Vladimir Milić

Robust H∞ position control synthesis of an electro-hydraulic servo system

This paper focuses on the use of the techniques based on linear matrix inequalities for robust H(infinity) position control synthesis of an electro-hydraulic servo system. A nonlinear dynamic model of the hydraulic cylindrical actuator with a proportional valve has been developed. For the purpose of the feedback control an uncertain linearized mathematical model of the system has been derived. The structured (parametric) perturbations in the electro-hydraulic coefficients are taken into account. H(infinity) controller extended with an integral action is proposed. To estimate internal states of the electro-hydraulic servo system an observer is designed. Developed control algorithms have been tested experimentally in the laboratory model of an electro-hydraulic servo system.

Initial conditions optimization of nonlinear dynamic systems with applications to output identification and control

The paper presents a gradient-based algorithm for initial conditions optimization of nonlinear multivariable systems with boundary and state vectors constraints. The algorithm has a backward-in-time recurrent structure similar to the backpropagation-through-time (BPTT) algorithm, which is mostly used as a learning algorithm for dynamic neural networks. It is shown that dynamic parameter optimization problem can be formulated as the initial conditions optimization problem. Further, it is shown that output parameter identification and output controller design problems can be formulated as dynamic parameter optimization problem. The effectiveness of the proposed algorithm is demonstrated on the problem of output identification and control of a nonlinear two-mass torsional system.

A computational approach to parameter identification of spatially distributed nonlinear systems with unknown initial conditions

In this paper, a high-precision algorithm for parameter identification of nonlinear multivariable dynamic systems is proposed. The proposed computational approach is based on the following assumptions: a) system is nonlinearly parameterized by a vector of unknown system parameters; b) only partial measurement of system state is available; c) there are no state observers; d) initial conditions are unknown except for measurable system states. The identification problem is formulated as a continuous dynamic optimization problem which is discretized by higher-order Adams method and numerically solved by a backward-in-time recurrent algorithm which is similar to the backpropagation-through-time (BPTT) algorithm. The proposed algorithm is especially effective for identification of homogenous spatially distributed nonlinear systems what is demonstrated on the parameter identification of a multi-degree-of-freedom torsional system with nonlinearly parameterized elastic forces, unknown initial velocities and positions measurement only.

A BPTT‐like Min‐Max Optimal Control Algorithm for Nonlinear Systems

This paper presents a conjugate gradient‐based algorithm for feedback min‐max optimal control of nonlinear systems. The algorithm has a backward‐in‐time recurrent structure similar to the back propagation through time (BPTT) algorithm. The control law is given as the output of the one‐layer neural network. Main contribution of the paper includes the integration of BPTT techniques, conjugate gradient methods, Adams method for solving ODEs and automatic differentiation (AD), to provide an effective, novel algorithm for solving numerically optimally min‐max control problems. The proposed algorithm is applied to the rotational/translational actuator (RTAC) nonlinear benchmark problem with control and state vector constraints.

A case study in distributed control: Elastically interconnected seesaw-cart systems

As the main contribution of the paper, we present a network of electro-mechanical systems as a suitable platform for education, testing and verification of real-life implementation of decentralised and distributed control solutions. The overall system (network) consists of a set of elastically interconnected seesaw-chart systems. Additionally, suitable, control oriented, structured model of the systems dynamics is derived and presented. Results of a case study in distributed control are presented, together with comparison with achievable centralized control behaviour.

Frequency-shifting-based stable on-line algebraic parameter identification of linear systems

Abstract In this paper a new approach to algebraic parameter identification of the linear SISO systems is proposed. The standard approach to the algebraic parameter identification is based on the algebraic derivatives in Laplace domain as the main tool for algebraic manipulations like elimination of the initial conditions and generation of linearly independent equations. This approach leads to the unstable time-varying state-space realization of the filters for the on-line parameter estimation. In this paper, the finite difference and shift operators in combination with the frequency-shifting property of Laplace transform is applied instead of algebraic derivatives. Resulting state-space realization of the estimator filters is asymptotically stable and doesn’t require switch-of mechanism to prevent overflow of the estimator variables. The proposed method is especially suitable for applications in closed-loop on-line identification where the stable behavior of the estimators is a necessary requirement. The efficiency of the proposed algorithm is illustrated on three simulation examples.

Robust decentralized global asymptotic tracking control of a class of nonlinear mechanical systems

In this paper, a RISE type of tracking controllers for a class of nonlinear mechanical systems is proposed. The proposed chattering-free controller provides global asymptotic tracking in the presence of external disturbances. The proof of global asymptotic stability is based on a novel approach to the construction of a Lyapunov function which is parameterized by a time-varying function of reference and disturbance vector. The explicit conditions on the controller gains to ensure global asymptotic tracking are obtained. The simulation results on a system of three inverted pendulums interconnected by two springs illustrate the performances of the proposed controller.

An analytical fuzzy-based approach to -gain optimal control of input-affine nonlinear systems using Newton-type algorithm

This paper is concerned with -gain optimisation of input-affine nonlinear systems controlled by analytic fuzzy logic system. Unlike the conventional fuzzy-based strategies, the non-conventional analytic fuzzy control method does not require an explicit fuzzy rule base. As the first contribution of this paper, we prove, by using the Stone–Weierstrass theorem, that the proposed fuzzy system without rule base is universal approximator. The second contribution of this paper is an algorithm for solving a finite-horizon minimax problem for -gain optimisation. The proposed algorithm consists of recursive chain rule for first- and second-order derivatives, Newton’s method, multi-step Adams method and automatic differentiation. Finally, the results of this paper are evaluated on a second-order nonlinear system.

A Newton-Like Algorithm for L2-Gain Optimal Control of an Electro-Hydraulic Servo-System

This paper is concerned with L2-gain optimal control approach for rotary electro-hydraulic servo-system. The electro-hydraulic dynamics with respect to hydraulic motor velocity, with input voltage to the servo valve as control input and load torque as disturbance input, is formulated. The mathematical model results in input-affine nonlinear system. A numerical algorithm based on Newton method to solve a finite-horizon minimax problem for L2-gain minimisation of electro-hydraulic system is presented. The feedback control and disturbance variables are formulated as linear combination of approximation functions. The proposed algorithm, which has recursive matrix structure, directly finds approximations of the feedback control and the “worst case” disturbance variables. Developed controller has been tested experimentally in the laboratory model of an electro-hydraulic servo system.

A numerical algorithm for nonlinear L 2 -gain optimal control with application to vehicle yaw stability control

This paper is concerned with L2-gain optimal control approach for coordinating the active front steering and differential braking to improve vehicle yaw stability and cornering control. The vehicle dynamics with respect to the tire slip angles is formulated and disturbances are added on the front and rear cornering forces characteristics modelling, for instance, variability on road friction. The mathematical model results in input-affine nonlinear system. A numerical algorithm based on conjugate gradient method to solve L2-gain optimal control problem is presented. The proposed algorithm, which has backward-in-time structure, directly finds the feedback control and the “worst case” disturbance variables. Simulations of the controller in closed-loop with the nonlinear vehicle model are shown and discussed.