L/sub 1/ state feedback control of active suspension

Control system design is discussed for a semi-active suspension system of vehicles. For the disturbance rejection problem, l1 state feedback controllers are designed. An l1 controller can specify the maximum magnitude of outputs against certain road disturbances in the time domain, regardless of the frequency of the road disturbances. That property enables a semi-active suspension to be formulated as an unconstrained linear system, while it is usually modeled as a bilinear system or a linear system with a constraint. In this paper, not only a controller for a nominal model, but also a controller considering robust performance is designed. Static nonlinear first order homogeneous state feedback controllers, which require a moderate amount of calculation, are constructed for the linear system by applying l1 near-optimal control theory with an appropriate approximation method.

Design of disk drive servo controller using H/sub /spl infin//-optimization technique to recover the loop transfer function is presented here. In the first phase of the two step algorithm, a full state feedback controller is designed to obtain desired gain and phase margins, and satisfactory sensitivity and complementary sensitivity for the nominal plant model. The observer gains are determined in the second phase, loop transfer recovery (LTR), so that the characteristics of the full state feedback are preserved. Recovery is achieved using minimization of the H/sub /spl infin//-norm of a transfer function called the recovery function, which represents the difference between the loop gain of the static full state feedback and feedback with observer. Simulation results for the continuous time design are shown.

In contrast with /spl Hscr//sub /spl infin// and /spl Hscr//sub 2/ control theories, the problem of persistent disturbance rejection (l/sup 1/ optimal control) leads to dynamic controllers, even when the states of the plant are available for feedback. Using viability theory, Shamma showed (1993), in a nonconstructive way, that in the state-feedback case the same performance achieved by any dynamic linear time-invariant controller can be achieved using memoryless nonlinear state feedback. In this paper we give an alternative, constructive proof of these results for discrete- and continuous-time systems. The main result of the paper shows that in both cases, the l/sup 1/ norm achieved by any stabilizing state-feedback linear dynamic controller can be also achieved using a memoryless variable structure controller.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Just like the algebraic Riccati equations (AREs) or inequalities (ARIs) in the linear H[infinity] control theory, the Hamilton-Jacobi equations (HJEs) or inequalities (HJIs) play an essential role in the nonlinear H[infinity] control theory. In this thesis, a successive algorithm for finding an approximate solution of HJE is proposed. Using the existing nonlinear H[infinity] controller formulas, a numerical difficulty could be encountered when a critical assumption is not satisfied. We propose modified nonlinear H[infinity] controller formulas to eliminate the numerical difficulty. The proposed nonlinear H[infinity] controller is identical to the existing nonlinear H[infinity] controller if the assumption is satisfied, and its linear version will be the same as that designed by conventional linear H[infinity] approaches. An important application of the modified nonlinear H[infinity] controller formulas is the H[infinity] approximate input/output (I/O) linearization problem, which essentially is a nonlinear H[infinity] control problem without satisfying the critical assumption. Like the feedback I/O linearization, the H[infinity] approximate I/O linearization modifies a nonlinear system so that its I/O relationship resembles that of a linear system. However, the H[infinity] approximate I/O linearization can handle more general problem since it does not require minimum phase plant or full state feedback. The linearization technique together with [mu]-synthesis is used to design a robust nonlinear controller. An inverted pendulum control problem and a nonminimum phase longitudinal flight control problem are employed to illustrate the design of robust nonlinear controllers.

This paper is concerned with the nonlinear static state feedback stabilization of time-invariant linear multivariable continuous-time systems with friction driven backlash in the control inputs. A time-invariant static nonlinear state feedback compensator is proposed, easily obtainable solving an algebraic Riccati equation. The global asymptotic stability of the resulting closed-loop nonlinear system is proved using the Lyapunov's direct method and the La Salle's invariance principle. A simulation study shows that the proposed nonlinear state feedback compensator achieves an overall stabilization performance significantly better than the known backlash inverse compensator.

