbance rejection controller for obtaining good set point tracking and load disturbance rejection, respectively. The set point tracking controller is designed using the classical direct synthesis method based on the process model without considering the time delay. The disturbance rejection controller is considered as a proportional-derivative (PD) controller and is designed using optimal gain and phase margin approaches. Set point weighting is considered for reducing undesirable overshoots and settling times in the modified Smith predictor. Guidelines are provided for selection of the desired closed loop tuning parameter in the direct synthesis method and the set point weighting parameter. The method gives significant load disturbance rejection performances. Illustrative examples are considered to show the performances of the proposed method. A significant improvement in control performance is obtained when compared to recently reported methods.     

Design of a new PID controller using predictive functional control optimization for chamber pressure in a coke furnace

An improved proportional-integral-derivative (PID) controller based on predictive functional control (PFC) is proposed and tested on the chamber pressure in an industrial coke furnace. The proposed design is motivated by the fact that PID controllers for industrial processes with time delay may not achieve the desired control performance because of the unavoidable model/plant mismatches, while model predictive control (MPC) is suitable for such situations. In this paper, PID control and PFC algorithm are combined to form a new PID controller that has the basic characteristic of PFC algorithm and at the same time, the simple structure of traditional PID controller. The proposed controller was tested in terms of set-point tracking and disturbance rejection, where the obtained results showed that the proposed controller had the better ensemble performance compared with traditional PID controllers.     

H(infinity) PID controller design for runaway processes with time delay

This paper presents an efficient method for designing proportional-integra-derivative (PID) controllers for runaway processes with time delay. The method is developed based on the H(infinity) control theory in frequency domain. The constraints imposed by the internal stability and asymptotic properties of the closed-loop system are first investigated, a new procedure is then developed for analytically designing the controller, and simple design formulas are obtained. It is shown that the new controller can be designed to meet specified time domain performances. Typical design examples are provided to illustrate the proposed method.     

Fuzzy Lyapunov Reinforcement Learning for Non Linear Systems

We propose a fuzzy reinforcement learning (RL) based controller that generates a stable control action by lyapunov constraining fuzzy linguistic rules. In particular, we attempt at lyapunov constraining the consequent part of fuzzy rules in a fuzzy RL setup. Ours is a first attempt at designing a linguistic RL controller with lyapunov constrained fuzzy consequents to progressively learn a stable optimal policy. The proposed controller does not need system model or desired response and can effectively handle disturbances in continuous state-action space problems. Proposed controller has been employed on the benchmark Inverted Pendulum (IP) and Rotational/Translational Proof-Mass Actuator (RTAC) control problems (with and without disturbances). Simulation results and comparison against a) baseline fuzzy Q learning, b) Lyapunov theory based Actor-Critic, and c) Lyapunov theory based Markov game controller, elucidate stability and viability of the proposed control scheme.