Multi-Model Predictive Control of a Distillation Column

This paper presents a model predictive control (MPC) algorithm designed for the cooling system of a small commercial building under a time-dependent electricity price profile. The proposed approach includes a problem formulation in terms of cooling power, a variable-length prediction horizon and the consideration of the equipment duty cycle as a constraint in the optimization algorithm. The cooling system is equipped with an ice bank for thermal energy storage. A simple linear building thermal model is used to calculate the required amount of cooling power to maintain thermal comfort. The MPC algorithm uses this information to find the optimal operating points for the chiller and the ice bank to minimize the electric energy cost. The results of the MPC algorithm are compared against those of the reactive rule-based control algorithm currently in use in the building.

This paper is concerned with a computationally efficient (suboptimal) nonlinear Model Predictive Control (MPC) algorithm based on neural Wiener models. The model contains a linear dynamic part in series with a steady-state nonlinear part which is realised by a neural network. The model is linearised on-line, as a result the nonlinear MPC algorithm needs solving a quadratic programming problem. The algorithm gives control performance similar to that obtained in nonlinear MPC, which hinges on non-convex optimisation. In order to demonstrate accuracy and computational efficiency of the considered MPC algorithm, a polymerisation reactor is studied.

This paper discusses the possibility of using a Jordan neural network as a model of dynamic systems and it presents a Model Predictive Control (MPC) algorithm in which such a network is used for prediction. The Jordan network is a simple recurrent neural structure in which only one value of the process input signal (from the previous sampling instant) and only one value of the delayed output signal of the model (from the previous sampling instant) are used as the inputs of the network. In order to obtain a computationally simple MPC algorithm, the nonlinear Jordan neural model is repeatedly linearised on-line around an operating point, which leads to a quadratic optimisation problem. Effectiveness of the described MPC algorithm is compared with that of the truly nonlinear MPC scheme with on-line nonlinear optimisation performed at each sampling instant.

In this work, we formulate a new, nonlinear, and time-variant transmitter equalization method based on the Model Predictive Control (MPC) algorithm. MPC is a class of control algorithms in which the current control action is obtained by solving, perhaps approximately, an online open-loop optimal control problem. One important advantage of the MPC in peak-power constrained link environment is its ability to cope with hard constraints on controls and states. Knowing the state of the channel enables a very fine nonlinear equalization. We utilize this flexibility to create various MPC formulations that control the entire eye-mask, receive signal dynamic range as well as the required quantization. Our MPC equalization significantly outperforms traditional transmitter techniques such as linear feed-forward and Tomlinson-Harashima equalizers, and gets very close to the optimized decision-feedback equalization at lower transmitter resolutions. We also describe the possible complexity reduction techniques that enable efficient implementation of our MPC algorithm in hardware.

Discussion on: “Improved MPC Design based on Saturating Control Laws”

This paper performs a feasibility analysis of deploying Model Predictive Control (MPC) for vehicle platooning on an On-Board Unit (OBU) and performance benchmarking considering interference from other (system) tasks running on an OBU. MPC is a control strategy that solves an implicit (on-line) or explicit (off-line) optimisation problem for computing the control input in every sample. OBUs have limited computational resources. The challenge is to implement an MPC algorithm on such automotive Electronic Control Units (ECUs) with an acceptable timing behavior. Moreover, we should be able to stop the execution if necessary at the cost of performance. We measured the computational capability of a unit developed by Cohda Wireless and NXP under the influence of its Operating System (OS). Next, we analysed the computational requirements of different state-of-the-art MPC algorithms by estimating their execution times. We use off-the-shelf and free automatic code generators for MPC to run a number of relevant MPC algorithms on the platform. From the results, we conclude that it is feasible to implement MPC on automotive ECUs for vehicle platooning and we further benchmark their performance in terms of MPC parameters such as prediction horizon and system dimension.

When the structure information of a redundant manipulator is unknown, motion control methods that do not rely on its model are attractive. Due to the numerous advantages of model predictive control (MPC), such as the direct handling of constraints, this paper proposes a model-free MPC algorithm for redundant manipulators with unknown structure information. In this paper, a cerebellum-inspired model based on the echo state network (ESN) is employed to replace the kinematic model of the redundant manipulator, and an MPC algorithm based on the cerebellum model and neural dynamics (ND) approach is developed. Unlike existing studies, this work considers both performance optimization and system constraints of the redundant manipulator, and can achieve high-precision prediction and tracking by designing an online training algorithm for the cerebellum model. Furthermore, this paper proposes an ND-based correction algorithm to modify the prediction model and an ND solver to solve the MPC scheme. Theoretical analyses confirm the convergence of both the ND-based correction algorithm and ND solver. Simulation and experimental results consistently demonstrate that the proposed cerebellum-inspired MPC (CIMPC) algorithm is effective and outperforms comparison algorithms in terms of tracking performance.

