Internal Model Control-Based Fractional Order Controller Design for Process Plants Satisfying Desired Gain Margin and Phase Margin

The advantages of using fractional calculus in designing control algorithms has been long discussed and demonstrated. In this paper, the theory of fractional calculus is used in combination with the Internal Model Control methodology to offer an alternative control solution for the concentration of biodegradable organic matter in the aeration tank of a waste water treatment facility. In contrast to the integer order Internal Model Controller, the fractional order controller has two tuning parameters, which allow for an increased flexibility in the tuning procedure. The fractional order Internal Model Controller is designed based on a simplified model of the process that occurs in the aeration tank. The dynamics of this controller is then analyzed using the nonlinear model of the process. Simulation results are provided including set point tracking, disturbance rejection and overall robustness.

Fractional calculus is a well-known tool that improves the closed loop performance of processes when compared to integer order approaches. The study presents a generalization of the popular Internal Model Control (IMC) strategy for fractional order processes of any complexity. The controller is based on the inverse fractional order transfer function to which a fractional order filter is added. The velocity of a scalable nanorobot operating in submersed environments is the chosen process to exemplify the proposed control strategy. The Fractional Order Internal Model Control (FOIMC) is developed for the fractional dynamics of the robot. The validity of method is proved through simulations regarding reference tracking, disturbance rejection and robustness to gain variations.

ABSTRACTThe paper proposes a novel method for the nonlinear redundantly actuated parallel robot based on force/position hybrid control structure. In order to solve the limitation of making a compromise for internal model controller, a two-DOF fractional order internal model control algorithm combining the internal model control principle and the fractional order theory is proposed for the position branch of the parallel robot redundantly actuated. This algorithm can realise the adjustment of the dynamic performance and anti-interference of 6PUS-UPU respectively. Aiming at the big force control error fractional order internal model, fuzzy control theory and the fractional order internal model controller are integrated into a new controller-fuzzy fractional order internal model(FFOIM) force control algorithm. Then Admas/Matlab simulation results demonstrate that the proposed algorithm can further reduce the driving force error of the system, and also retain the strong anti-interference of fractional order internal model controller.

In this paper, a self-tuning hierarchical controller in which a Fuzzy logic controller supervises the control actions of a conventional PID has been proposed, implemented and presented. The controller has been applied to a control study of Fluid Catalytic Cracking (FCC) unit riser temperature, and regenerator temperature respectively. Performance comparison of the proposed Fuzzy-PID controller and the conventional PID was made in simulation studies of regulatory and servo performances of the two controller types. Six performance measures: Percent overshoot (OS), settling time (ST), integral absolute error (IAE), integral square error (ISE), integral time absolute error (ITAE) and integral time square error (ITSE) were employed as the tools for performance comparison between the conventional PID and the Fuzzy-PID controller. For the tracking of riser temperature with a set point at 524oC, the performance indicators under PID control gave the following results overshoot (14.5%); settling time (40 seconds) Integral absolute error (8.246), integral square error (3.3); integral time absolute error(1762);integral time square error (43.77) while for the same indicators under Fuzzy-PID control the following values: overshoot (3.3%); settling time (40 seconds) ;Integral absolute error (8.811); integral square error (14.5); integral time absolute error(280),;integral time square error (31.11) .The results allude to the superiority of the fuzzy-PID scheme over the PID scheme in tracking the optimal set point of riser temperature. More so, for tracking the regenerator set point temperature of 746oC, comparative study of step response under the two schemes gave the following results in six performance indicators: overshoot (PID(12.6%)/Fuzzy-PID(6%)); settling time (PID(80 seconds)/Fuzzy-PID(20seconds));Integral absolute error(PID(14.29)/Fuzzy-PID(8.63)); integral square error(PID(6.713).Fuzzy-PID(4.506)); integral time absolute error(PID(2858)/Fuzzy-PID(305.9)), integral time square error (PID(77.55)/Fuzzy-PID(33.05)).Moreover, the fuzzy-PID controller also showed superior performance over the conventional PID controller in terms disturbance rejection (regulatory response) of both riser and regenerator temperature. The results from this study suggest that the application of fuzzy-PID scheme to temperature control offers good promise of improved fluid catalytic cracking unit (FCCU) operations.

