Analysis of the energy‐based swing‐up control for the double pendulum on a cart

Designing and analyzing controllers for mechanical systems with underactuation degree (difference between the number of degrees of freedom and that of inputs) greater than one is a challenging problem. In this paper, for the double pendulum on a cart, which has three degrees of freedom and only one control input, we study an unsolved problem of analyzing the energy‐based swing‐up control which aims at controlling the total mechanical energy of the cart‐double‐pendulum system, the velocity and displacement of the cart. Under the energy‐based controller, we show that for all initial states of the cart‐double‐pendulum system, the velocity and displacement of the cart converge to their desired values. Then, by using a property of the mechanical parameters of the double pendulum, we show that if the convergent value of the total mechanical energy is not equal to the potential energy at the up–up equilibrium point, where two links are in the upright position, then the system remains at the up–down, down–up, and down–down equilibrium points, where two links are in the upright–down, down–upright, and down–down positions, respectively. Moreover, we show that each of these three equilibrium points is strictly unstable in the closed‐loop system by showing that the Jacobian matrix valued at each equilibrium point has at least one eigenvalue in the open right half plane. This shows that for all initial states with the exception of a set of Lebesgue measure zero, the total mechanical energy converges to the potential energy at the up–up equilibrium point. This paper provides insight into the energy‐based control approach to mechanical systems with underactuation degree greater than one. Copyright © 2010 John Wiley & Sons, Ltd.     

Globally stable PID-like control of mechanical systems

Decoupled PID control with actuator constraints and velocity measurement or estimation achieves global asymptotic stability of the desired configuration, if there is some friction in the controlled mechanical system and the signals to be integrated are limited accordingly. Stability analysis using the direct Lyapunov method and Gershgorin's “circle theorem” gives these limits and physically meaningful lower bounds on position control gains. A simple procedure is proposed for selecting the design parameters and determining the gains of the controllers.     

A “mixed” small gain and passivity theorem in the frequency domain

We show that the negative feedback interconnection of two causal, stable, linear time-invariant systems, with a “mixed” small gain and passivity property, is guaranteed to be finite-gain stable. This “mixed” small gain and passivity property refers to the characteristic that, at a particular frequency, systems in the feedback interconnection are either both “input and output strictly passive”; or both have “gain less than one”; or are both “input and output strictly passive” and simultaneously both have “gain less than one”. The “mixed” small gain and passivity property is described mathematically using the notion of dissipativity of systems, and finite-gain stability of the interconnection is proven via a stability result for dissipative interconnected systems.     

Global stabilization of an inverted pendulum-Control strategy and experimental verification

The problem of swinging up an inverted pendulum on a cart and controlling it around the upright position has traditionally been treated as two separate problems. This paper proposes a control strategy that is globally asymptotically stable under actuator saturation and, in addition, locally exponentially stable. The proposed methodology, which performs swing up and control simultaneously, uses elements from input-output linearization, energy control, and singular perturbation theory. Experimental results on a laboratory-scale setup are presented to illustrate the approach and its implementation.     

Systematic design method of stabilization fuzzy controllers for pendulum systems

A systematic method to construct stabilization fuzzy controllers for a single pendulum system and a series-type double pendulum system is presented based on the single input rule modules (SIRMs) dynamically connected fuzzy inference model. The angle and angular velocity of each pendulum and the position and velocity of the cart are selected as the input items. Each input item is given with a SIRM and a dynamic importance degree. All the SIRMs have the same rule setting. The dynamic importance degrees use the absolute value(s) of the angle(s) of the pendulum(s) as the antecedent variable(s). The dynamic importance degrees are designed such that the upper pendulum angular control takes the highest priority and the cart position control takes the lowest priority when the upper pendulum is not balanced upright. The control priority orders are automatically adjusted according to control situations. The simulation results show that the proposed fuzzy controllers have high generalization ability to completely stabilize a wide range of single pendulum systems and series-type double pendulum systems in short time. By extending the architecture, a stabilization fuzzy controller for a series-type triple pendulum system is even possible. © 2001 John Wiley & Sons, Inc.     

Stabilization of the inverted pendulum around its homoclinic orbit

The inverted pendulum has been used as a benchmark for motivating the study of nonlinear control techniques. We propose a simple controller for balancing the inverted pendulum and raise it to its upper equilibrium position while the cart displacement is brought to zero. The control strategy is based on an energy approach of the cart and pendulum system.     

