Generalized Predictive Control Algorithms with Guaranteed Frozen-Time Stability and Bounded Tracking Error

Generalized predictive controller (GPC) has robust performance when faced to control non-minimum phase and open-loop unstable processes. GPC has been originally developed with linear predictor models which leads to a formulation that can be solved analytically. If a nonlinear model is used then nonlinear optimization and nonlinear modeling techniques are necessary. This paper presents a new method of multivariable GPC design for nonlinear systems. The proposed GPC design incorporates the neural network model based on radial basis function neural network and optimization methodology of cost function by Lamarckian hybrid method using evolutionary programming and Nelder-Mead’s simplex algorithm. Steps of the control law implementation and intelligent procedure are discussed. Simulation results on a nonlinear MIMO (multi-input multi-output) system are presented to show the effectiveness of the neuro-evolutionary GPC method. The new GPC design is applicable for improve the approximation of nonlinear systems with unknown interactor matrix using neural network model and an efficient control law optimization task by simplex-evolutionary hybrid methodology.

The paper considers the discrete time-invariant linear systems affected by input disturbances and construct the explicit description of the constrained generalized predictive control (GPC) law taking in account the constraints existence from the design stage. The explicit formulation of the predictive controllers gives a useful insight on the closed loop capabilities. The GPC is a special case of model predictive control (MPC) whose explicit formulation is known to be a piecewise affine function of state. As novelty the present work shows that this piecewise linear dependence on the context parameters can be found by exploiting the fact that the optimum of a min-max multiparametric program is placed on the vertices of a parameterized polyhedron. As these parameterized vertices have specific validity domains, the control law is expressed as a piecewise linear function of the current system parameters. The resulting GPC law is formulated in terms of a look-up table with two-degree of freedom polynomials in the backward shift operator (also known as the RST formulation)

The multivariable generalized predictive control (GPC) law is derived in a stochastic setting which closely follows the usual polynomial solution of the LQG problem. The assumptions which must be made to ensure a GPC type of control law emerges are clear from the analysis which provides insights into the relationship between LQG and GPC control. The form of the single degree-of-freedom control law obtained closely parallels the GPC solution but ensures closed loop stability. The solution of the multi-step cost-function problem is shown to include an LQG controller which must be implemented for the actual feedback system and a set of controllers which are needed to calculate the predicted future controls and outputs. This is of importance when constraints are to be applied based on the future predicted signals. The alternative method outlined, referred to as the vector-matrix solution, does not require this sequence of controllers to be found and it is very similar to the GPC form of solution. However, the LQG stability properties for the feedback loop are still retained.

Batch to batch temperature control of a semi-batch chemical reactor with heating/cooling system was discussed in this study. Without extensive modeling investigations, a two-dimensional (2D) general predictive iterative learning control (2D-MGPILC) strategy based on the multi-model with time-varying weights was introduced for optimizing the tracking performance of desired temperature profile. This strategy was modeled based on an iterative learning control (ILC) algorithm for a 2D system and designed in the generalized predictive control (GPC) framework. Firstly, a multi-model structure with time-varying weights was developed to describe the complex operation of a general semi-batch reactor. Secondly, the 2D-MGPILC algorithm was proposed to optimize simultaneously the dynamic performance along the time and batch axes. Finally, simulation for the controller design of a semi-batch reactor with multiple reactions was involved to demonstrate that the satisfactory performance could be achieved despite of the repetitive or non-repetitive disturbances.

Standard generalised predictive control (GPC) and constrained receding-horizon predictive control (CRHPC) stability results have traditionally been derived in the state-space, using the properties of the solution of the Riccati equation associated with the control law. Unfortunately this type of study does not readily extend to constrained control laws which are nonlinear. By invoking the monotonicity, with respect to time, of the receding-horizon cost function, however, an extension of the stability properties of a subclass of GPC, termed GPC∞, and of CRHPC may be obtained, when inequality constraints are added to the control objective. The problem of feasibility (i.e. the compatibility of the constraints) is also becoming a major area of interest in predictive control. In GPC∞ and CRHPC, the feasibility problem is compounded by the use of end-point equality constraints on the tracking error. A new concept called setpoint conditioning is introduced here, which may be used to resolve the incompatibilities between the inequality and the end-point equality constraints, without compromising stability.

ACTIVE CONTROL OF A STRUCTURE WITH SLOSHING PHENOMENA

In the complex heating systems, higher order, large inertia, large delay and uncertainty typically exist. This work introduces generalized predictive PID control algorithm to adjust the system. The purpose of the control algorithm is to achieve a steady state in a shorter time. On the basis of analyzing PID control algorithm and Generalized Predictive Control (GPC), configuring a given performance function index control-weighted sequences to GPC control. Derived form of generalized predictive control algorithm with PID. The Matlab simulation shows that using generalized predictive PID control algorithm can produce better results in shorter time than simple using PID or GPC in the heating system.

Generalized predictive control (GPC) is nowadays, widely ,spread in control theory as well as in the industrial world. Generalized predictive control (GPC) belong to this family has been demonstrated as a powerful controlling process plants, In this work a polynomial approach of generalized predictive control is proposed whose aim to find optimal values for the tuning control and application of predictive control with polynomial form RST and application of induction motor and developed prediction optimal equation with cost function and resolved of the Diophantine equations this application is reserved in our work for the induction motor with example of a dynamic system and non linear multivariable with load torque.