Fractional-order modeling and controller design by a simplified way is the demanding research area and is gearing more and more momentum. This paper is the attempt of application of fractional-order modeling and controller design for the power plant gas turbine. The Gas Turbine is most important equipment in power, aviation and automotive industry. It converts the thermal energy of fuel into the mechanical power. Therefore, important requirement of gas turbine system is to control the flow of input fuel. The existing identified model of the gas turbine between the input fuel flow and the output speed, is of high-order and integer type, which is reduced to the simple and compact integer-order (IO) and fractional-order (FO) models using local optimization technique. The fractional-order internal model controller (FO-IMC) is designed and to show the performance efficacy it is compared with integer-order internal model controller (IO-IMC), which is also designed using the same methodology and specification. Simulation results show that FO-IMC based controller gives better performance for the set point tracking, plant uncertainty and disturbance rejection than the IO-IMC. FO-IMC controller also satisfy the robust stability condition.

Failure conditions for inverse-based multivariable controllers: internal model control structure

The design of control methods for unstable plants is somewhat complex than that of stable plants. This is because unstable process models contain one or more poles lying on the right of the s-plane which yields unbounded closed-loop response. Further, the presence of the dead-time induces more complexity as it decreases the gain and phase margins which in turn deteriorates the closed-loop performance. The design of control strategies become more challenging for plants of unstable nature with positive zeros because they exhibit a phenomenon called inverse response. This paper suggests a method to design a double-loop scheme for unstable plants with/without inverse response. Accordingly, a proportional-derivative (PD)/proportional (P) controllers are used in the inner-loop for stabilizing the plant. A fractional order internal model controller (FOIMC) scheme is used to obtain the outer-loop controller using the stabilized plant model. The P/PD controller settings have been obtained by using the Routh-stability criteria and the maximum sensitivity approach. Procedure for selecting the outer-loop tuning parameter and fractional order is also given. Linear and nonlinear models of unstable plants including bioreactors and isothermal chemical reactors are used to demonstrate the merits of the suggested strategy. Robustness of the design and effect of measurement noise are also studied. Integrated absolute/squared error measures are also calculated. The suggested design is found to be more effective in controlling unstable processes than some reported works.

In this paper, an H2 optimal input load disturbance rejection (ILDR) controller for three typical integrating processes with dead time is proposed based on the Internal Model Control (IMC) structure. Different from other load disturbance rejection methods, the proposed design method is to minimizing the ILDR criterion for integrating processes with dead time. Compared with previous advanced control methods, the proposed design method has three main advantages. First, the proposed design method can optimally suppress the input load disturbance. Second, the design procedure is simple. No weight functions need to be chosen in the design method. The designed controller is given in an analytical form. Third, the robustness stability can be achieved by monotonously tuning the parameters given in the designed controller. Numerical simulations are given to illustrate the effectiveness of the proposed method.

In this paper, two fractional order controllers are employed to control the angular velocity of a permanent magnet DC motor. A fractional order PI controller with isodamping property is appropriately designed to achieve the desired phase margin and gain crossover frequency requirements. Moreover, by selecting a fractional order filter in internal model control (IMC) structure, an IMC-based fractional order controller is designed. These two fractional order controllers are utilised for velocity control of a laboratory DC servomechanism system. The experimental results demonstrate the capability of these fractional order controllers in the desired angular velocity tracking and load disturbance rejection.

In this paper we have introduced as a model in the adaptive Internal Model Control (IMC) structure a fractional order system to obtain a fractional adaptive IMC scheme. We have shown that this adaptive control scheme always provides theoretical guarantees of stability when a stable fractional order transfer function is used as an IMC parameter and that the use of this fractional IMC parameter can improve the performances of the control system along with its robustness against noises. A comparative simulation example is given to illustrate the efficiency of the proposed fractional order adaptive control scheme. Copyright © 2010 John Wiley & Sons, Ltd.

