Low-gain Control Research Articles

Time-Varying and Adaptive Discrete-Time Low-Gain Control of Infinite-Dimensional Linear Systems with Input Nonlinearities

Discrete-time low-gain control strategies are presented for tracking constant reference signals for infinite-dimensional, discrete-time, power-stable, linear systems subject to input nonlinearities. Both non-adaptive (but time-varying) and adaptive controls are considered. The discrete-time results are applied in the development of sampled-data integral control for infinite-dimensional, continuous-time, exponentially stable, regular, linear systems with input nonlinearities.

Near Optimal Tuning Rules for PI and PID Controllers

Abstract Tuning rules for PI and PID controllers for stable non oscillating plants are presented in this paper. These rules are based on an optimization procedure, where both low frequency performance, mid frequency stability margins and high frequency control activity are taken into account. The required plant knowledge is typically the phase crossover frequency of the plant and the corresponding gain at this frequency, like in Ziegler Nichols frequency design method. Near optimal tuning rules are presented based on this knowledge and the plant low frequency gain, both for PI and PID controllers. Related results are also given for plants with very high or no phase crossover frequency at all.

A Temperature Controller for VAV Air-Handling Units Based on Simplified Physical Models

A feedforward controller based on simplified physical models is described for air-handling units to supplement conventional PI control. Inverse static models of the controlled processes produce feedforward control action and the PI feedback loop compensates for modeling errors and unmeasured disturbances. The models are configurable from plant design information and they operate using the sensor signals typically available to an air-handling unit controller. The incorporation of feedforward control reduces the reliance on the feedback loop and makes the tuning of the PI controller less critical. Low gain (default) control parameters may then be used in the feedback loop, thereby eliminating the need for on-site tuning. This paper describes the control scheme and models, and presents results from tests carried out using a simulated air-handling unit.

A General Theorem on the Semiglobal Stabilization of Uncertain Nonlinear Systems via Measurement Feedback

In this paper we study the problem of semiglobally stabilizing uncertain nonlinear systems via measurement feedback. We give a general theorem for the regional stabilization of a class of uncertain nonlinear systems via measurement feedback. These systems are characterized by a nominal linear part and (measurable) uncertain nonlinear terms, which are known only up to some nonlinear bounds. The combination of our theorems gives sufficient conditions for semiglobal stabilization via high and low-gain control laws, recovering well-known results for the case of uncorrupted outputs and saturated inputs.

A Design Method of Disturbance Observer to Cope with Frequency Variation

A well known control system which can reduce the adverse effect of a periodic disturbance with single frequency is the disturbance obsever. However, in many cases of industrial systems disturbance frequency is varied for some frequency range. Therefore, it may be difficult to reduce the adverse effect of the disturbance by the use of the traditional disturbance observer.In this paper, a design method of new disturbance observer which can cope with the frequency variation is proposed. The main idea of this design method is to synthesize the disturbance observer as a gain-scheduled controller. The proposed disturbance observer is constructed as low degree and low gain controller with superior steadystate characteristic. As compared with the traditional disturbance observer and the H∞ controller, the usefulness of the proposed disturbance observer was shown by numerical simulations.

Stability of Actively Controlled Structures with Actuator Saturation

Because of the stochastic nature of earthquakes and limited capacities of actuators, it is conceivable that the actuators used for the control of civil engineering structures may be saturated during strong earthquakes. In this paper, the stability of actively controlled linear structures under a variety of popular control methods during actuator saturation is investigated. Sufficient conditions to guarantee the asymptotic stability of the structure during actuator saturation are examined and discussed. These conditions involve the solution of a system of simultaneous linear matrix inequalities (LMI). A simple and efficient computer code to solve a system of LMI, based on the MATLAB LMI toolbox, is presented for use by the readers. Based on sufficient conditions, a method for designing general controllers, that guarantee asymptotic stability during actuator saturation, is presented. It is shown analytically that Lyapunov controllers, H∞-type controllers, and sliding-mode controllers are asymptotically stable during actuator saturation. For multi–degrees-of-freedom (MDOF) systems using pole assignment and linear quadratic regulator (LQR) controllers, it has been shown through extensive simulations results that: (1) asymptotic stability of structures is more likely to be guaranteed for low-gain controllers than for high-gain controllers; (2) adding active damping to the structure is much more beneficial than adding active stiffness, in terms of asymptotic stability; and (3) asymptotic stability can be guaranteed for quite high levels of added active damping to various modes of the structure. Further extensive simulation results demonstrate that static output feedback controllers using only velocity feedback are always asymptotically stable in the range of practical applications. Likewise, for static output controllers using collocated sensors, the region of asymptotic stability is quite large.

Discrete-time low-gain control of uncertain infinite-dimensional systems

Using a frequency-domain analysis, it is shown that the application of a feedback controller of the form k/(z-1) or kz/(z-1), where k/spl isin/R, to a power-stable infinite-dimensional discrete-time system with square transfer-function matrix G(z) will result in a power-stable closed-loop system which achieves asymptotic tracking of arbitrary constant reference signals, provided that i) all the eigenvalues of G(1) have positive real parts, and ii) the gain parameter k is positive and sufficiently small, Moreover, if G(1) is positive definite, we show how the gain parameter gain X can be tuned adaptively. The resulting adaptive tracking controllers are universal in the sense that they apply to any power-stable system with G(1)>0; in particular, they are not based on system identification or plant parameter estimation algorithms, nor is the injection of probing signals required. Finally, we apply these discrete-time results to obtain adaptive sampled-data low-gain controllers for the class of regular systems, a rather general class of infinite-dimensional continuous-time systems for which convenient representations are known to exist, both in state space and in frequency domain. We emphasize that our results guarantee not only asymptotic tracking at the sampling instants but also in the sampling interval.