Feedback linearisation is perhaps the most important nonlinear control design strategy developed during the last few decades [5]. The main objective of the approach is to algebraically transform a nonlinear dynamic system into a linear dynamic system by using a static state feedback and a nonlinear coordinate transformation based on a differential geometric analysis of the system. By eliminating nonlinearities in the closed loop system, conventional linear control techniques can be applied. Our presentation of relative degree, normal forms, zero dynamics and feedback linearisation for nonlinear control affine systems given in Section 3.1 follows the notation that is used in the mainstream nonlinear control literature [5, 56]. The method of input-output feedback linearisation for nonlinear MIMO control affine systems, which is central in this book, is presented in Section 3.1.3. Other linearisation techniques, such as exact linearisation and Volterra linearisation, are reviewed in Section 3.2. Finally, two feedback linearisation techniques that are applicable to systems that are not control affine are briefly presented in Section 3.3.KeywordsRelative DegreeFeedback LinearisationCharacteristic MatrixZero DynamicDynamic Neural NetworkThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Ropeways must be stopped when there is strong cross-wind because the ensuing oscillations are a safety risk. In this paper, we developed a controller for an actuated mass onboard the gondola aiming to increase the gondola's damping, thus reducing the oscillations and permitting operation to continue. We modeled the gondola as a pendulum, acknowledged the limitation on the actuated mass' displacement, and included input and parametric uncertainty. We synthesized the controller through a two-step process. First, we used numerical optimization to compute a static full state feedback controller specifically designed to reduce the effects that cross-wind gusts and random disturbances have on the gondola. For this purpose, we included a wind model in the cost function. Then, we used this controller in a model to synthesize an H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> controller with reduced actuator requirements. Analysis of the linearized system showed that the proposed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> controller robustly stabilized the system despite the modeled uncertainty. Furthermore, it made the peak magnitude of the gondola's oscillations in the median of 1005 simulations 51.4 percent less than that of the uncontrolled system, and 19.3 percent less than that of the system using a passive dynamic vibration absorber.

A nonlinear feedback control for a flexible joint manipulator is investigated. It is shown that if the elastic (parasitic) modes are weakly observable from the output of the system, a state-space coordinate transformation and a static state feedback and control space transformation will turn the flexible system into a linear controllable and observable system. In contrast, if the parasitics are strongly observable, a dynamic state feedback is required for input-output linearization. Numerical simulations for a single link flexible joint manipulator are reported, illustrating the application of the methodology. >

Investigates the application of nonlinear H/sub /spl infin// control theory to flight vehicles whose complete six degree-of-freedom nonlinear equations of motion are considered directly without linearization. Nonlinear flight control modes such as velocity control, body-rate control, attitude control, and hovering control are designed in a unified framework such that the derived nonlinear H/sub /spl infin// control law is valid for arbitrary flight vehicles. The most difficult and challenging task involved in applying the nonlinear H/sub /spl infin// control theory is to solve the associated Hamilton-Jacobi partial differential inequality (HJPDI). In this paper we show that the HJPDI of flight control problems can be solved analytically with simple manipulations. A closed-form expression for the nonlinear H/sub /spl infin// flight controller is derived from the solution of HJPDI and shown to be in the simple structure of proportional feedback. The numerical simulations show that the derived nonlinear H/sub /spl infin// control law can ensure global and asymptotical stability of the closed loop system and have strong robustness against wind gusts with varying statistical characteristics.

This paper concentrates on the problem of H/sub /spl infin// control via measurement feedback with internal stability for discrete-time nonlinear systems. Using the theory of discrete-time dissipative systems and differential games, we first present a characterization of all static state feedback H/sub /spl infin// nonlinear controllers. Then, sufficient conditions are derived for the existence of a dynamic output compensator which solves the problem of disturbance attenuation with internal stability. >

This technical note focuses on finite-time rendezvous problems which refer to agreement on states in finite time within certain available information range. Using semistability theory for discontinuous dynamical systems, we develop a framework for designing finite-time semistable rendezvous protocols for multiagent dynamical systems. Specifically, we present distributed nonsmooth static state and dynamic output feedback controller architectures for finite-time rendezvous with a novel two-step proof of stability and finite-time convergence.