In this note, we present a model predictive control (MPC) algorithm for uncertain time-varying systems with input constraints and state-delay. Uncertainty is assumed to be polytopic, and delay is assumed to be unknown but with a known upper bound. For a memoryless state-feedback MPC law, we define an optimization problem that minimizes a cost function and relaxes it to two other optimization problems by finding an upper bound of the cost function. One is solvable and the other is not. We prove equivalence and feasibilities of the two optimization problems under a certain assumption on the weighting matrix. Based on these properties and optimality, we show that feasible MPC from the optimization problems stabilizes the closed-loop system. Then, we present an improved MPC algorithm that includes relaxation procedures of the assumption on the weighting matrix and stabilizes the closed-loop system. Finally, a numerical example illustrates the performance of the proposed algorithm.

Impedance control has been suggested as the strategy employed by the central nervous system to control human postures and movements. A realization of this strategy is presented that uses a model predictive control algorithm as a higher motor controller. External disturbances are explicitly included in the model. The combination of 3 key factors—joint impedance control, model predictive controller, and external disturbance input—forms the basis for the generality of this model. The model was applied to 3 different types of joint movements: a tracking movement with an unpredicted disturbance, a rhythmic movement, and an unstable biped model of human walking. Computer simulation results showed excellent performance of the model in all 3 cases for optimal values of active joint impedances and an exact match between the musculoskeletal system and the model internal to the model predictive controller. The controller was also able to maintain acceptable performance in the presence of a 25% mismatch between the musculoskeletal system and its internal model.

FCC unit modeling, identification and model predictive control, a simulation study

A discretized rotor reference frame dq-model of the PMSM is the basis of Model Predictive Control (MPC) and Deadbeat Predictive Control (DBC). A modified self-tuning field orientation control (FOC) of PMSM was developed for comparison with the predictive control methods. Since torque is proportional to q-axis current and control of current results in control of torque, speed, and rotor position, the MPC, DBC, and FOC algorithms ensure that the actual motor dq-currents track their respective references. The models were implemented in MA TLAB/Simulink. The results show effective tracking of current and speed references with minimal transients. The MPC showed the fastest speed settling time of 0.025 seconds (87.5% faster) and about 16% overshoot while the DBC has a settling time of 0.12 seconds (40% faster) with no overshoot. The FOC has its settling time as 0.2 seconds with no overshoot. Compared to FOC, both developed models have improved performance.

In this article, two new algorithms of the redundant force branch of 6-PUS/UPU parallel robot are proposed. They are model predictive control combining with proportional, integral, and differential algorithm and fuzzy combining with model predictive control algorithm. The shortcoming of the traditional model predictive control algorithm is complex adjustment, large amount of calculation, the dynamic performance effect of the system. The proposed PID model predictive control algorithm can make the controller parameters adjustment more convenient. However, PID model predictive control algorithm can’t obtain good control performance under sudden change in situation. Combining model predictive control algorithm with fuzzy theory, fuzzy model predictive control algorithm has better anti-interference ability than PID model predictive control algorithm and can reduce predictive horizon length as possible as it can. Simulation results show that fuzzy model predictive control algorithm can effectively improve real-time performance of control system, the dynamic tracking performance and robustness than the traditional model predictive control and PID model predictive control algorithm.

Formulation of a model predictive control algorithm to enhance the performance of a latent heat solar thermal system

This paper presents an application of the neural network (NN) model for forecasting and filtering problems. Instead of using the gradient descent method as used by the standard back-propagation network, the present study adopted the Levenberg-Marquardt algorithm. It was shown that the Levenberg-Marquardt algorithm tends to reach termination criteria more quickly making the searches employing the full model less time consuming. In the first part of forecasting problem, multilayer feedforward (MLFF) network was constructed by trials to forecast the tidal-level variations at the Chao Phraya river mouth in Thailand. Unlike the well-known conventional harmonic analysis, the neural network model uses a set of previous data for learning and then forecasting directly the time series of tidal levels. It was found that lead time of 1 to 24 hourly tidal levels can be successfully predicted using only a short-time hourly learning data.In the second part of filtering problem, the MLFF network was also used to establish a stage-discharge relationship for tidal river. Comparisons were made among conventional methods, i.e. by using multivariate functions (Linear and power models) and the NN model. The NN model was found to be able to model the transfer function too much higher accuracy than multiple regression analysis. The root mean square errors (RMSE) and the mean relative error (MRE) for the NN model are about 8 cm and 6.4% whereas the same errors for multiple regression analysis are 16 cm and 12%, respectively. The efficiency index for the linear, power, and NN models is 0.4, 0.7, and 0.9, respectively. In addition, the obtained stage-discharge relationship by the NN model can indicate reasonably important behavior of the tidal influences, i.e. there are stronger influences of tide during the dry period than the flood period.

Iterative learning control (ILC) is often used to eliminate repetitive disturbances and improve the tracking performance in the industrial processes. Due to its disability of reacting against real-time disturbances, the integration of model predictive control (MPC) and ILC constitutes the model predictive iterative learning control (MPILC) to improve its ability of rejecting non-repetitive disturbances. MPILC is suitable for linear models which has poor performance for highly nonlinear systems. A nonlinear MPILC (NMPILC) global controller based on T-S model is put forward in this paper. The global controller is composed of a set of local MPILC controllers designed applying the local linear models of the T-S model. The convergence property has been demonstrated. A PWR nuclear power plant is adopted to illustrate the performance of the NMPILC.