Linear Quadratic Regulator Optimal Control Research Articles

Semiactive Control of Nonlinear Isolated Bridges with Time Delay

The effectiveness of semiactive control using variable dampers is studied for nonlinear isolated bridges, which exhibit inelastic response at both the columns and the isolators, under near-field ground motions. The linear quadratic regulator optimal control algorithm is used to command variable dampers. Time delay is inevitable in the operation of control systems and may deteriorate the control performance. A time-delay compensation method based on the Newmark's method is proposed to mitigate the degradation of control performance due to time delay. A five-span viaduct with high-damping-rubber isolators is utilized for analysis. The results show that semiactive control with variable dampers is effective in reducing the seismic response and provides the similar performance by linear quadratic regulator active control. The semiactive control also shows similar or better performance than the passive control with the maximum damping coefficient of the variable damper. The proposed Newmark compensation method shows superior compensation performance on the time-delayed nonlinear system under semiactive control.

Closed-loop optimal control-enabled piezoelectric microforce sensors

This paper presents a closed-loop optimally controlled force-sensing technology with applications in both micromanipulation and microassembly. The microforce-sensing technology in this paper is based on a cantilevered composite beam structure with embedded piezoelectric polyvinylidene fluoride (PVDF) actuating and sensing layers. In this type of sensor, the application of an external load causes deformation within the PVDF sensing layer. This generates a signal that is fed through a linear quadratic regulator (LQR) optimal servoed controller to the PVDF actuating layer. This in turn generates a balancing force to counteract the externally applied load. As a result, a closed feedback loop is formed, which causes the tip of this highly sensitive sensor to remain in its equilibrium position, even in the presence of dynamically applied external loads. The sensor's stiffness is virtually improved as a result of the equilibrium position whenever the control loop is active, thereby enabling accurate motion control of the sensor tip for fine micromanipulation and microassembly. Furthermore, the applied force can be determined in real time through measurement of the balance force

Panel flutter suppression with an optimal controller based on the nonlinear model using piezoelectric materials

This work intends to develop an optimal control strategy to suppress the flutter of a supersonic composite panel using piezoelectric actuators. In this study, an optimal control design based on the nonlinear model is investigated in order to obtain the higher maximum suppressible dynamic pressure with a lower control input as compared to a controller based on the linear model. The actuator for the suppression of panel flutter is implemented by using piezoceramic PZT and the shape and location of the PZT patches are determined by using genetic algorithms. The governing equations are derived through the use of the principle of virtual displacements and a finite element discretization is performed with the C 1 conforming rectangular element. The discretized dynamic equations of motion are transformed into a nonlinear coupled-modal equation by using the proper modal coordinates and the nonlinear coupled-modal equations are then transformed into a state space model in order to design controller. Linear quadratic regulator (LQR) optimal control scheme is employed to determine the feedback gain. The flutter suppression results by an optimal controller based on the linear and nonlinear model are compared in the time domain using the Newmark- β method for a simply supported piezolaminated composite panel subjected to uniform thermal loading. As the time advances by the time integration, since the system matrix is the function of nonlinear modal stiffness matrix, the system matrix also is modified after each iteration within each time step. The results show that an optimal controller based on the nonlinear equation effectively attenuate the flutter to a relatively higher dynamic pressure with a lower control input as compared to a controller based on the linear model.

Panel flutter suppression with an optimal controller based on the nonlinear model using piezoelectric materials

This work intends to develop an optimal control strategy to suppress the flutter of a supersonic composite panel using piezoelectric actuators. In this study, an optimal control design based on the nonlinear model is investigated in order to obtain the higher maximum suppressible dynamic pressure with a lower control input as compared to a controller based on the linear model. The actuator for the suppression of panel flutter is implemented by using piezoceramic PZT and the shape and location of the PZT patches are determined by using genetic algorithms. The governing equations are derived through the use of the principle of virtual displacements and a finite element discretization is performed with the C1 conforming rectangular element. The discretized dynamic equations of motion are transformed into a nonlinear coupled-modal equation by using the proper modal coordinates and the nonlinear coupled-modal equations are then transformed into a state space model in order to design controller. Linear quadratic regulator (LQR) optimal control scheme is employed to determine the feedback gain. The flutter suppression results by an optimal controller based on the linear and nonlinear model are compared in the time domain using the Newmark-β method for a simply supported piezolaminated composite panel subjected to uniform thermal loading. As the time advances by the time integration, since the system matrix is the function of nonlinear modal stiffness matrix, the system matrix also is modified after each iteration within each time step. The results show that an optimal controller based on the nonlinear equation effectively attenuate the flutter to a relatively higher dynamic pressure with a lower control input as compared to a controller based on the linear model.

