Neural network controller for a multivariable model of submarine dynamics

Recently, there have been many attempts to use neural networks as a feedback controller. However, most of the reported cases seek to control Single-Input Single-Output (SISO) systems using some sort of adaptive strategy. In this paper, we demonstrate that neural networks can be used for the control of complex multivariable, rather than simply SISO, systems. A modified direct control scheme using a neural network architecture is used with backpropagation as the adaptive algorithm. The proposed algorithm is designed for Multi-Input Multi-Output (MIMO) systems, and is similar to that proposed by Saerens and Soquet [1] and Goldenthal and Farrell [2] for (SISO) systems, and differs only in the form of the gradient approximation. As an example of the application of this approach, we investigate the control of the dynamics of a submarine vehicle with four inputs and four outputs, in which the differential stern, bow and rudder control surfaces are dynamically coordinated to cause the submarine to follow commanded changes in roll, yaw rate, depth rate and pitch attitude. Results obtained using this scheme are compared with those obtained using optimal linear quadratic control.     

An inverse-model approach to multivariable norm optimal iterative learning control with auxiliary optimisation

Motivated by the commonly encountered problem in which tracking is only required at selected intermediate points within the time interval, a general optimisation-based iterative learning control (ILC) algorithm is derived that ensures convergence of tracking errors to zero whilst simultaneously minimising a specified quadratic objective function of the input signals and chosen auxiliary (state) variables. In practice, the proposed solutions enable a repeated tracking task to be accurately completed whilst simultaneously reducing undesirable effects such as payload spillage, vibration tendencies and actuator wear. The theory is developed using the well-known norm optimal ILC (NOILC) framework, using general linear, functional operators between real Hilbert spaces. Solutions are derived using feedforward action, convergence is proved and robustness bounds are presented using both norm bounds and positivity conditions. Algorithms are specified for both continuous and discrete-time state-space representations, with the latter including application to multi-rate sampled systems. Experimental results using a robotic manipulator confirm the practical utility of the algorithms and the closeness with which observed results match theoretical predictions.     

Constrained multivariable control of a distillation column using a simplified model predictive control algorithm

Distillation columns are important process units in petroleum refining and need to be maintained close to optimum operating conditions because of economic incentives. Model predictive control has been used for control of these units. However, the constrained optimization problem involved in the control has generally been solved in practice in a piece-meal fashion. To solve the problem without decomposition, the use of a linear programming (LP) formulation using a simplified model predictive control algorithm has been suggested in the literature. In this paper, the LP approach is applied for control of an industrial distillation column. The approach involved a very small size optimization problem and required very modest computational resources. The control algorithm eliminated the large cycling in the product composition that was present using SISO controllers. This resulted in a 2.5% increase in production rate, a 0.5% increase in product recovery, and a significant increase in profit.     

Interaction bounds in multivariable control systems

Time-domain limitations due to right half-plane zeros and poles in linear multivariable control systems are studied. Lower bounds on the interaction are derived. They show not only how the location of zeros and poles are critical in multivariable systems, but also how the zero and pole directions influence the performance. The results are illustrated on the quadruple-tank process, which is a new multivariable laboratory process.     

Scenario-integrated on-line optimisation of batch reactors

A key problem area in recipe design for exothermic batch reactors is the possible occurrence of failure situations, in particular malfunctions of the cooling system. Scenario-integrated optimization has recently been developed in order to tackle these problems rigorously. This paper extends the ideas presented earlier to the on-line solution of scenario-integrated optimization problems. Due to high computational requirements, the problems are formulated only for special cases and on short time horizons. It is shown that the resulting MPC scheme can indeed optimize batch reactor recipes while simultaneously guaranteeing the enforcement of constraints, both for nominal operation as well as for failure situations. A literature example and an industrial polymerization reactor are treated to illustrate these properties.     

Observer-based multivariable flatness control of a cold rolling mill

The synthesis methodology developed by Kimura (1985) based on the design theory of output regulators essentially due to Wonham (1974) has been applied successfully to the flatness control system for a 6-high cold rolling mill. The system has the following remarkable features.

1. (1) The structure of the controller is simple. This makes it easy to tune the control system.

2. (2) The controller copes well with the detection time delay, and thus high performance is obtained even at a low rolling speed.

3. (3) The flatness error caused by the rolling force variation in mill acceleration and deceleration time would be kept to a minimum by the function to adjust roll bending force using the signal of rolling force.

Neural network methods for the modeling and control of welding processes

While welding processes are of great importance in manufacturing, their modeling and control is still subject of research. The highly nonlinear, strongly coupled, and multivariable nature of these processes renders the use of analytical tools practically impossible. In this article a novel approach is presented which employs networks of simple nonlinear units: a neural network. A widely used welding process, the Gas Tungsten Arc Welding is presented and the problem of its modeling and control is exhibited. A very brief introduction to neural networks is followed by presenting the experimental results for modeling the static and dynamic behavior of the process, as well as some practical recommendations regarding the use of the neural network techniques for controlling these processes.     