This work presents an analysis, design, and comparison of the PI (Proportional and Integral) controller and control schemes PI linear and nonlinear controllers reset-based. The parameters of these control schemes have been set by trial and error to finally be tested in a nonlinear process with variable dead time. Controller performance is measured using integral square error (ISE), integral time square error (ITSE), total variations of control efforts (TVU), maximum overshoot (\(M_{p}\)) and settling time \(\left( {t_{s} } \right)\). The results show that reset control systems overcome fundamental limitations coming from linear control systems.

Combustion control system is a typical system with large time delays and complex couplings. The traditional PID control approach is a classical method often used. However, control performances of PID are unsatisfied such as overshoot and switch time. Internal model control (IMC) is a new control strategy with controller design based on process mathematical model. IMC is widely applied in combustion system because of its outstanding control performance and the simplicity of design. In this paper, an IMC structure is established firstly. Then, adaptive weight particle swarm optimization (AWPSO) algorithm is used in optimizing parameters of IMC and PID with the control evaluation index based on integral of time-weighted absolute value of the error (ITAE). Finally, these adjusted parameters are applied in process object. Result shows that the proposed approach can achieve better control performance than PID.

In paper industries, Multiple Stage Evaporator (MSE) is used to concentrate black liquor. Due to the energy intensive nature of MSE, the global energy scenario stresses on optimizing its energy efficiency. Moreover, the necessity of a tight control of product quality demands superior understanding of system dynamics for controller design. This paper presents a robust fractional‐order Proportional–Integral–Derivative (FOPID) controller for concentration control of black liquor in Heptad's effect MSE. First, the steady‐state unknown process parameters are estimated by solving the nonlinear steady‐state model. Thereafter, these optimal process parameters are utilized to simulate the nonlinear dynamic model to obtain the transfer functions. By using these transfer functions, the FOPID controller is designed whose parameters are tuned via Water Cycle Algorithm (WCA). The competence of WCA toward controller tuning is validated by comparing with other optimization techniques (Genetic Algorithm [GA], Simulated Annealing [SA], Particle Swarm Optimization [PSO], and Krill Herd [KH]). Moreover, the performance of the proposed FOPID controller in concentration control, set‐point tracking, and noise suppression is validated by comparing with conventional PID, two‐degree of freedom‐PID (2‐DOF‐PID), and Internal Model Control (IMC) controllers. The results demonstrate that FOPID controller reduces the Integral Square Error (ISE) by 91.05%, 89.81%, and 78.84%, respectively, with respect to PID, 2‐DOF‐PID, and IMC. Also, the proposed FOPID controller improves the system transience with high robustness.

This article proposes an enhanced control of integrating cascade processes. The importance of the scheme shows by controlling a double integrating process with time delay under significant parametric uncertainties and load disturbances. A novel design is proposed based on the Smith predictor principle and uses a fractional-order internal model controller in the outer loop. The required fractional-order tuning parameter follows the desired gain and phase margins. At the same time, another tuning parameter, such as the fractional filter’s time constant, is calculated from the desired performance constraint. Numerical analysis and comparison are performed to showcase the feature of the hybrid structure. The simulation results show that the fractional-order internal model controller–based scheme provides enhanced tracking and faster regulation capabilities and works well under nominal and parameter uncertainty conditions.

This paper takes up the challenge of modelling a complex nonlinear distillation column type-A and designs four optimal controllers for the same. The nonlinear plant is first linearized into a linear higher-order model. Thereafter, it is reduced into a lower-order model. Subsequently, the controllers are designed for the lower-order linear model. The controllers are designed by reducing the error cost functions, namely Integral Square Error (ISE), Integral Absolute Error (IAE) and Integral Time Absolute Error (ITAE). The process of optimization is done heuristically using the Genetic Algorithm method of tuning. The four controllers designed are Proportional Integral Derivative, Fractional-order Proportional Integral Derivative, Tilt Integral Derivative and Fractional-order Internal Model Control. A thorough comparison is made between the three designed controllers, first on the Single Input Single Output (SISO), then to the reduced-order linear model and finally to the main plant. The FO-IMC controller is shown as an exhibition controller designed using GA to demonstrate the novelty of its kind. It has also been compared, but the results show poor performances as it has not been tuned with the same parameters as the rest.