Design of motion trajectory and tracking control for underactuated cart‐pendulum system

A cart‐pendulum system is a nonlinear underactuated mechanical system with two degrees of freedom. This paper addresses the motion trajectory design and tracking control problems for this underactuated system. First, a friction‐like control law is designed for the system. Then, the characteristics of the closed‐loop control system are analyzed. Second, a new method of constructing an optimal trajectory for the system is developed. Then, a tracking control law is designed to quickly track the constructed trajectory. It guarantees that the motion control of the cart‐pendulum system is achieved along a reference trajectory. Finally, a numerical example is presented to demonstrate the effectiveness of the theoretical results. This study constructs an optimal trajectory for the cart‐pendulum system in its whole motion space and solves the motion control objective by tracking the constructed trajectory. It has many advantages compared with other motion control methods, eg, the optimal motion control objective of the system is achieved by a single control law; and the motion process and transient characteristics (eg, the settling time) of the control system can be accurately predicted.     

Comparison of input signals in subspace identification of multivariable ill-conditioned systems

Ill-conditioned processes often produce data of low quality for model identification in general, and for subspace identification in particular, because data vectors of different outputs are typically close to collinearity, being aligned in the “strong” direction. One of the solutions suggested in the literature is the use of appropriate input signals, usually called “rotated” inputs, which must excite sufficiently the process in the “weak” direction. In this paper open-loop (uncorrelated and rotated) random signals are compared against inputs generated in closed-loop operation, with the aim of finding the most appropriate ones to be used in multivariable subspace identification of ill-conditioned processes. Two multivariable ill-conditioned processes are investigated and as a result it is found that closed-loop identification gives superior models, both in the sense of lower error in the frequency response and in terms of higher performance when used to build a model predictive control system.     

When success turns into failure: a package-driven business process re-engineering project in the financial services industry

This article discusses a Business Process Re-engineering project that involved the implementation of an enterprise resource planning software package. Although the project was deemed to be a success when the system was first delivered, this initial success soon turned to failure. While the short-term financial results were spectacular, the long-term implications of the changes were more worrying. This paper raises many questions about the meaning of “success.” In particular, it shows how a “successful implementation” can, within a relatively short space of time, turn into failure.     

Critical success factors revisited: success and failure cases of information systems for senior executives

The literature suggests the existence of critical success factors (CSFs) for the development of information systems that support senior executives. Our study of six organizations gives evidence for this notion of CSFs. The study further shows an interesting pattern, namely that companies either “get it right”, and essentially succeed on all CSFs, or “get it completely wrong”, that is, fall short on each of the CSFs. Among the six cases for which data were collected through in-depth interviews with company executives, three organizations seemed to manage all the CSFs properly, while two others managed all CSFs poorly. Only one organization showed a mixed scorecard, managing some factors well and some not so well. At the completion of the study, this organization could neither be judged as a success, nor as a failure. This dichotomy between success and failure cases suggests the existence of an even smaller set of “meta-success” factors. Based on our findings, we speculate that these “meta-success” factors are “championship”, “availability of resources”, and “link to organization objectives”.     

Optimal operation of Petlyuk distillation: steady-state behavior

The “Petlyuk” or “dividing-wall” or “fully thermally coupled” distillation column is an interesting alternative to the conventional cascaded binary columns for separation of multi-component mixtures. However, the industrial use has been limited, and difficulties in operation have been reported as one reason. With three product compositions controlled, the system has two degrees of freedom left for on-line optimization. We show that the steady-state optimal solution surface is quite narrow, and depends strongly on disturbances and design parameters. Thus it seems difficult to achieve the potential energy savings compared to conventional approaches without a good control strategy. We discuss candidate variables which may be used as feedback variables in order to keep the column operation close to optimal in a “self-optimizing” control scheme.     

A feedforward–feedback glucose control strategy for type 1 diabetes mellitus

As the “artificial pancreas” becomes closer to reality, automated insulin delivery based on real-time glucose measurements becomes feasible for people with diabetes. This paper is concerned with the development of novel feedforward–feedback control strategies for real-time glucose control and type 1 diabetes. Improved post-meal responses can be achieved by a pre-prandial snack or bolus, or by reducing the glucose setpoint prior to the meal. Several feedforward–feedback control strategies provide attractive alternatives to the standard meal insulin bolus and are evaluated in simulations using a physiological model.     

Stability and performance analysis of mixed product run-to-run control

Run-to-run control has been widely used in batch manufacturing processes to reduce variations. However, in batch processes, many different products are fabricated on the same set of process tool with different recipes. Two intuitive ways of defining a control scheme for such a mixed production mode are (i) each run of different products is used to estimate a common tool disturbance parameter, i.e., a “tool-based” approach, (ii) only a single disturbance parameter that describe the combined effect of both tool and product is estimated by results of runs of a particular product on a specific tool, i.e., a “product-based” approach. In this study, a model two-product plant was developed to investigate the “tool-based” and “product-based” approaches. The closed-loop responses are derived analytically and control performances are evaluated. We found that a “tool-based” approach is unstable when the plant is non-stationary and the plant-model mismatches are different for different products. A “product-based” control is stable but its performance will be inferior to single product control when the drift is significant. While the controller for frequent products can be tuned in a similar manner as in single product control, a more active controller should be used for the infrequent products which experience a larger drift between runs. The results were substantiated for a larger system with multiple products, multiple plants and random production schedule.     