Low-Gain Control of Uncertain Regular Linear Systems

It is well known that closing the loop around an exponentially stable, finite-dimensional, linear, time-invariant plant with square transfer-function matrix $\BG(s)$ compensated by a controller of the form $(k/s)\Gamma_0$, where $k\in {\Bbb R}$ and $\Gamma_0in {\Bbb R}\mm$, will result in an exponentially stable closed-loop system which achieves tracking of arbitrary constant reference signals, provided that (i) all the eigenvalues of $\BG(0)\Gamma_0$ have positive real parts and (ii) the gain parameter k is positive and sufficiently small. In this paper we consider a rather general class of infinite-dimensional linear systems, called regular systems, for which convenient representations are known to exist, both in time and in frequency domain. The purpose of the paper is twofold: (i) we extend the above result to the class of exponentially stable regular systems and (ii) we show how the parameters k and $\Gamma_0$ can be tuned adaptively. The resulting adaptive tracking controllers are not based on system identification or parameter estimation algorithms, nor is the injection of probing signals required.

ON LINEAR-SATURATION (LS) CONTROL OF BUILDINGS

This paper proposes the Linear-Saturation (LS) control as a new and suitable control algorithm for buildings with an Active Mass Damper (AM D) system. It takes into account the physical constraints on the AMD system and uncertainties in the loading. The LS control consists of a low-gain linear control when the system is close to the zero state and bang-bang control otherwise. This paper provides a precise formulation of the saturation control and presents optimal solutions which can be implemented in the state space. A numerical scheme to synthesize the switching surface which is needed to implement the bang-bang control is developed. Furthermore, a method to demarcate the region for linear control is proposed. The effectiveness of the LS control is verified through numerical simulations with one- and multi-storey buildings subjected to earthquakes. It is shown that the LS control provides better performance compared to even the gain-scheduled LQ control.

LQR for State-Bounded Structural Control

In order to prevent structural damages, it is more important to bound the vibration amplitude than to reduce the vibration energy. However, in the performance index for linear quadratic regulator (LQR), the instantaneous amplitude of vibration is not minimized. An ordinary LQR may have an unacceptable amplitude at some time instant but still have a good performance. In this paper, we have developed an LQR with adjustable gains to guarantee bounds on the vibration amplitude. For scalar systems, the weighting for control is switched between two values which give a low-gain control when the amplitude is inside the bound and a high-gain control when the amplitude is going to violate the given bound. For multivariable systems, by assuming a matching condition, a similar controller structure has been obtained. This controller is favored for application since the main structure of a common LQR is not changed; the additional high-gain control is required only if the vibration amplitude fails to stay inside the bound. We have applied this controller to a five-story building with active tendon controllers. The results show that the largest oscillation at the first story stays within a given bound when the building is subject to earthquake excitation.

Generalized PI controllability

Integral controllable systems can be stabilized by all sufficiently low-gain integral controllers. The concept of integral controllability is extended to two generalized stability regions and to proportional controllability and PI controllability with respect to those regions. Furthermore, closed eigenvalue formulae are derived for the maximal low integral gain and the maximal low proportional gain for generalized stability. Related eigenvalue formulae are then used in combination to find all low-gain PI controllers that place the closed-loop eigenvalues in the desired region.

Linear-quadratic-gaussian synthesis with reduced parameter sensitivity

We present a method for improving the tolerance of a conventional LQG controller to parameter errors in the plant model. The improvement is achieved by introducing additional terms reflecting the structure of the parameter errors into the LQR cost function, and also the process and measurement noise models. Adjusting the sizes of these additional terms permits a trade-off between robustness and nominal performance. Manipulation of some of the additional terms leads to high gain controllers while other terms lead to low gain controllers. Conditions are developed under which the high-gain approach asymptotically recovers the robustness of the corresponding full-state feedback design, and the low-gain approach makes the closed-loop poles asymptotically insensitive to parameter errors.

A study of a servo damper with a preview action. A principle of vibration control by a preview action.

This paper deals with an active control of an impact vibration using a preview control. It is the purpose of this paper to realize a servo damper system with the preview control and to verify the capability of suppressing the impact vibration. First, with a view to clarifying the mechanism of a vibration control by preview action, this paper presents a control chart to estimate the preview control effect. Then, based upon the control chart, the superiority of the preview control over a feedforward control is discussed. Next, by placing an emphasis on realizing the servo damper system, a preview control element is modified to be an approximate integral form, with the result that a low gain control element is obtained. Moreover, a hybrid control compensator is proposed, which consists of a digital and an analog component ; that is, one to control a preview time and the other to calculate the control signal. Finally, an experiment is carried out, demonstrating the control effect of the servo damper system with the preview control.

Low-gain control of unknown infinite-dimensional systems: a frequency-domain approach

This paper presents a frequency-domain based input-output theory of multivariable low-gain Pl-control of infinite-dimensional stable systems. It is known that under very mild assumptions a large class of infinite-dimensional systems can be stabilized and regulated by multivariable Pl-controUers with sufficiently low gain. The controller design can be accomplished using plant step data only. No other knowledge of the plant is required. The application of the input-output results to distributed parameter systems and neutral systems is discussed.