An improved auto-tuning scheme for PI controllers

Ziegler-Nichols tuned PI and PID controllers are usually found to provide poor performances for high-order and nonlinear systems. In this study, an improved auto-tuning scheme is presented for Ziegler-Nichols tuned PI controllers (ZNPICs). With a view to improving the transient response, the proportional and integral gains of the proposed controller are continuously modified based on the current process trend. The proposed controller is tested for a number of high-order linear and nonlinear dead-time processes under both set-point change and load disturbance. It exhibits significantly improved performance compared to ZNPIC, and Refined Ziegler-Nichols tuned PI controller (RZNPIC). Robustness of the proposed scheme is established by varying the controller parameters as well as the dead-time of the process under control.     

Auto-tuning of TITO decoupling controllers from step tests

This paper considers auto-tuning of simple lead-lag decoupler plus decentralized PI/PID controllers for effective control of two-input and two-output (TITO) processes. A new robust identification method from step tests is presented first for SISO processes and then sequentially applied to TITO processes. The resulting 1st-order plus dead-time model is used for decoupler design and the 2nd-order one is used for decentralized PID sequential tuning. The simulation is given for illustration of the proposed tuning.     

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.     

Improving dynamic performances of PWM-driven servo-pneumatic systems via a novel pneumatic circuit

In this paper, the effect of pneumatic circuit design on the input–output behavior of PWM-driven servo-pneumatic systems is investigated and their control performances are improved using linear controllers instead of complex and costly nonlinear ones. Generally, servo-pneumatic systems are well known for their nonlinear behavior. However, PWM-driven servo-pneumatic systems have the advantage of flexibility in the design of pneumatic circuits which affects the input–output linearity of the whole system. A simple pneumatic circuit with only one fast switching valve is designed which leads to a quasi-linear input–output relation. The quasi-linear behavior of the proposed circuit is verified both experimentally and by simulations. Closed loop position control experiments are then carried out using linear P- and PD-controllers. Since the output position is noisy and cannot be directly differentiated, a Kalman filter is designed to estimate the velocity of the cylinder. Highly improved tracking performances are obtained using these linear controllers, compared to previous works with nonlinear controllers.     

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.     

Two-degree-of-freedom fractional order-PID controllers design for fractional order processes with dead-time

Recently, fractional order (FO) processes with dead-time have attracted more and more attention of many researchers in control field, but FO-PID controllers design techniques available for the FO processes with dead-time suffer from lack of direct systematic approaches. In this paper, a simple design and parameters tuning approach of two-degree-of-freedom (2-DOF) FO-PID controller based on internal model control (IMC) is proposed for FO processes with dead-time, conventional one-degree-of-freedom control exhibited the shortcoming of coupling of robustness and dynamic response performance. 2-DOF control can overcome the above weakness which means it realizes decoupling of robustness and dynamic performance from each other. The adjustable parameter η₂ of FO-PID controller is directly related to the robustness of closed-loop system, and the analytical expression is given between the maximum sensitivity specification M_s and parameters η₂. In addition, according to the dynamic performance requirement of the practical system, the parameters η₁ can also be selected easily. By approximating the dead-time term of the process model with the first-order Padé or Taylor series, the expressions for 2-DOF FO-PID controller parameters are derived for three classes of FO processes with dead-time. Moreover, compared with other methods, the proposed method is simple and easy to implement. Finally, the simulation results are given to illustrate the effectiveness of this method.     

Auto-tuning of PID controller parameters with supervised receding horizon optimization

In this paper, a novel two-layer online auto-tuning algorithm is presented for a nonlinear time-varying system. The lower layer consists of a conventional proportional-integral-derivative (PID) controller and a plant process, while the upper layer is composed of identification and tuning modules. The purpose of the upper layer is to find a set of optimal PID parameters for the lower layer via an online receding horizon optimization approach, which result in a time-varying PID controller. Through mathematical analysis, the proposed system performance is equivalent to that of a standard generalized predictive control. Simulation and experiment demonstrate that the new method has a better control system performance compared with conventional PID controllers.     

A novel auto-tuning method for fractional order PI/PD controllers

Fractional order PID controllers benefit from an increasing amount of interest from the research community due to their proven advantages. The classical tuning approach for these controllers is based on specifying a certain gain crossover frequency, a phase margin and a robustness to gain variations. To tune the fractional order controllers, the modulus, phase and phase slope of the process at the imposed gain crossover frequency are required. Usually these values are obtained from a mathematical model of the process, e.g. a transfer function. In the absence of such model, an auto-tuning method that is able to estimate these values is a valuable alternative. Auto-tuning methods are among the least discussed design methods for fractional order PID controllers. This paper proposes a novel approach for the auto-tuning of fractional order controllers. The method is based on a simple experiment that is able to determine the modulus, phase and phase slope of the process required in the computation of the controller parameters. The proposed design technique is simple and efficient in ensuring the robustness of the closed loop system. Several simulation examples are presented, including the control of processes exhibiting integer and fractional order dynamics.     