The standard state space solutions to the /spl Hscr//sub /spl infin// control problem for linear time-invariant systems are generalized to nonlinear time-invariant systems. A class of local nonlinear (output feedback) /spl Hscr//sub /spl infin//-controllers are parameterized as nonlinear fractional transformations on contractive, stable nonlinear parameters. As in the linear case, the /spl Hscr//sub /spl infin// control problem is solved by its reduction to state feedback and output estimation problems, together with a separation argument. Sufficient conditions for /spl Hscr//sub /spl infin//-control problem to be locally solved are also derived with this machinery. >

A survey of the authors' recent contributions are given to a new multi-constrained and multi-criteria optimization approach to the design of optimal compensators for general MIMO nonlinear feedback control systems in several practical considerations including such as robust stabilization with the presence of uncertainty, tracking and model matching, and disturbance rejection problems. First, the general framework for nonlinear closed-loop feedback systems is described in a Banach space setting in the time domain. Then, several typical optimal feedback design problems are formulated. Moreover, existence, uniqueness and characteristics theorems are established. Finally, a convergent recursive algorithm for solving the general constrained optimization is included.

A state feedback /spl Hscr//sub /spl infin//-suboptimal control problem on TSO(3) for a rigid spacecraft with three control torques and disturbances is addressed, the Hamilton-Jacobi inequality associated with a corresponding state feedback /spl Hscr//sub /spl infin//-suboptimal control problem on TS/sup 3/ is solved globally. The /spl Hscr//sub /spl infin//-suboptimal state feedback on TS/sup 3/ involves the Euler parameters and solves the original problem on TSO(3) when the initial values of the Euler parameters are appropriately chosen.

In this paper, an optimal controller is investigate d based on the Linear Quadratic Control method. The controller simulation is execut ed based on a small-scale autonomous model helicopter, Yamaha R-50. Genetic algorithms are employed to generate weighting matrices by optimizing the performance index of the control system. As a result, this method produces optimal weighting matrices which further improve the Linear Quadratic Controller. A full state feedback approach is used in the control design process. A Kalman observer is integrated into the controller to predi ct full state variables, since only a limited number of state variables are measured. Finally, th e performance of the controller is evaluated in the time domain with and without disturbances when the model helicopter is in hovering flight and forward flight. I. Introduction utonomous helicopters offer special advantages for major operations in both civilian and military sect ors, particularly in cases that are considered either in accessible or dangerous for human beings, due to th eir vertical take-off and landing (VTOL) capabilities. The contr ol system of autonomous helicopters plays a key rol e in its ability to carry out the assigned task effectively. This has lead to a growing interest in the design and analysis of the control system of autonomous helicopters. In 1990s, classic control theory was widely used for autonom ous helicopter control systems, which is mainly a succe ssive loop closure approach. The control gains are selected separately using tools such as Root locus, Bode and Nyquist plots. The controller parameters are usual ly tuned based on the controller performance measured either in ti me domain or in frequency domain. This design procedure becomes increasingly difficult as more and more loo ps are added, specifically, when the dynamics invol ve multiple inputs, multiple outputs, or multiple feedback loop s with complex performance criteria. To control an autonomous helicopter modeled as a complex Multiple Input Multiple Output (MIMO) system, the performance criteria can not be easily met by the approach based on classis cont rol theory. Several researchers have developed a number of diff erent ways for the control system design of autonom ous helicopters in the literature. Shim et al 1 presented three different control methods using li near robust, fuzzy logic, and nonlinear tracking controls, for an autonomous helicopter in hover and low speed flight. Johnson a nd Kannan 2