Anca Maxim

Tuning algorithms for fractional order internal model controllers for time delay processes

ABSTRACT This paper presents two tuning algorithms for fractional-order internal model control (IMC) controllers for time delay processes. The two tuning algorithms are based on two specific closed-loop control configurations: the IMC control structure and the Smith predictor structure. In the latter, the equivalency between IMC and Smith predictor control structures is used to tune a fractional-order IMC controller as the primary controller of the Smith predictor structure. Fractional-order IMC controllers are designed in both cases in order to enhance the closed-loop performance and robustness of classical integer order IMC controllers. The tuning procedures are exemplified for both single-input-single-output as well as multivariable processes, described by first-order and second-order transfer functions with time delays. Different numerical examples are provided, including a general multivariable time delay process. Integer order IMC controllers are designed in each case, as well as fractional-order IMC controllers. The simulation results show that the proposed fractional-order IMC controller ensures an increased robustness to modelling uncertainties. Experimental results are also provided, for the design of a multivariable fractional-order IMC controller in a Smith predictor structure for a quadruple-tank system.

Multivariable model-based control strategies for level control in a quadruple tank process

This paper presents three model-based control strategies applied to a multivariable process. First, a simple and rather naive approach is employed, i.e. treating the process as two SISO (Single Input Single Output) loops and design PID controllers. Obviously, this approach is effective, but does not take into account the interaction between the loops. Next, interaction is compensated by using dynamic decouplers and control performance is improved. Finally, a multivariable IMC (Internal Model Control) method is applied. All the results were validated on the laboratory setup with coupled quadruple tanks from Quanser. This is an interesting and challenging testbed for control, i.e. it poses non-minimum phase transmission zeros. Our experimental results show that the IMC outperforms the PID control at the cost of additional design complexity. All controllers were successfully tested for setpoint trajectory and disturbance rejection and tackled well the noise in the system.

Distributed model predictive control algorithm for vehicle platooning

This paper proposes a distributed model predictive control algorithm applied in a vehicle platooning control problem. The control objective of each vehicle in the platoon is to follow a imposed position trajectory by means of distributed model predictive control, while maintaining a constant spacing between vehicles. A delay-free communication architecture is proposed and two cases are evaluated, namely: i) an unconstrained optimization problem and ii) an optimization problem in which the constraints are imposed based on the received information. The simulation results show that introducing constraints helps improving the results.

A Computationally Efficient Non-cooperative Distributed Model Predictive Control Algorithm for Two Agent Systems

This paper presents a non-cooperative distributed model predictive control algorithm used in cyber-physical systems for two agent systems coupled through the inputs. Each agent computes the optimal input trajectory for its corresponding subsystem as the minimum of a local optimization problem. The input trajectory of the neighbor, which is used in the local optimization problem, is obtained based on the previous optimal control sequence and is received in a communication session. After that, the optimization problem is solved and the optimal input is sent to the process. This approach is computationally efficient because the communication between the two agents is reduced at minimum (only one session each sampling period) and the optimal input is obtained solving one optimization problem thus diminishing the overall computational time. The algorithm was implemented in Matlab and the obtained performances were compared with a cooperative distributed model predictive control strategy. Both methods were tested in simulation on a quadruple tanks process and the results recommend the non-cooperative strategy which has similar results with less computational requirements.

Distributed model predictive control for vehicle platooning: A brief survey

Vehicle platooning (enforcing the vehicles to follow each other and to maintain a safe distance between them) could be the solution to the stringent problems that appear on existing highways. Moreover, it has been already proved that by including communication between vehicles (yielding cooperative vehicles) the performances of the resulting platoons are much greater than those obtained without communication between vehicles. The specific particularities of the vehicle platoons, i.e., the chain structure of the involved sub-systems (vehicles), make them suitable as distributed model predictive control applications. As such, this paper intends to make a survey on the recent results regarding distributed model predictive control for the vehicle platooning problem, starting with inter-vehicle communications in a platoon, vehicle and platoon modeling and control, distributed model predictive control solutions and ending with some conclusions and future research directions.

Modelling and identification of a coupled sextuple water tank system

This paper presents the modelling and identification procedure applied to a coupled, non-minimum phase system consisting of six water tanks. This process is composed of three inter-connected sub-systems coupled through the inputs. Using the process description, the theoretical nonlinear model was derived and linearised around a chosen operating point. After that, a three part experiment was conducted on the sextuple plant from Quanser in which one of the systems inputs was varied while the others remained constant. The experimental data was used to compute the systems static characteristic which describes the output variation limits for different input values. Then, the dynamic characteristic was used to analyse the system evolution in transient time to provide insight knowledge about the model orders required in the parametric identification. The results obtained clearly show that the computed linear model proper characterizes the dynamics of the real process and can be further used in simulations.

Robust autotuning MPC for a class of process control applications

This paper introduces a robust methodology for autotuning design parameters in the EPSAC (Extended Prediction Self-Adaptive Control) approach to MPC (Model based Predictive Control). The method requires from the user solely a well-chosen sampling period of the process and, in case of process with time delay, the amount of delayed samples. The main design parameter, the prediction horizon, is related to the open loop dynamics of the system and set to a relatively large value for a robust control performance. Process model is obtained apriori from step response in presence of 20% noise and later updated during closed loop simulations. The results indicate in both simulation and experimental study that the methodology is suitable for some classes of chemical processes or other processes with similar dynamic profiles.

Validation of a multivariable relay-based PID autotuner with specified robustness

This paper presents a multivariable relay-based PID autotuning strategy, which ensures a specified modulus margin (i.e. robustness). The algorithm is applied on the coupled quadruple tanks from Quanser. The system is challenging for control since it presents non-minimum phase transmission zeros. The performance of the autotuner is validated against a computer-aided design tool based on the frequency response, i.e. FRTool. The experimental results suggest that the proposed autotuning procedure has similar performance as the control design based on full knowledge of the system. This is a remarkable conclusion and provides a good motivation to claim that our algorithm may be useful in chemical process applications where full knowledge of the systems model is still a burden for the control engineer.

Cruise and headway control for vehicle platooning using a distributed model predictive control algorithm

A cruise and headway control strategy using distributed model predictive control, developed for a vehicle platooning application is proposed in this paper. The cruise control (i.e. driving the vehicle with a constant velocity demanded by the driver) is designed for the platoons leading vehicle, whereas for the rest of the platoon, a headway control strategy is developed. Thus, the control objective for the follower vehicles is to maintain a specified distance with respect to the vehicle immediately in front. Each vehicle is controlled through a distributed model predictive control strategy with input constraints. Moreover, terminal constraints which ensure the string stability of the platoon are enforced on the follower vehicles. The simulation results show the feasibility of the control strategy.

Multivariable control of sextuple tank system with non-minimum phase dynamics

In this paper we present experimental results of a multivariable linear predictive control strategy applied to a coupled, non-minimum phase dynamics system of six coupled water tanks with 3 controlled water levels (cm) and 3 manipulated pump outputs (V). The setup can be considered as three interacting sub-systems, with coupled dynamics due to the specific water flow directions. The experimental results indicate that the proposed strategy is robust to significant modelling errors, while maintaining good performance.