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.     

Globally linearized control on diabatic continuous stirred tank reactor: a case study

This paper focuses on the promise of globally linearized control (GLC) structure in the realm of strongly nonlinear reactor system control. The proposed nonlinear control strategy is comprised of: (i) an input-output linearizing state feedback law (transformer), (ii) a state observer, and (iii) an external linear controller. The synthesis of discrete-time GLC controller for single-input single-output diabatic continuous stirred tank reactor (DCSTR) has been studied first, followed by the synthesis of feedforward/feedback controller for the same reactor having dead time in process as well as in disturbance. Subsequently, the multivariable GLC structure has been designed and then applied on multi-input multi-output DCSTR system. The simulation study shows high quality performance of the derived nonlinear controllers. The better-performed GLC in conjunction with reduced-order observer has been compared with the conventional proportional integral controller on the example reactor and superior performance has been achieved by the proposed GLC control scheme.     

Performance improvement of PI controllers through dynamic set-point weighting

Responses of high-order systems under Ziegler-Nichols tuned PI controllers (ZNPIs) are characterized by excessive oscillation with a large overshoot. Although, a fixed set-point weighting based PI controller (FSWPI) may decrease the overshoot considerably, it fails to reduce the oscillation in the set-point response. Moreover, both FSWPI and ZNPI exhibit equally poor load regulation. Keeping in mind an overall improved performance, we propose an online dynamic set-point weighting technique for ZNPIs. The dynamic set-point weighting factor (β_d) is heuristically derived from the instantaneous process trend. Performance of the proposed dynamic set-point weighting based PI controller (DSWPI) for various second- and third-order processes including a pH process shows a significant improvement during both the set-point and load disturbance responses over other methods. Stability and robustness of the proposed DSWPI are addressed. Effectiveness of the DSWPI is demonstrated through the real-time implementation on a practical DC position control system.     

A new two-degree-of-freedom level control scheme

In this paper, a two-degree-of-freedom level control scheme for delay free processes is analyzed. The nominal performance and robustness are examined. And sufficient and necessary conditions for robust stability are derived. An alternative level control scheme is developed for processes with dead time and suboptimal controllers that can produce smooth response are derived analytically based on the internal model control. The scheme has an important feature in that it is simple and transparent in design and in the corporation of performance and robust stability issues. Numerical examples are provided to compare the proposed scheme with those developed.     

Multivariable design of improved linear quadratic regulation control for MIMO industrial processes

In this study, a multivariable linear quadratic control system using a new state space structure was developed for the chamber pressure in the industrial coke furnace. Such processes typically have complex and nonlinear dynamic behavior, which causes the performance of controllers using conventional design and tuning to be poor or to require significant effort in practice. The process model is first treated into a new state space form and the implementation of linear quadratic control is designed using this new model structure. Performance in terms of regulatory/servo, disturbance rejection and measurement noise problems were all compared with the recent model predictive control strategy. Results revealed that the control system showed more robustness and improved the closed-loop process performance under model/process mismatches.     

Fuzzy Gain Scheduled Continuous Stirred Tank Reactor with Particle Swarm Optimization based PID control Minimizing Integral Square Error

In this paper, a new control scheme, the gain scheduled Particle Swarm Optimization (PSO) based PID, is proposed for a continuous stirred tank reactor (CSTR). CSTR is a highly nonlinear process that exhibits stability in certain regions and instability in some regions. Generally, PID controllers are used in these processes. Tuning of the PID controller is required to guarantee the best performance of the CSTR. The proposed scheme implements the characteristics of the PSO's global optimization to tune the PID's control parameters: k_p, k_i, k_d, to obtain the best control effect by minimizing Integral Square Error online. The PID controller parameters tuned for each region using PSO are gain scheduled using fuzzy control. Fuzzy gain-scheduling is a special form of fuzzy control that uses linguistic rules and fuzzy reasoning to determine the controller parameter transition policy for the dynamic plant subject to large changes in its operating state. Simulation results show the feasibility of using the proposed controller for the control of the dynamic nonlinear CSTR.     

