Peter H. Meckl

Optimized s-curve motion profiles for minimum residual vibration

A method for developing optimized point-to-point motion profiles to achieve fast motions with minimum vibration is presented. The proposed approach uses the well-known s-curve motion profiles, but optimizes the selection of the ramp-up (and ramp-down) time. The selection of ramp-up time is based on a frequency analysis that minimizes the excitation energy of the input forcing function at the system natural frequency. Simulation results on a lightly-damped system undergoing point-to-point motions demonstrate that the proposed approach decreases residual vibration by almost an order of magnitude over other approaches, even when the actual natural frequency is in error by 10%.

Robust motion control of flexible systems using feedforward forcing functions

Forcing functions are developed to produce vibration-free motions in flexible systems. These forcing functions are constructed from ramped simusoid basis functions so as to minimize excitation in a range of frequencies surrounding the system natural frequency. A closed-loop control system is developed which utilizes these forcing functions to generate a reference profile, and also feeds them forward directly to the system to enhance closed-loop bandwidth. Simulation results indicate superior vibration attenuation compared to the minimum-energy forcing function, especially when some error in natural frequency exists.

An analytical comparison of a neural network and a model-based adaptive controller

A neural network inverse dynamics controller with adjustable weights is compared with a computed-torque type adaptive controller. Lyapunov stability techniques, usually applied to adaptive systems, are used to derive a globally asymptotically stable adaptation law for a single-layer neural network controller that bears similarities to the well-known delta rule for neural networks. This alternative learning rule allows the learning rates of each connection weight to be individually adjusted to give faster convergence. The role of persistently exciting inputs in ensuring parameter convergence, often mentioned in the context of adaptive systems, is emphasized in relation to the convergence of neural network weights. A coupled, compound pendulum system is used to develop inverse dynamics controllers based on adaptive and neural network techniques. Adaptation performance is compared for a model-based adaptive controller and a simple neural network utilizing both delta-rule learning and the alternative adaptation law.

Controlling velocity-limited systems to reduce residual vibration

To avoid vibration of robot arms when they are moved very rapidly, a set of shaped force profiles have been developed to minimize the excitation energy at the systems first natural frequency during motion. The system is assumed to be velocity-limited. The force profiles are constructed from a versine (one-cosine) function and its harmonics, with coefficients chosen to minimize the spectral magnitude near the system natural frequency. The profiles can be tuned to the closed-loop natural frequency of a closed-loop system with motor position and velocity feedback. When integrated twice, the force profile becomes a reference trajectory which serves to bring the system to peak velocity with minimum excitation at the first natural frequency. Using a suitable dwell time between acceleration and deceleration, a specified position can be reached quickly with minimum residual vibration and within while never exceeding the velocity limit.<<ETX>>

Reducing residual vibration in systems with uncertain resonances

Robots that perform rapid motions tend to excite system resonant frequencies. To perform a sequence of tasks more quickly, the settling time required for the vibration to decay should be minimal. Input functions are derived that produce rapid open-loop moves with greatly reduced residual vibration amplitude. To accommodate errors in the assumed system natural frequency, these forcing function are constructed so that the magnitude of their frequency spectra remains sufficiently small over a range of frequencies that bound the system natural frequency by +or-10%. These input functions are derived as a series expansion of ramped sinusoid functions with coefficients chosen to minimize spectral magnitude in this frequency band. Some simulations are performed to indicate that these functions can reduce residual vibration considerably even when the assumed natural frequency is in error by 10%. These inputs can then serve as the basis for a closed-loop implementation to generate reference trajectories that minimally excite system resonances.<<ETX>>

