Adaptive Internal Model Control with fractional order parameter

This paper considers the design and analysis of a discrete-time H2 optimal robust adaptive controller based on the internal model control structure. The certainty equivalence principle of adaptive control is used to combine a discrete-time robust adaptive law with a discrete-time H2 internal model controller to obtain a discrete-time adaptive H2 internal model control scheme with provable guarantees of stability and robustness. The approach used parallels the earlier results obtained for the continuous-time case. Nevertheless, there are some differences which, together with the widespread use of digital computers for controls applications, justifies a separate exposition. Copyright © 2001 John Wiley & Sons, Ltd.

Considers the design and analysis of a robust adaptive model algorithmic controller based on the internal model control structure. The certainty equivalence principle of adaptive control is used to combine a discrete-time robust adaptive law with a model algorithmic internal model controller to obtain an adaptive model algorithmic internal model control scheme with provable guarantees of stability and robustness. The approach used parallels the earlier results obtained for adaptive internal model control. Nevertheless, there are some important differences which, together with the widespread interest in model algorithmic control, justifies a separate exposition.

This paper adopts the adaptive neural internal model control strategy to design a control system for complex and uncertain process with delay. Because of the shortage of the classic internal model control system the performance of the control system will slip back if there exist large errors between the real plant and the model, an adaptive mechanism based on single neuron which can tune the parameters of the internal model and that of controller in the control system on line is designed. The multimodel approach is exploited to represent the direct model by a model basis made up of five linear models, and to construct a controller trained by the corresponding reverse models. The simulation results shows that the adaptive internal model control system designed in this paper has good performance of overcoming deviations of model parameters.

Adaptive internal model control: H2 optimization for stable plants

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

This paper develops a fractional order adaptive fuzzy backstepping control scheme for an incommensurate fractional order uncertain nonlinear multiple-input multiple-output (MIMO) systems with external disturbance and input saturation. Combined with the adaptive and backstepping technique, the fuzzy logic system is used to approximate the unknown nonlinear uncertainties in each step of the backstepping, and the incommensurate fractional order parameters update laws for fuzzy logic system, unknown parameters as well as the external disturbances are proposed in the controller to compensate the unknown nonlinearities, unknown parameters and disturbances. With the aids of the frequency distributed model of fractional integrator for the fractional order systems in the procedure of controller design, the stability of the closed loop system is established. At last, two simulation examples are demonstrated to verify the robustness and effectiveness of the proposed controller.

This chapter considers the design of a fractional order (FO) internal model controller (IMC) for first order plus time delay (FOPTD) processes to satisfy a given set of desired stability margins in terms of gain margin \((A_m)\) and phase margin \((\phi _{m})\). The highlight of the design is the choice of a fractional order (FO) filter in the IMC structure which has two parameters (\(\lambda \) and \(\beta \)) to tune as compared to only one tuning parameter (\(\lambda \)) for traditionally used integer order (IO) filter. These parameters are evaluated for the controller so that \(A_m\) and \(\phi _{m}\) can be chosen independently. This is the first time when the IMC controller is designed without any approximation of the delay in the IMC which has always been approximated using Taylor’s series approximation or Pade approximation. Simulation studies are carried out for three different FOPTD processes and the proposed methodology is validated experimentally on a DC servo-motor system. The results are compared with different well-known IMC techniques and the performance of controllers is evaluated in terms of rise time (\(T_r\)), settling time (\(T_s\)), maximum overshoot (\(\% M_p\)) and integral square error (ISE).

Adaptive internal model control is analyzed for a single-input-single-output nonlinear system represented by the Hammerstein model wherein the nonlinearity is an odd order polynomial. The recursive least-squares method of Chang and Luus (1971) is used for parameter estimation. To obtain a stable approximation to the inverse of the process model for use as the controller, Vogel-Edgar's method (1980) for linear system is employed. Simulation results have shown that the adaptive internal model control (IMC) performs well even with non-minimum phase Hammerstein systems in the presence of unmeasured load changes and dead-time variations. The performance of nonlinear IMC is found to be superior to that of linear IMC.

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, we introduce a direct fractional order adaptive control design based on model reference adaptive control (MRAC) structure for a class of commensurate fractional order linear systems with an arbitrary relative degree, and whose parameters are unknown. By generalising the application of standard direct MRAC strategy to plants described by fractional order models, we develop a fractional adaptive control scheme (FOMRAC) based on the output feedback. We also define an adaptation control law ensuring the stability of the closed-loop system and the good tracking of the reference trajectory. The asymptotic stability of the fractional order control system is proven using an extension of the Lyapunov theorem. Simulation results show the effectiveness of the proposed control method even for plants with model parametric variations and additive noises.

The application of internal model control (IMC) for process control has received much attention during the past decade. In this paper, the application of IMC for robot control is investigated. Although the IMC approach is shown to be more robust compared to conventional robot control approaches, such as the computed-torque approach, its performance degrades in the presence of large modelling uncertainties and external disturbances. In this paper, a neuro-based adaptive internal model control scheme is proposed. Within the framework of this control structure, a backpropagation neural network algorithm is incorporated into a fired structure internal model controller for robot control. Simulation results, based on a two-link robot confirm the effectiveness of the proposed control algorithm even in the presence of large modelling uncertainties and external disturbances.

This paper proposes a new adaptive fuzzy nonlinear control strategy that allows designers to systematically construct fuzzy control. The control strategy proposes the use of fuzzy logic systems within a well understood control structure that is called nonlinear internal model control (NIMC) structure. The attractive feature of the NIMC structure is that the relations between some designed parameters and the performance of the control system can be found explicitly. Thus, this control structure allows designers to systematically construct fuzzy control. In addition to using fuzzy logic systems within a well understood control structure, an adaptive control strategy is also proposed in this paper. The control strategy is applied to control the inverted pendulum model. The results show that the proposed strategy can maintain the system stability and give a good control performance.

Several processes are nonlinear and operate under input constraints. Their effective control requires model-based techniques whose performance is often affected by modelling uncertainties. The paper addresses the control of single-input single-output nonlinear systems with input constraints in the presence of modelling errors. A nonlinear internal model control based on input output linearisation is designed, and an internal model control with antiwindup which removes the nonlinear mismatch due to input constraints is given. An adaptive internal model control with anti-windup to account for parameter uncertainty and an augmented internal model control with anti-windup to attenuate the effect of modelling errors, are proposed and analysed theoretically. Simulation results on temperature control of a continuous stirred tank reactor demonstrate the benefits of the proposed anti-windup schemes.

In this paper we focus on the adaptive control of structural acoustics using intelligent structures with embedded piezoelectric (PZT) patches and low cost digital signal processor systems. After a discussion on the adaptive feedforward control scheme, a hybrid adaptive control scheme is proposed, which takes advantage of both feedback control and adaptive feedforward control. The two schemes are realized on a low-cost, small volume, convenient and universal digital signal processing (DSP) board. A carbon fiber reinforced polymer plate with two embedded PZT patches is developed and used in two experiments. The first experiment is adaptive interior noise control using the intelligent plate, in which the adaptive feedforward control scheme is employed. Obvious noise reduction is obtained for constant frequency, swept frequency and varying amplitude harmonic disturbances. The second experiment is adaptive control of sound-induced vibration of the plate, where two embedded PZT patches are used as an actuator and a sensor, respectively, and the hybrid adaptive controller is applied. The full vibration reduction for various harmonic excitations is obtained, verifying the advantage of the hybrid adaptive control. It is demonstrated that active control of structural acoustics can be efficiently achieved by employing intelligent structures, advanced adaptive control schemes and the low-cost DSP board.

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.