Modified Smith predictor based cascade control of unstable time delay processes

An improved cascade control structure with a modified Smith predictor is proposed for controlling open-loop unstable time delay processes. The proposed structure has three controllers of which one is meant for servo response and the other two are for regulatory responses. An analytical design method is derived for the two disturbance rejection controllers by proposing the desired closed-loop complementary sensitivity functions. These two closed-loop controllers are considered in the form of proportional-integral-derivative (PID) controller cascaded with a second order lead/lag filter. The direct synthesis method is used to design the setpoint tracking controller. By virtue of the enhanced structure, the proposed control scheme decouples the servo response from the regulatory response in case of nominal systems i.e., the setpoint tracking controller and the disturbance rejection controller can be tuned independently. Internal stability of the proposed cascade structure is analyzed. Kharitonov's theorem is used for the robustness analysis. The disturbance rejection capability of the proposed scheme is superior as compared to existing methods. Examples are also included to illustrate the simplicity and usefulness of the proposed method.     

Multi-loop nonlinear control design for performance improvement of LTI systems

This paper puts forward a multi-loop nonlinear control (MLNC) strategy to overcome the limited performance of LTI controllers due to the so-called “waterbed” effect. According to “Bode's sensitivity integral”, increasing the bandwidth or additional integral gain of LTI controller to improve the low-frequency disturbance attenuation irrefutably increases the sensitivity to high-frequency disturbances or measurement noise. Hence, it is impossible to attain the best of both worlds in the case of linear controllers. Therefore, with an aim to improve the transient and steady state performance of linear controllers, in this paper, a nonlinear control framework using circle criterion method and saturation nonlinearity, which adjusts the integral gain based on the error threshold, is discussed. The global asymptotic stability (GAS) of the MLNC strategy is theoretically proved using LaSalle's invariance principle and experimentally validated using measured frequency response function (FRF). Moreover, the performance of the MLNC strategy is compared with that of the multi-loop linear control (MLLC) strategy on a benchmark magnetic levitation system for tracking application. The cumulative power spectral density (CPSD) of tracking error, which is used as the performance index to assess the overall closed loop performance, accentuates that MLNC can yield better steady state and transient performance compared to MLLC scheme.     

Semiactive nonlinear control of a building with a magnetorheological damper system

This paper proposes a linear matrix inequality (LMI)-based systematic design methodology for nonlinear control of building structures equipped with a magnetorheological (MR) damper. This approach considers stability performance as well as transient characteristics in a unified framework. First, multiple Lyapunov-based controllers are designed via LMIs such that global asymptotical stability of the building structure is guaranteed and the performance on transient responses is also satisfied. Such Lyapunov-based state feedback controllers are converted into output feedback regulators using a set of Kalman estimators. Then, these Lyapunov-based controllers and Kalman observers are integrated into a global nonlinear control system via fuzzy logic. To demonstrate the effectiveness of the proposed approach, a three-story building structure employing an MR damper is studied. The performance of the nonlinear control system is compared with that of a traditional linear optimal controller, i.e., H₂/linear quadratic Gaussian (LQG), while the uncontrolled system response is used as the baseline. It is demonstrated from comparison of the uncontrolled and semiactive controlled responses that the proposed nonlinear control system design framework is effective in reducing the vibration of a seismically excited building structure equipped with an MR damper. Furthermore, the newly developed controller is more effective in mitigating responses of the structure than the H₂/LQG controller.     

Machining force control with intelligent compensation

Force control is an effective means of improving the quality and efficiency of machining operations, so various approaches for force control have been proposed. However, due to the nonlinear, time-varying and uncertain characteristics of machining processes, it is difficult to develop force control systems that are stable and robust over the full range of operating conditions. This study proposed two control schemes to address such difficulties in the field of nonlinear force control by using a linear feedback proportional-derivate (PD) controller respectively with two different nonlinear intelligent compensators: fuzzy logic compensator (FLC) and neural network compensator (NNC). The PD controller is used to improve the transient response while maintaining the stability of the process system, and the FLC or NNC is employed to eliminate the steady-state error and compensate for the system nonlinearity (or uncertainty). The applications of the proposed schemes in machining processes show that the controllers adapt well to nonlinearity under time-varying cutting conditions in comparison to PID, PD, and FLC. The online updating of the NNC parameters through the Feedback-Error Learning can further improve the system performance.     

Design of nonlinear PID controller and nonlinear model predictive controller for a continuous stirred tank reactor

In this paper, the authors have represented the nonlinear system as a family of local linear state space models, local PID controllers have been designed on the basis of linear models, and the weighted sum of the output from the local PID controllers (Nonlinear PID controller) has been used to control the nonlinear process. Further, Nonlinear Model Predictive Controller using the family of local linear state space models (F-NMPC) has been developed. The effectiveness of the proposed control schemes has been demonstrated on a CSTR process, which exhibits dynamic nonlinearity.