Enhancing the performance of parallel cascade control using Smith predictor

Parallel cascade controllers are used in chemical processing industries to improve the dynamic performance of a control system in the presence of disturbances. In the present work, a delay compensator has been incorporated in the primary loop of the parallel cascade control system. The secondary controller is designed using the internal model control (IMC) method. The primary controller is designed based on a direct synthesis method for the delay-free system. Design of controllers for slow (when the secondary loop dynamics is slow i.e. process contains poles sufficiently slower than the desired closed loop response) as well as fast dynamics (when the inner loop dynamics is fast i.e. process contains poles sufficiently faster than the desired closed loop response) of the secondary process is considered. The method provides robust control performances. Significant improvement in the closed loop performances are obtained with the delay compensator over that of a conventional parallel cascade control system. Several case studies are considered to show the advantage of the proposed method when compared to other recently reported methods.     

An optimal PID controller via LQR for standard second order plus time delay systems

An improved tuning methodology of PID controller for standard second order plus time delay systems (SOPTD) is developed using the approach of Linear Quadratic Regulator (LQR) and pole placement technique to obtain the desired performance measures. The pole placement method together with LQR is ingeniously used for SOPTD systems where the time delay part is handled in the controller output equation instead of characteristic equation. The effectiveness of the proposed methodology has been demonstrated via simulation of stable open loop oscillatory, over damped, critical damped and unstable open loop systems. Results show improved closed loop time response over the existing LQR based PI/PID tuning methods with less control effort. The effect of non-dominant pole on the stability and robustness of the controller has also been discussed.     

A simple method of tuning parallel cascade controllers for unstable FOPTD systems

A simple method is proposed to design parallel cascade controllers for open loop unstable processes. A proportional (P)controller is considered for the secondary loop and a proportional integral (PI) controller is considered for the primary loop (P/PI control configuration). Coefficients of the corresponding powers of s (Laplace variable), in the numerator is matched with the coefficients of the corresponding powers of s in the denominator of a closed loop transfer function for a servo problem. Three simulation case studies are considered in this paper. The first case involves a stable secondary loop process and an unstable primary process, the second case involves both unstable primary and secondary processes and the third one, a simulation application to a nonlinear bioreactor model equations. For comparison purposes, P/PI controller design is also carried out by improved simultaneous relay autotuning method, synthesis method and minimizing ISE criterion method. It is found that the proposed method gives a better performance. Robust stability analysis using the complimentary sensitivity function is carried out. The present method is found to be more robust.     

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.     

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.     

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.     

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.     

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.     

A sliding mode control proposal for open-loop unstable processes

This papers presents a sliding mode controller based on a first-order-plus-dead-time model of the process for controlling open-loop unstable systems. The proposed controller has a simple and fixed structure with a set of tuning equations as a function of the desired performance. Both linear and nonlinear models were used to study the controller performance by computer simulations.     

Discrete-time domain two-degree-of-freedom control design for integrating and unstable processes with time delay

A discrete-time domain two-degree-of-freedom (2DOF) design method is proposed for integrating and unstable processes with time delay. Based on a 2DOF control structure recently developed, a controller is analytically designed in terms of the H₂ optimal control performance specification for the set-point tracking, and another controller is derived by proposing the desired closed-loop transfer function for load disturbance rejection. Both controllers can be tuned relatively independent to realize control optimization. Analytical expression of the set-point response is given for quantitatively tuning the single adjustable parameter in the set-point tracking controller. At the meantime, sufficient and necessary conditions for holding robust stability of the closed-loop control system are established for tuning another adjustable parameter in the disturbance rejection controller, along with numerical tuning guidelines. Illustrative examples from the literature are used to demonstrate the effectiveness of the proposed method.     

Improving performance using cascade control and a Smith predictor

Many investigations have been done on tuning proportional-integral-derivative (PID) controllers in single-input single-output (SISO) systems. However, only a few investigations have been carried out on tuning PID controllers in cascade control systems. In this paper, a new approach, namely the use of a Smith predictor in the outer loop of a cascade control system, is investigated. The method can be used in temperature control problems where the secondary part of the process (the inner loop) may have a negligible delay while the primary loop (the outer loop) has a time-delay. Two different approaches, including an autotuning method, to find the controller parameters are proposed. It is shown by some examples that the proposed structure as expected can provide better performance than conventional cascade control, a Smith predictor scheme or single feedback control system.     

Disturbance-rejection-based tuning of proportional–integral–derivative controllers by exploiting closed-loop plant data

A systematic data-based design method for tuning proportional–integral–derivative (PID) controllers for disturbance attenuation is proposed. In this method, a set of closed-loop plant data are directly exploited without using a process model. PID controller parameters for a control system that behaves as closely as possible to the reference model for disturbance rejection are derived. Two algorithms are developed to calculate the PID parameters. One algorithm determines the optimal time delay in the reference model by solving an optimization problem, whereas the other algorithm avoids the nonlinear optimization by using a simple approximation for the time delay term, enabling derivation of analytical PID tuning formulas. Because plant data integrals are used in the regression equations for calculating PID parameters, the two proposed algorithms are robust against measurement noises. Moreover, the controller tuning involves an adjustable design parameter that enables the user to achieve a trade-off between performance and robustness. Because of its closed-loop tuning capability, the proposed method can be applied online to improve (retune) existing underperforming controllers for stable, integrating, and unstable plants. Simulation examples covering a wide variety of process dynamics, including two examples related to reactor systems, are presented to demonstrate the effectiveness of the proposed tuning method.     