Semi-intrusive multivariable model invalidation

This paper introduces a mechanism for testing multivariable models employed by model-based controllers. Although external excitation is not necessary, the data collection includes a stage where the controller is switched to open-loop operation (manual mode). The main idea is to measure a certain “distance” between the closed-loop and the open-loop signals, and then trigger a flag if this “distance” is larger than a threshold level. Moreover, a provision is made for accommodating model uncertainty. Since no hard bounds are assumed with respect to the noise amplitude, the model invalidation mechanism works in a probabilistic framework.     

Neural network compensation control for mechanical systems with disturbances

Two novel compensation schemes based on accelerometer measurements to attenuate the effect of external vibrations on mechanical systems are proposed in this paper. The first compensation algorithm exploits the neural network as the feedback-feedforward compensator whereas the second is the neural network feedforward compensator. Each compensation strategy includes a feedback controller and a neural network compensator with the help of a sensor to detect external vibrations. The feedback controller is employed to guarantee the stability of the mechanical systems, while the neural network is used to provide the required compensation input for trajectory tracking. Dynamics knowledge of the plant, disturbances and the sensor is not required. The stability of the proposed schemes is analyzed by the Lyapunov criterion. Simulation results show that the proposed controllers perform well for a hard disk drive system and a two-link manipulator.     

Multivariable norm optimal iterative learning control with auxiliary optimisation

The paper describes a substantial extension of norm optimal iterative learning control (NOILC) that permits tracking of a class of finite dimensional reference signals whilst simultaneously converging to the solution of a constrained quadratic optimisation problem. The theory is presented in a general functional analytical framework using operators between chosen real Hilbert spaces. This is applied to solve problems in continuous time where tracking is only required at selected intermediate points of the time interval but, simultaneously, the solution is required to minimise a specified quadratic objective function of the input signals and chosen auxiliary (state) variables. Applications to the discrete time case, including the case of multi-rate sampling, are also summarised. The algorithms are motivated by practical need and provide a methodology for reducing undesirable effects such as payload spillage, vibration tendencies and actuator wear whilst maintaining the desired tracking accuracy necessary for task completion. Solutions in terms of NOILC methodologies involving both feedforward and feedback components offer the possibilities of greater robustness than purely feedforward actions. Results describing the inherent robustness of the feedforward implementation are presented and the work is illustrated by experimental results from a robotic manipulator.     

Operational predictive optimal control of Barcelona water transport network

This paper describes the application of model-based predictive control (MPC) techniques to the supervisory flow management in large-scale drinking water networks including a telemetry/telecontrol system. MPC is used to generate flow control strategies (set-points for the regulatory controllers) from the sources to the consumer areas to meet future demands, optimizing performance indexes associated to operational goals such as economic cost, safety storage volumes in the network and smoothness of the flow control actions. The designed management strategies are applied to a model of a real case study: the drinking water transport network of Barcelona (Spain).     

Adaptive dynamic surface control for linear multivariable systems

In this paper, an output-feedback adaptive control is presented for linear time-invariant multivariable plants. By using the dynamic surface control technique, it is shown that the explosion of complexity problem in multivariable backstepping design can be eliminated. The proposed scheme has the following features: (1) The L_∞ performance of the system’s tracking error can be guaranteed, (2) it has least number of updated parameters in comparison with other multivariable adaptive schemes, and (3) the adaptive law is necessary only at the first design step, which significantly reduces the design procedure. Simulation results are presented to demonstrate the effectiveness of the proposed scheme.     

对角CARIMA模型多变量自适应约束广义预测控制

为了简化约束存在时多变量广义预测控制算法的设计与实现,依据对角CARIMA模型的结构特点,将多输入多输出对象的参数辨识和模型预报问题转化为一系列多输入单输出子对象的参数辨识和模型预报问题.推导了输入输出的约束形式及优化求解过程.简化了多变量对象的参数辨识、模型预报、目标函数和约束条件系数矩阵的计算.在由DCS控制的非线性液位装置上的对比实验结果表明了该方法的有效性.     