Modeling of SMA Tendons for Active Control of Structures

The use of shape memory alloy (SMA) wires as active tendons to reduce vibra-tion of a building model is analytically investigated. Approximate dynamic equations for one bay of a multi-story building with SMA tendons are derived based on laws of thermodynamics and Brinsons constitutive equations. These equations are used to provide comparisons between us-ing SMA tendons passively and active for vibration control. In this model, the modes of transfor-mation considered are austenite to martensite (and detwinned martensite), martensite to detwinned martensite and martensite to austenite. In the active case, the wire opposing the direc-tion of the floor mass displacement is heated by passing a current through it to take advantage of the thermomechanical properties of SMAs. The current to a wire is shut off as soon as the tendon is 100% austenite. In the passive case, no current is supplied to the wire. A numerical integration program was developed to include internal and potential energy changes, input work into the ten-dons, and energy transfers associated with the latent heat of transformation. In this program, for numerical stability of the subroutine used, the current is shut off to the tendon as soon as the martensite volume fracture of that tendon goes below 0. 1%. Displacement profiles are presented for both the passive and active implementations of the SMA wire. Simulation results show a fac-tor of twelve improvements in steady state tracking error between the first floor and the base of the model structure when the tendons are used passively. The results are further improved by a factor of seven when the tendons are used actively. Also the effect of different cooling rates is ex-amined. Comparing tracking errors for the system using free convection and convection coeffi-cients of 80 and 100 W/m2K, it is shown that lower cooling rates can result in a reduction in tracking error.

Input shaping for nonlinear systems

Torque profiles that guarantee minimum residual vibration for point-to-point motions in a rigid-link flexible-joint manipulator have been developed using two different techniques: (1) the inverse dynamics formulation and, (2) an open-loop optimal approach. The torque profiles obtained by each technique are compared considering characteristics such as energy consumption, torque and trajectory profiles and sensitivity to parameter variations. Both methods produce torque profiles that achieve motion without residual vibration. The inverse dynamics formulation produces smoother link tip trajectories, while the optimal approach requires less input energy. Both methods are susceptible to parameter errors.

Intelligent feedforward control and payload estimation for a two-link robotic manipulator

Conventional model-based computed torque control fails to produce a good trajectory tracking performance in the presence of payload uncertainty and modeling error. The challenge is to provide accurate dynamics information to the controller. A new control architecture that incorporates a neural-network, fuzzy logic and a simple proportional-derivative (PD) controller is proposed to control an articulated robot carrying a variable payload. An off-line trained feedforward (multilayer) neural network takes payload mass estimates from a fuzzy-logic mass estimator as one of the inputs to represent the inverse dynamics of the articulated robot. The effectiveness of the proposed architecture is demonstrated by experiment on a two-link planar manipulator with changing payload mass. Experimental results show that this control architecture achieves excellent tracking performance in the presence of payload uncertainty.

Multivariable PI tuning for disturbance rejection and application to engine idle speed control simulation

In this paper, a new multivariable proportional-integral (PI) tuning strategy is developed and the advantage of the new design is illustrated in simulation on an internal combustion engine model. The multivariable control design technique developed here has disturbance rejection as its main objective rather than set-point tracking, which is the focus of most of the multivariable PI tuning techniques so far in the literature. The benefit of the new design is that it does not try to minimize cross couplings in the multivariable plant; instead it uses the cross couplings to achieve better disturbance rejection. The application of the control design method is in multivariable speed and air/fuel ratio control of a lean-burn natural gas engine to achieve smooth and effective idle speed regulation. When applied to a simulation model of the engine, the new PI tuning strategy effectively reduces speed undershoot during the application of a transient torque load during idle.

Model-Independent Control of a Flexible-Joint Robot Manipulator

Flexibility at the joint of a manipulator is an intrinsic property. Even “rigid-joint” robots, in fact, possess a certain amount of flexibility. Previous experiments confirmed that joint flexibility should be explicitly included in the model when designing a high-performance controller for a manipulator because the flexibility, if not dealt with, can excite system natural frequencies and cause severe damage. However, control design for a flexible-joint robot manipulator is still an open problem. Besides being described by a complicated system model for which the passivity property does not hold, the manipulator is also underactuated, that is, the control input does not drive the link directly, but through the flexible dynamics. Our work offers another possible solution to this open problem. We use three-layer neural networks to represent the system model. Their weights are adapted in real time and from scratch, which means we do not need the mathematical model of the robot in our control algorithm. All uncertainties are handled by variable-structure control. Backstepping structure allows input efforts to be applied to each subsystem where they are needed. Control laws to adjust all adjustable parameters are devised using Lyapunov’s second method to ensure that error trajectories are globally uniformly ultimately bounded. We present two state-feedback schemes: first, when neural networks are used to represent the unknown plant, and second, when neural networks are used to represent the unknown parts of the control laws. In the former case, we also design an observer to enable us to design a control law using only output signals—the link positions. We use simulations to compare our algorithms with some other well-known techniques. We use experiments to demonstrate the practicality of our algorithms.