Stabilization and PID tuning algorithms for second-order unstable processes with time-delays

Open-loop unstable systems with time-delays are often encountered in process industry, which are often more difficult to control than stable processes. In this paper, the stabilization by PID controller of second-order unstable processes, which can be represented as second-order deadtime with an unstable pole (SODUP) and second-order deadtime with two unstable poles (SODTUP), is performed via the necessary and sufficient criteria of Routh-Hurwitz stability analysis. The stability analysis provides improved understanding on the existence of a stabilizing range of each PID parameter. Three simple PID tuning algorithms are proposed to provide desired closed-loop performance-robustness within the stable regions of controller parameters obtained via the stability analysis. The proposed PID controllers show improved performance over those derived via some existing methods.     

Enhanced IMC design of load disturbance rejection for integrating and unstable processes with slow dynamics

In view of the deficiencies in existing internal model control (IMC)-based methods for load disturbance rejection for integrating and unstable processes with slow dynamics, a modified IMC-based controller design is proposed to deal with step- or ramp-type load disturbance that is often encountered in engineering practices. By classifying the ways through which such load disturbance enters into the process, analytical controller formulae are correspondingly developed, based on a two-degree-of-freedom (2DOF) control structure that allows for separate optimization of load disturbance rejection from setpoint tracking. An obvious merit is that there is only a single adjustable parameter in the proposed controller, which in essence corresponds to the time constant of the closed-loop transfer function for load disturbance rejection, and can be monotonically tuned to meet a good trade-off between disturbance rejection performance and closed-loop robust stability. At the same time, robust tuning constraints are given to accommodate process uncertainties in practice. Illustrative examples from the recent literature are used to show effectiveness and merits of the proposed method for different cases of load disturbance.     

Simultaneous online automatic tuning of cascade control for open loop stable processes

In this paper, we present a new simultaneous online automatic tuning method for cascade control using a relay feedback approach. Departing from the traditional approach towards tuning of cascade control systems where the secondary and primary loops are tuned in strict sequence, the proposed approach is to carry out the entire tuning process in one experiment. For ease of practical applications, the entire procedure of controller design may be automated and carried out online. A direct controller tuning approach to tune the controllers is proposed here. Robustness analysis of the new cascade control design is further carried out in the paper by drawing on existing results for SISO feedback systems. Simulations are provided to illustrate the applicability and effectiveness of both the online autotuning approach and the new cascade control design.     

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.     

Improved automatic tuning of PID controller for stable processes

This paper presents an improved automatic tuning method for stable processes using a modified relay in the presence of static load disturbances and measurement noise. The modified relay consists of a standard relay in series with a PI controller of unity proportional gain. The integral time constant of the PI controller of the modified relay is chosen so as to ensure a minimum loop phase margin of 30. A limit cycle is then obtained using the modified relay. Hereafter, the PID controller is designed using the limit cycle output data. The derivative time constant is obtained by maintaining the above mentioned loop phase margin. Minimizing the distance of Nyquist curve of the loop transfer function from the imaginary axis of the complex plane gives the proportional gain. The integral time constant of the PID controller is set equal to the integral time constant of the PI controller of the modified relay. The effectiveness of the proposed technique is verified by simulation results.     

Design and robust tuning of control scheme based on the PD controller plus Disturbance Observer and low-order integrating first-order plus dead-time model

This paper presents an effective design and robust tuning method for the control structure based on a series PD controller and a simple Disturbance Observer. All elements of the proposed controller are directly obtained from the low-order Integrating First-Order Plus Dead-Time (IFOPDT) model, used to approximate essential dynamic characteristics of lag-dominant stable, integrating and unstable plants. The structure of the proposed controller is an effective, easy to implement and tune, extension of the series PID controller. For the same robustness, a better disturbance rejection response is obtained by the proposed controller than that of the PID, by adjusting only two parameters with a clear meaning. A comparison with well-tuned PIDs, done by simulations, and the experimental results, obtained on a real thermal power plant, confirm that high performance and robustness are obtained, for dynamic characteristics common to industrial processes.     

Design, implementation, and testing of a single axis levitation system for the suspension of a platform

This paper describes the design and implementation of a single axis DC attraction type suspension system, where a platform (vehicle structure) of around 14 kg mass is made to remain suspended at the desired operating gap under a ferromagnetic guide-way. The prototype has four electromagnetic actuators of attraction type and four inductive gap sensors, all located at the corners of the platform. The four actuators are controlled independently through four identical controllers, and the stable levitation of the platform is achieved through the single input and single output (SISO) control of each air-gap. The emphasis of this work is on the design and development of the switched mode power amplifier cum controller unit for the four actuators. The proposed single switch-based power circuit simplifies the overall hardware, and it can be extended to any number of magnet-coils. A cascade lead compensation control scheme utilizing an inner current loop and outer position loop has been designed and implemented for the stabilization of such a highly unstable and strongly nonlinear system. The prototype has been successfully tested, and stable levitation was demonstrated with the desired operating gap.