Economic optimization using model predictive control with a terminal cost

In the standard model predictive control implementation, first a steady-state optimization yields the equilibrium point with minimal economic cost. Then, the deviation from the computed best steady state is chosen as the stage cost for the dynamic regulation problem. The computed best equilibrium point may not be the global minimum of the economic cost, and hence, choosing the economic cost as the stage cost for the dynamic regulation problem, rather than the deviation from the best steady state, offers potential for improving the economic performance of the system. It has been previously shown that the existing framework for MPC stability analysis, which addresses to the standard class of problems with a regulation objective, does not extend to economic MPC. Previous work on economic MPC developed new tools for stability analysis and identified sufficient conditions for asymptotic stability. These tools were developed for the terminal constraint MPC formulation, in which the system is stabilized by forcing the state to the best equilibrium point at the end of the horizon. In this work, we relax this constraint by imposing a region constraint on the terminal state instead of a point constraint, and adding a penalty on the terminal state to the regulator cost. We extend the stability analysis tools, developed for terminal constraint economic MPC, to the proposed formulation and establish that strict dissipativity is sufficient for guaranteeing asymptotic stability of the closed-loop system. We also show that the average closed-loop performance outperforms the best steady-state performance. For implementing the proposed formulation, a rigorous analysis for computing the appropriate terminal penalty and the terminal region is presented. A further extension, in which the terminal constraint is completely removed by modifying the regulator cost function, is also presented along with its stability analysis. Finally, an illustrative example is presented to demonstrate the differences between the terminal constraint and the proposed terminal penalty formulation.     

A reliable multi-objective control strategy for batch processes based on bootstrap aggregated neural network models

This paper presents a reliable multi-objective optimal control method for batch processes based on bootstrap aggregated neural networks. In order to overcome the difficulty in developing detailed mechanistic models, bootstrap aggregated neural networks are used to model batch processes. Apart from being able to offer enhanced model prediction accuracy, bootstrap aggregated neural networks can also provide prediction confidence bounds indicating the reliability of the corresponding model predictions. In addition to the process operation objectives, the reliability of model prediction is incorporated in multi-objective optimisation in order to improve the reliability of the obtained optimal control policy. The standard error of the individual neural network predictions is taken as the indication of model prediction reliability. The additional objective of enhancing model prediction reliability forces the calculated optimal control policies to be within the regions where the model predictions are reliable. By such a means, the resulting control policies are reliable. The proposed method is demonstrated on a simulated fed-batch reactor and a simulated batch polymerisation process. It is shown that by incorporating model prediction reliability in the optimisation criteria, reliable control policy is obtained.     

Realization issues,tuning, and testing of a distributed predictive control algorithm

A non-iterative, non-cooperative distributed state-feedback control algorithm based on neighbor-to-neighbor communication, named distributed predictive control (DPC), has been recently proposed in the literature for constrained linear discrete-time systems, see  [15], [14], [2], [4]. The theoretical properties of DPC, such as convergence and stability, its extensions to the output feedback and tracking problems, and applications to simulated plants have been investigated in these papers. However, for a practical use of DPC some realization issues are still open, such as the automatic selection of some tuning parameters, the initialization of the algorithm, or its response to unexpected disturbances which could lead to the lack of the recursive feasibility, a fundamental property for any model predictive control (MPC) technique.This paper presents novel solutions to all these issues, with the goal to make DPC attractive for industrial and practical applications. Three realistic simulation examples are also discussed to evaluate the proposed numerical algorithms and to compare the performances of DPC to those of a standard centralized MPC algorithm.     

A global piecewise smooth Newton method for fast large-scale model predictive control

In this paper, the strictly convex quadratic program (QP) arising in model predictive control (MPC) for constrained linear systems is reformulated as a system of piecewise affine equations. A regularized piecewise smooth Newton method with exact line search on a convex, differentiable, piecewise-quadratic merit function is proposed for the solution of the reformulated problem. The algorithm has considerable merits when applied to MPC over standard active set or interior point algorithms. Its performance is tested and compared against state-of-the-art QP solvers on a series of benchmark problems. The proposed algorithm is orders of magnitudes faster, especially for large-scale problems and long horizons. For example, for the challenging crude distillation unit model of Pannocchia, Rawlings, and Wright (2007) with 252 states, 32 inputs, and 90 outputs, the average running time of the proposed approach is 1.57 ms.     

Stability analysis of a multi-model predictive control algorithm with application to control of chemical reactors

We study a stabilizing multi-model predictive control strategy for controlling nonlinear process at different operating conditions. The control algorithm is a receding horizon scheme with a quasi-infinite horizon objective function that has finite and infinite horizon cost components. The finite horizon cost consists of free input variables that direct the system towards a terminal region which contains the desired operating point. The infinite horizon cost has an upper bound and steers the system to the desired operating point. The system is represented by a sequence of piecewise linear models. Based on the condition of the system states, the sequence of piecewise linear models is updated and the controller’s objective function switches form quasi-infinite to infinite horizon objective function. This results in a hybrid control structure. A recent approach in the analysis of hybrid systems that uses multiple Lyapunov functions is employed in the stability analysis of the closed-loop system. The stabilizing hybrid control strategy is illustrated on two examples and their closed-loop stability properties are studied.