FINITE ELEMENT FORMULATION AND ACTIVE VIBRATION CONTROL STUDY ON BEAMS USING SMART CONSTRAINED LAYER DAMPING (SCLD) TREATMENT

This work deals with the active vibration control of beams with smart constrained layer damping (SCLD) treatment. SCLD design consists of viscoelastic shear layer sandwiched between two layers of piezoelectric sensors and actuator. This composite SCLD when bonded to a vibrating structure acts as a smart treatment. The sensor piezoelectric layer measures the vibration response of the structure and a feedback controller is provided which regulates the axial deformation of the piezoelectric actuator (constraining layer), thereby providing adjustable and significant damping in the structure. The damping offered by SCLD treatment has two components, active action and passive action. The active action is transmitted from the piezoelectric actuator to the host structure through the viscoelastic layer. The passive action is through the shear deformation in the viscoelastic layer. The active action apart from providing direct active control also adjusts the passive action by regulating the shear deformation in the structure. The passive damping component of this design eliminates spillover, reduces power consumption, improves robustness and reliability of the system, and reduces vibration response at high-frequency ranges where active damping is difficult to implement. A beam finite element model has been developed based on Timoshenko's beam theory with partially covered SCLD. The Golla–Hughes–McTavish (GHM) method has been used to model the viscoelastic layer. The dissipation co-ordinates, defined using GHM approach, describe the frequency-dependent viscoelastic material properties. Models of PCLD and purely active systems could be obtained as a special case of SCLD. Using linear quadratic regulator (LQR) optimal control, the effects of the SCLD on vibration suppression performance and control effort requirements are investigated. The effects of the viscoelastic layer thickness and material properties on the vibration control performance are investigated.

Active–passive hybrid damping in beams with enhanced smart constrained layer treatment

This paper deals with the assessment of vibration control performance using enhanced smart constrained layer damping (ESCLD) treatment with edge elements. A beam finite element model has been developed based on Timoshenko beam theory with partially covered ESCLD. The edge elements are modeled as equivalent springs mounted at the boundaries of the piezoelectric layer. The Golla–Hughes–McTavish (GHM) method has been used to model the viscoelastic layer. The model is validated against published experimental results. Using linear quadratic regulator (LQR) optimal control, the effects of the ESCLD on vibration suppression performance and control effort requirements are investigated. Analysis shows that edge elements significantly improve the active action transmissibility of the SCLD treatment. Due to combined overall active and passive actions, the ESCLD treatment with sufficiently stiff edge elements could outperform both the SCLD treated system and the purely active system.

Analysis of robust pole clustering in a sector region for uncertain LQR control systems

This paper presents a general analysis of robust pole clustering in a sector region for uncertain H 2 optimal linear quadratic regulator (LQR) control systems. Control system poles located in a sector region of the left half-plane provide a good performance, such as the transient behavior, overshoot, damping ratio and so on, for control systems. The general Lyapunov theory and Rayleigh principle along the norm theory are applied to analyze robust pole clustering. The H 2 optimal state feedback LQR control systems are considered. The concerned uncertainties are both unstructured and structured uncertainties, including interval matrices. The preservation of H 2 optimality of the LQR in face of uncertainties is discussed. The results are useful for analysis and design of robust control combining robust stability and robust performance.

Stochastic optimal LQR control with integral quadratic constraints and indefinite control weights

A standard assumption in traditional (deterministic and stochastic) optimal (minimizing) linear quadratic regulator (LQR) theory is that the control weighting matrix in the cost functional is strictly positive definite. In the deterministic case, this assumption is in fact necessary for the problem to be well-posed because positive definiteness is required to make it a convex optimization problem. However, it has recently been shown that in the stochastic case, when the diffusion term is dependent on the control, the control weighting matrix may have negative eigenvalues but the problem remains well-posed. In this paper, the completely observed stochastic LQR problem with integral quadratic constraints is studied. Sufficient conditions for the well-posedness of this problem are given. Indeed, we show that in certain cases, these conditions may be satisfied, even when the control weighting matrices in the cost and all of the constraint functionals have negative eigenvalues. It is revealed that the seemingly nonconvex problem (with indefinite control weights) can actually be a convex one by virtue of the uncertainty in the system. Finally, when these conditions are satisfied, the optimal control is explicitly derived using results from duality theory.

Arm-free paraplegic standing--Part I: Control model synthesis and simulation.

