Industrial Process Control Using LPV

International audience

On the practical integration of anomaly detection techniques in industrial control applications

This paper presents a Linear Parameter Varying (LPV) approach to model and control two-mass systems with backlash. The maximum amplitude of the backlash angle is assumed to be unknown and variable having no knowledge about the upper and lower bounds of it. Proper affine state space model together with the admissible variations of the LPV parameters is designed in order to realize a viable convex polytope. Utilizing H ∞ LPV lemmas and theories lead to a set of Linear Matrix Inequalities (LMIs). By solving these LMIs, appropriate scheduled state feedback gains are obtained. The designed robust control strategy can easily handle the variations of the backlash angle and load disturbance torque. A simulated two-mass backlash system verifies the efficiency of the designed control law.

We introduce a controller design methodology for nonlinear systems via complementary Linear Parameter Varying (LPV) controller and observer structures. The recently developed method is able to control physiological systems even with complex nonlinearities — without using Linear Matrix Inequalities (LMI) or other techniques requiring iterations. The developed method is based on the classical state feedback theorems, matrix similarity theorems and supplementary controller and observer structure which efficiently uses the mathematical properties of the parameter space of the LPV system. The main benefits of the proposed method is that the controller design does not require mathematical tools needing iteration thus high computational capacity. We used a nonlinear compartmental model in order to demonstrate the application of the method. The results showed that the developed complementary LPV controller and observer structures perform well on both the LPV systems and the original nonlinear system as well.

This paper proposes \(H_{2}\)/\(H_{\infty }\) full state-feedback synthesis for robot manipulators, using uncertain polytopic linear parameter-varying (LPV) system modeling, with pole placement constraints to assign the poles of closed-loop system in a desired linear matrix inequality (LMI) region. The desired state trajectory of the system is used for generating an uncertain polytopic model of the system applying usual Lagrangian equations. The control gain matrix is derived by solving a set of LMIs to design a robust pole placement controller such that a prescribed mixed \(H_{2}\)/\(H_{\infty }\) performance is fulfilled and the response of the manipulator has a proper damping ratio. A sufficient condition is proposed to guarantee the asymptotic stability of the closed-loop uncertain polytopic LPV system against the uncertainties on the vertices. The proposed scheme is applied to controller synthesis of a two-degree-of-freedom manipulator trajectory-tracking problem. The simulation results show the effectiveness of the proposed controller.

This paper considers the optimal control of polytopic, discrete-time linear parameter varying (LPV) systems with a guaranteed l2 to l∞ gain. Additionally, to guarantee robust stability of the closed-loop system under parameter variations, H∞ performance criterion is also considered as well. Controllers with a guaranteed l2 to l∞ gain and a guaranteed H∞ performance (l2 to l2 gain) are a special family of mixed H2=H∞ controllers. Normally, H2 controllers are obtained by considering a quadratic cost function that balances the output performance with the control input needed to achieve that performance. However, to obtain an optimal controller with a guaranteed l2 to l∞ gain (closely related to the physical performance constraint), the cost function used in the H2 control synthesis minimizes the control input subject to maximal singular-value performance constraints on the output. This problem can be efficiently solved by a convex optimization with linear matrix inequality (LMI) constraints. The main contribution of this paper is the characterization of the control synthesis LMIs used to obtain an LPV controller with a guaranteed l2 to l∞ gain and >H∞ performance. A numerical example is presented to demonstrate the effectiveness of the convex optimization.

Trajectory tracking is extremely difficult for rotorcrafts based on the nonlinear model and taking into account all the parameters of the system and especially considering the effects of flapping and the main rotor and its control tail in all directions. This paper describes the tracking route, based on nonlinear model and velocity control and feedback mode and Polytopic linear parameter varying (LPV) modeling with the help of solving linear matrix inequalities (LMI) equations for different conditions and complex maneuvers for an unmanned rotorcraft that has been examined in all directions including, longitudinal, altitudinal, latitudinal directions. Based on the different operating points of the system and the different flight conditions, first a Polytopic modeling of the system is performed, and then the control signal is generated based on the state feedback and solution of the linear matrix inequalities (LMI) equations. The final control signal consists of feedback of changes of the state variables around the nominal trajectory under the designed feedback gains, in addition to the nominal control signal for the desired trajectory. In calculating the nominal control signal for the optimum trajectory, the Polytopic system model is used instead of the nonlinear system model. Therefore, the final control signal does not require a dynamic system model and all control calculations are performed using a Polytopic system model and have high computational speed. System simulation shows the capabilities of the proposed control system in different operating conditions.

The problem of modelling the complex behaviour of freeway flow leads to a nonlinear macroscopic model. Unfortunately, high dimensional non-linear characteristics could not be performed easily. The paper´s purpose is to introduce a new, general modelling formalism for freeway traffic flow modelling, respectively control. Linear Parameter Varying (LPV) systems represent a numerically tractable class of complex non-linear systems. The main idea is to derive some arbitrary, time dependent parameters by capturing the nonlinearities in the system. Even if the transformation of the full nonlinear model to affine and quasi Linear Parameter Varying (qLPV) system is not unique, an appropriate qLPV model is presented and a computationally low demanding form is given. More, the paper investigates the problem of selecting the adequate scheduling variables, endogenous parameters and some linear approximations giving a novel way to describe freeway traffic systems. An important aspect of the model selection is the feasibili ty of the resulted system throughout the controller and observer design. The paper describes the problem of quadratic stabilizability and detectability for LPV flow models. The Linear Matrix Inequality (LMI) conditions are developed to verify these important properties. Finally, a numeric example suggests the application of the LPV structure for a general freeway section with on- and off-ramps. The comparison of the simulation response of the non-linear and the derived nominal LPV model has also been investigated.

