Robust control design via game theoretic methods

The cross-coupled control (CCC) has been recognized as an efficient motion controller that reduces contouring errors, but theoretical analysis of it is lacking, and there is no systematic design approach for obtaining a CCC system with guaranteed control performance. Consequently, the compensators C in CCC are commonly implemented in a PID structure and their contouring accuracy is usually degraded in real applications under different operating conditions. In an attempt to overcome the CCC design limitations described above, this paper introduces a robust CCC design based on a novel formulation: the contouring error transfer function (CETF), leading to an equivalent formulation as in the feedback control design problem. Then, methods in robust control design can be readily employed to achieve robust CCC with specified stability margins and guaranteed contouring performance. Furthermore, the proposed design has been verified as being internally stable. All provided experimental results indicate that the proposed robust CCC design consistently renders satisfactory contouring accuracy under different operating conditions.

The paper presents a robust PID control design method for spacecraft attitude tracking. Spacecraft control for large-angle control is subject to nonlinear couplings and uncertainties. Although nonlinear robust control design methods, such as nonlinear H/sub /spl infin// control can be applied to address these issues. The solving of the associated Hamilton-Jacobi equation is often extremely complicated and the resulting controller is not easy to implement. In the paper, the PID controller architecture is assumed for the spacecraft attitude control and concepts in nonlinear H/sub /spl infin// control theory are applied to obtain robustness properties. Results of both PD control and PID control are derived and applied to the ROCSAT-3 satellite of a science model system for verification.

Robust velocity and height control problem is dealt with for hypersonic vehicles subject to highly nonlinearity and uncertainties. The linear robust controller design for nonlinear systems suffers from the conservation problem, because the nonlinear dynamics are considered as uncertainties. In this paper, a feedback linearization controller is firstly applied to achieve the dynamic decoupling of the velocity and height channels. Then, robust controllers are designed for each channel to restrain the effects of the parametric uncertainties, external disturbances, and nonlinear dynamics, which cannot be counteracted accurately by the feedback linearization technique. This method can guarantee the robust stability and robust tracking properties of the closed-loop control system, while the conservation of the robust controller design can be reduced because the nonlinear information of dynamic system is used. Simulation comparisons are given to show the advantages of the proposed robust nonlinear control method.

We discuss the fragility of controllers against small inaccuracies of controller parameters. A useful way to gain insight into controller fragility is to consider the fragility of poles and zeros. Certain controller design methods and controller parametrizations are especially vulnerable to fragility problems. It is hoped that the controversy and debate around the claimed fragility of designs obtained by modern robust and optimal control theories calls attention to the relevance of the work on fixed wordlength effects in controller implementation. A case study on a paper machine headbox control problem is included to illustrate that if a good robust control design method is used, together with a reasonable controller realization (parametrization), it should be possible to combat controller fragility in a fairly satisfactory, although indirect, manner. However, it would certainly be interesting to study whether controller fragility could be directly addressed within some generalized robust control design theory.

Robust STATCOM voltage controller design using loop-shaping technique

Performance-guaranteed Robust PID Controller Design for Systems with Unstable Zero

A nonlinear robust controller design method is proposed for the lateral control of heavy vehicles for automated highway systems. In the controller design, the actuator dynamics is explicitly taken into account. A first order pre-filter is introduced to reduce chattering which is inherent in the nonlinear robust controller and to prevent the saturation in the front wheel steering angle and steering system slew rate. A constructive backstepping design technique is utilized in the design of a robust controller for the augmented system. Simulation results are shown.

A systematic and complete method to design robust predictive controllers for unconstrained linear systems is proposed. The synthesis procedure is based on rigorous theoretical foundations, without resorting to approximations or ad hoc design guidelines, yet it remains a viable tool for practical application. A significant feature is that the robust predictive controller retains the servo performance of a nominal predictive controller designed using conventional methods. In addition, the robust predictive controller can be designed to guarantee perfect steady‐state rejection of asymptotically constant disturbances. The robust design method is developed for systems affected by unmodeled dynamics and is based on solving a discrete‐time model‐matching problem. It is shown that the robust controller can be classified legitimately as a predictive controller because it minimizes the same performance functional as the nominal predictive controller. An illustrative design example is given.

The problem of robust velocity and height control is dealt with for hypersonic vehicles subject to high nonlinearity and uncertainties. Robust linear controller design for nonlinear systems suffers from the problem of conservation because the nonlinear dynamics are considered as uncertainties. In this paper, a feedback linearization controller is firstly applied to achieve dynamic decoupling of the velocity and height channels. Robust controllers are then designed for each channel to achieve the desired tracking and restrain the effects of parametric uncertainties, external disturbances, and nonlinear dynamics, which cannot be accurately counteracted by the feedback linearization technique. This method can guarantee the robust stability and robust tracking properties of the closed-loop control system. Moreover, the conservation of the robust controller design can be reduced because the nonlinear information of the dynamic system is used. Simulation results are given to show the advantages of the proposed robust nonlinear control method compared with its linear counterpart.

Robust Anticipative Controller Design with Application to A High Dynamic Engine Testbed

In this paper, a novel robust controller for a Static Synchronous Compensator (STATCOM) is presented to enhance the fault ride-through (FRT) capability of fixed speed induction generators (FSIGs), the most common type of generators that can be found in wind farms. The effects of STATCOM rating and wind farm integration on FRT capability of FSIGs are studied analytically using the power-voltage and torque-slip relationships as well as through simulations. The wind generator is a highly nonlinear system, which is modelled in this work as a linear part plus a nonlinear part, the nonlinear term being the Cauchy remainder term in the Taylor series expansion and of the equations used to model the wind farm. Bounds derived for this Cauchy remainder term are used to define an uncertain linear model for which a robust control design is performed. The controller resulting from this robust design provides an acceptable performance over a wide range of conditions needed to operate the wind farm during severe faults. The performance of the designed controller is demonstrated by large disturbance simulations on a test system.

Hybrid Passive/Active Control Performance in Buildings Using Robust Control Design Approaches

A robust adaptive backstepping controller design method is proposed for a nonlinear system with uncertainty and unknown parameters based on the CMAC neural network. The CMAC neural network was used not only to approach the arbitrary model uncertainties but also to eliminate the bad effects of the uncertainties with robust terms in the controller and virtual controllers. Novel update and control laws are proposed to guarantee that all the signals in the closed-loop control system are uniformly ultimately bounded in a Lyapunov sense. Simulation experimental showed the tracking control of the nonlinear system is achieved and this method is effectual.

We propose a robust control system which has robustness for disturbance and can deal with a nonlinear system with partially unknown structure by fusing reinforcement learning and robust control theory. First, we solved an optimal control problem without using unknown part of functions of the system, using neural network and the repetition learning of reinforcement learning algorithm. Second, we built the robust reinforcement learning control system which permits uncertainty and has robustness for disturbance by fusing the idea of H infinity control theory with above system.

This paper studies the robust discrete-time pole-placement state feedback controller design in the LMI framework. The inner ellipse is used to approximate originally non-convex discrete-time closed loop pole region respective to the prescribed damping factor. The resulting LMI conditions use parameter dependent Lyapunov function to reduce conservatism in robust controller design. Contribution of this paper is in the application of this procedure on the case study - unstable Magnetic Levitation System, analysis of the results and comparison with standard robust stabilizing controller design.