The following paper is the first part of our investigation into the feasibility of arm-free paraplegic standing. A novel control strategy for unsupported paraplegic standing which utilizes the residual sensory and motor abilities of the thoracic spinal cord injured subjects is proposed. The strategy is based on voluntary and reflex activity of the paraplegic person's upper body and artificially controlled stiffness in the ankles. The knees and hips are maintained in an extended position by functional electrical stimulation (FES). The analysis of a linearized double inverted pendulum model revealed that with properly selected ankle stiffness the system can be easily stabilized. We developed a closed-loop double inverted pendulum model including a neural system delay, trunk muscles dynamics, body segmental dynamics and linear quadratic regulator (LQR) optimal controller. Through simulations of the closed-loop model two different strategies for disturbance rejection were explained. We investigated the capability of the closed-loop model to reject disturbances, imposed at the ankle joint (in anterior and posterior directions) for various stiffness levels and neural system delays in the presence of biomechanical constraints. By limiting permissible excursions of the center of pressure, we found out that the length of the foot is the most important constraint, while the strength of the trunk muscles is not of major importance for successful balancing. An ankle stiffness of approximately 10 Nm/degree suffices for arm-free standing of paraplegic subjects.

On the Active-Passive Hybrid Control Actions of Structures With Active Constrained Layer Treatments

This paper is concerned with the analysis of active and passive hybrid actions in structures with active constrained damping layers (ACL). A system model is derived via Hamilton’s Principle, based on the constitutive equations of the elastic, viscoelastic, and piezoelectric materials. The model converges to a purely active piezotronic system as the thickness of the viscoelastic material (VEM) layer approaches zero. A mixed Galerkin-GHM (Golla-Hughes-McTavish) method is employed to discretize and analyze the model in time domain. With an LQR (linear quadratic regulator) optimal control, the effects of the active constrained layer configuration on the system vibration suppression performance and control effort requirements are investigated. Analysis illustrates that the active piezoelectric action with proper feedback control will always enhance the damping ability of the passive constrained layer. When compared to a purely active configuration, while the viscoelastic layer of the ACL treatment will enhance damping, it will also reduce the direct control authorities (active action transmissibility) from the active source to the host structure. Therefore, whether the ACL treatment is better than a purely active configuration depends on whether the effect of damping enhancement is greater than that of transmissibility reduction caused by the VEM layer. The significance of these effects depends very much on the viscoelastic layer thickness and material properties. With some parameter combinations, the ACL configuration could require more control effort while achieving less vibration reductions compared to a purely active system. Through analyzing the performance and control effort indices, the conditions where this active-passive hybrid approach can outperform both the passive and active configurations are quantified. Based on this study, design guidelines can be set up to effectively integrate the host structure with the piezoelectric and viscoelastic materials, such that a truly beneficial active-passive hybrid control system could be achieved.

Dynamics and control of a space station based Tethered Elevator System

A mathematical model is proposed for studying planar dynamics of a space station based Tethered Elevator System. The model accounts for finite dimensions of the station, offset of the tether attachment point from the station's mass center, and crawling motion of the elevator to or from a platform supported by the fixed length tether. The tether, assumed massless but elastic, is modeled as a double pendulum, while the elevator, end platform and moving offset attachment are treated as point masses. The system center of mass is assumed to follow an arbitrary elliptic orbit. The governing equations of motion, obtained using the Lagrangian procedure, are coupled, nonlinear, nonautonomous, and rather lengthy. Numerical results are given for the rigid tether model with the system mass center following a circular orbit. Simulation of the uncontrolled dynamics suggests that elevator maneuvers can excite unacceptably large amplitude station and tether pitch oscillations, which persist due to the absence of damping. An optimal Linear Quadratic Regulator control strategy is applied in conjunction with two distinctly different types of actuators: (i) thruster control ( T α , T γ ); and (ii) offset-thruster control ( E x , T y ); in presence of the station based momentum gyro output M ψ . Results show that both the schemes are effective during stationkeeping, but the elevator thruster ( T α ) is required during its rapid retrieval. A hybrid controller which utilizes both the thruster and offset strategies offers advantages from safety considerations.

A ball balancing demonstration of optimal and disturbance-accomodating control

The modeling, analysis, and design of a ball-balancing control system are considered. An optimal linear regulator control system is constructed, and an optimal hybrid controller capable of absorbing external disturbance is implemented. The controller design is based on the theory of disturbance-accommodating control, optimal linear quadratic regulator control, and a digital delayed-data observer. Experimental results presented are useful for demonstrating practical aspects of the analysis. Furthermore, the ball-balancing control system developed is ideal for demonstrating the design and hardware implementation of optimal controllers based on modern control theory.