The paper discusses state-space generalized predictive control and the preview control algorithms. The optimization procedure used in the derivation of predictive control algorithms is considered. The performance index associated with the generalized predictive controller (GPC) is examined and compared with the linear quadratic (LQ) optimal control formulation used in preview control. A new performance index and consequently a new algorithm is proposed dynamic performance predictive controller (DPPC) that combines the features of both GPC and preview controller. This algorithm minimizes the performance index through a dynamic optimization. A simple example illustrates the features of the three algorithms and prompts a discussion on what is actually minimized in predictive control. The DPPC algorithm, derived in this paper, provides for a minimum of the predictive performance index. The differences and similarities between the preview control and the predictive control have been discussed and optimization approach of predictive control has been explained.

This paper details a voltage control strategy based on Generalized Predictive Control (GPC) applied to a single-phase T-type neutral point clamped voltage source inverter in stand-alone operation mode. A performance comparison between the GPC and a Proportional-Integral (PI) controller is presented to highlight the improved performance of GPC under different load scenarios. The main results show that the GPC can achieve longer prediction horizons than other controllers based on model predictive control. Furthermore, in contrast to the PI controller, the GPC responds to load changes as disturbances. Finally, GPC can operate efficiently without an online optimization method nor recursive system identification method.

In this paper, a new GPC (Generalized Predictive Control) algorithm which always guarantees the stability of a closed loop system is proposed. The feedback part of the presented predictive control is shown to be equivalent to that of RHTC (Receding Horizon Tracking Control) with a terminal state constraint. The stability of the presented control law is proved and the simplest form of the stabilizing GPC is presented, which can be widely applied to various areas. The proposed control is different from Clarke's GPC in the sense that the latter guarantees stability for an indefinitely large horizon, while the former guarantees the stability for any horizon greater than the system order.

Some important applications require control systems capable of tracking high-degree polynomial references. However, polynomial reference tracking is difficult because the controller must have a fast response to track variable references. Generalized Predictive Control (GPC), used in industrial applications, has a fast response. However, up to now, GPC approaches in the literature are not designed for high-degree polynomial reference tracking. For that reason, this brief proposes a GPC system for the tracking of polynomial references of any degree. The high-order backward difference operator was used to develop an augmented prediction model designed to have an arbitrary number of embedded integrators. Thus, according to the internal model principle, the proposed predictive controller can track polynomial references of any degree. An optimization technique is used to define future control actions, while the control law is defined through the receding horizon principle. Simulation and experimental results prove that the proposed controller performs better than other approaches described in the literature.

This study presents a hybrid method based on generalised predictive control (GPC) and a proposed new hybrid shuffled frog leaping (NHSFL) algorithm to design stabilising signals to damp the multi-machine power system low-frequency oscillations. A linearised model predictive controller based on GPC is designed in which the proposed NHSFL algorithm is employed for optimising the cost function of the GPC. The numerical results are presented on a two-area four-machine and a five-area 16-machine power system. The effectiveness of the designed controllers is shown by considering various operating conditions. The proposed approach, which is called as GPC-NHSFL, is compared with a classical-based method, GPC algorithm and GPC-based standard SFL algorithm (GPC-SFL). The simulation results show the superiority and capability of the proposed approach to enhance power systems damping.

A relatively simple approach to non-linear predictive generalised minimum variance (NPGMV) control is introduced for non-linear discrete-time multivariable systems. The system is represented by a combination of a stable non-linear subsystem where no structure is assumed and a linear subsystem that may be unstable and modelled in polynomial matrix form. The multi-step predictive control cost index to be minimised involves both weighted error and control signal costing terms. The NPGMV control law involves an assumption on the choice of cost-function weights to ensure the existence of a stable non-linear closed-loop operator. A valuable feature of the control law is that in the asymptotic case, where the plant is linear, the controller reduces to a polynomial matrix version of the well known generalised predictive control (GPC) controller. In the limiting case when the plant is non-linear and the cost-function is single step the controller becomes equal to the polynomial matrix version of the so-called non-linear generalised minimum variance controller. The controller can be implemented in a form related to a non-linear version of the Smith predictor but unlike this compensator a stabilising control law can be obtained for open-loop unstable processes.

Usually speed and position of a permanent magnet brushless direct current motor (PMBLDCM) rotor is controlled in a conventional cascade structure. The inner current control loop runs at a larger bandwidth than the outer speed control loop to achieve an effective cascade control. This paper proposes a multirate based general predictive control (GPC) law performed for the conventional cascaded PI-PI scheme. Both speed and torque tracking objectives are achieved in matched and mismatched parameter case. The measured and unmeasured disturbances can be effectively rejected and the motor can run at desired speed at constant load. In addition, non-minimum phase characteristics and system constrains can effectively be handled by proposed GPC algorithm. The simulation results are provided to show that the proposed GPC strategy results in better performance than that of the conventional well tuned cascade PI- PI control strategy. The proposed controller has also been implemented to control the speed of a PMBLDCM and the results show an improvement over conventional scheme.