Liquid tank systems play important role in industrial application such as in food processing, beverage, dairy, filtration, effluent treatment, pharmaceutical industry, water purification system, industrial chemical processing and spray coating. Recently, classical PID controller based on the linear model is widely used in controlling industrial liquid level control application. However aggressive performance requirements may not be achievable with this controller due to the presence of nonlinear dynamics inherent in the liquid control system and system parameter variations caused by for example corrosive build-up in liquid level systems creates variation of cross section areas of the tank and discharge orifice. In order to allow advanced controller which can deal with system nonlinearities, a nonlinear model of the tank system is required. This paper describes a comparison study of mathematical-based and artificial neural network-based model of a coupled industrial tank system including its nonlinearity. First, a non-linear mathematical model is developed and its parameters are identified using extended Kalman filter (EKF) based on the experimental data. Next, a multi layer feedforward neural network trained by using backpropagation learning algorithm is used to develop the system model based on the experimental data. A series of validation test is carried out to evaluate the effectiveness of the both models. The results confirm that ANN-based model is more suitable model of the lab-scale industrial tank than EKF-based system.

This paper reviews robust feedback control applications in power system. Robust control concept in power system control area evolves by the way of uncertainty modeling. Uncertainties can be caused by variation of loading, load parameters, network topology and machine parameters. One direct way to take into consideration of uncertainties is to enumerate various system operating conditions and use a set of linear time invariant systems to model the power systems. Enumeration method is used in robust control signal selection and robust controller design. Another way is to model uncertainties as structured or unstructured uncertainties. Controllers are designed based on nominal system condition to tolerate uncertainty as much as possible. The controller synthesis problem is solved by either Algebraic Ricatti Equation (ARE) or Linear Matrix Inequality (LMI). LMI is shown to be more flexible in controller design since it provides a way to specify system dynamic performance. Most recently, linear parameter varying (LPV) concept expands the use of enumeration method to express a set of linear time invariant (LTI) systems with state space dependent on linear parameters. LPV based control methods extend gain scheduling to design linear control for each operating conditions and overall a nonlinear controller for the varying parameter system.

This paper presents a controller design method for dealing with the induced ℒ 2 -norm problem for switched linear parameter-varying (LPV) systems. Considering the arbitrary switchings caused by the parameters varying, a common parameter-dependent Lyapunov function is employed to derive sufficient linear matrix inequality (LMI) conditions for the switched LPV systems. A family of LPV controllers are designed according to the LMI conditions, and each of them is suitable for the corresponding parameter region. The proposed switching LPV control method is applied to an F-16 aircraft longitudinal model and simulation results demonstrate the effectiveness of the approach.

Applications of a quadrotor with payload, particularly for chemical spraying, have increased in recent times. The variation in payload mass over time causes a change in the moments of inertia (MOI). Moreover, large tilt angles are required for fast reference tracking and external disturbance rejection. These variations in plant parameters (i.e., mass and inertia) and large tilt angles can degrade the control scheme’s performance and stability. This article proposes a linear matrix inequalities (LMIs)-based linear parameter varying (LPV) control scheme for a quadrotor subject to time-varying mass, time-varying inertia, mass flow rate, and large tilt angles. The control strategy is designed by solving LMIs derived from quadratic H∞ performance and D-stability. The robust stability and quadratic H∞ performance are assessed by LMIs. The efficacy of the proposed methodology is established using numerical simulations, and its performance is compared to the linear time-invariant (LTI) H∞ design with pole placement constraints. The results obtained show that the LPV control scheme gives better tracking performance in the presence of time-varying parameters, noise, and external disturbances without actuator saturation. In comparison to the LTI design technique, the proposed LPV scheme improves the rise time (tr), settling time (ts), and mean squared error (MSE) by up to 14%, 15%, and 30%, respectively. Moreover, smooth transitions are observed in the tilt angles and control signals with the LPV scheme, contrary to the LTI controller, which exhibits significant oscillations.

Development of an autonomous fog computing platform using control-theoretic approach for robot-vision applications

In this paper, a linear parameter-varying (LPV) control design method is evaluated experimentally on an active magnetic bearing (AMB) system. Linear matrix inequality (LMI) conditions for control design of affine parameter-dependent systems using parameter-dependent Lyapunov functions are proposed. A speed-dependent LPV model of the AMB system is derived. Speed-dependent model uncertainties are identified using artificial neural networks (ANNs), and a parameter-dependent uncertainty weighting function is approximated for LPV control synthesis. Experiments are conducted to verify the robustness of LPV controllers for a wide range of rotor speeds. This LPV control approach eliminates the need for gain-scheduling, and provides better performance and less conservativeness over a wide range of rotational speeds than controllers designed with constant uncertainty weighting functions.

Linear Parameter Varying (LPV) system shows preferable performance in dealing with NonLinear (NL) systems and systems with time-varying parameters, based on a kind of wheel-legged robot with two-wheel and balance as Inverted Pendulum, this paper proposes a gain scheduling control method for balancing using LPV system on Equivalent model with Center Of Mass (COM). In order to ensure the stability and responsive of the system with possible values for all variable parameters, Higher Order Singular Value Decomposition (HOSVD) is used for constructing polytopic LPV system, then the robust controller is designed for the vertex systems forthputting Linear Matrix Inequality (LMI) approach, and the gain scheduling controller for global system is obtained by convex combination of vertex LTI systems. The simulation results show that the system can achieve the expected indicators.