A new controller for the inverted pendulum on a cart

This paper presents a complete solution to the problem of swinging‐up and stabilization of the inverted pendulum on a cart, with a single control law. The resulting law has two parts: first, an energy‐shaping law is able to swing and maintain the pendulum up. Then, the second part introduces additional control to stop the cart and it is based on forwarding control with bounded input. The resulting control law is the sum of both parts and does not commute between different laws although there exist switches inside the controller. Copyright © 2008 John Wiley & Sons, Ltd.     

Control design for recycled, multi unit processes

An integrated multi-unit chemical plant presents a challenging control design problem due to the existence of recycling streams. In this paper, we develop a framework for analyzing the effects of recycling dynamics on closed-loop performance from which a systematic design of a decentralized control system for a recycled, multi-unit plant is established. In the proposed approach, the recycled streams are treated as unmodelled dynamics of the “unit” model so that their effects on closed-loop stability and performance can be analyzed using the robust control theory. As a result, two measures are produced: (1) the ν-gap metric, which quantifies the strength of recycling effects, and (2) the maximum stability margin of “unit” controller, which represents the ability of the “unit” controller to compensate for such effects. A simple rule for the “unit” control design is then established using the combined two measures in order to guarantee the attainment of good overall closed-loop performances. As illustrated by several design examples, the controllability of a recycled, multi unit process under a decentralized “unit” controller can be determined without requiring any detailed design of the “unit” controller because the simple rule is calculated from the open-loop information only.     

Teaching programming: A spiral approach to syntax and semantics

Coupling the recently proposed syntactic/semantic model of programmer behavior [1] with classic educational psychological theories yields new insights to teaching programming to novices. These new insights should make programming education more natural to students. alleviate “computer shock” (the analog of “math anxiety” [2]) and promote the development of widespread “computer literacy”.The spiral approach is the parallel acquisition of syntactic and semantic knowledge in a sequence which provokes student interest by using meaningful examples, builds on previous knowledge, is in harmony with the student's cognitive skills, provides reinforcement of recently acquired material and develops confidence through successful accomplishment of increasingly difficult tasks. The relationship of structured programming and flowcharts to the spiral approach is discussed.     

Limited communication control

This work in limited communication control is directed towards bringing together classical control theory and communication theoretical issues that are of practical importance in the design of control systems. It is common to “decouple” the communication aspects from the underlying dynamics of a system, as this simplifies the analysis and generally works well for classical models. However, in situations where a single decision maker controls many subsystems over a communication channel of a finite capacity, the computation of control signals and their transmission to each system may take significant amounts of time. To address such cases, we consider a class of discrete-time models that jointly optimize over control and communication goals. Real-world examples where these models play a role include remotely controlled unmanned autonomous vehicles (UAVs), planetary rovers, arrays of microactuators and power control in mobile communication.     

Soft-computing combining of distributed power control algorithms

In traditional distributed power control (DPC) algorithms, every user in the system is treated in the same way, i.e., the same power control algorithm is applied to every user in the system. In this paper, we divide the users into different groups depending on their channel conditions and use different DPC accordingly. Our motivation comes from the fact that different DPC algorithms have its own advantages and drawbacks, and our aim in this paper is to “combine” the advantages of different DPC algorithms, and we use soft computing techniques for that. In the simulations results, we choose Foschini and Miljanic Algorithm in [3], which has relatively fast convergence but is not robust against time-varying link gain changes and CIR estimation errors, and fixed step algorithm of Kim [3], which is robust but its convergence is slow. By “combining” these two algorithms using soft computing techniques, the resulting algorithm has fast convergence and is robust. Acknowledgments This work was supported in part by GETA (Finnish Academy Graduate School on Electronics, Telecommunications and Automation), Finland.     

Steering rules for AGV based on primitive function and elementary movement control

The complete structure of an AGV control system is described in the first part of this paper. The AGV control system is hierarchical and consists of five levels. The structure of one level does not depend on the structures of the other levels. This means that the control system depends on the design of the AGV at the lowest level only, at the actuator servo-control level and its coordination in realizing AGV primitive functions.The second part of the paper describes rules applicable to AGV steering. The structure of these rules depends on two groups of factors. The first group is dependent on information groups fed to the AGV processor by the position sensor. The second group of factors represents aims and conditions and AGV steering such as positioning accuracy, positioning time, allowed room for maneuver, the shape of the given trajectory, etc. The AGV steering rules contain sequences of primitive functions. These primitive functions are of such types as “turn left”, “straighten” (correct), “go straight on”, etc. Trajectory, as one of the basic factors, is defined at the level of controlling an elementary movement. The term “to control an elementary movement” means to select a transport road throughout the transport network and to code it using “elementary movement” such as “go straight” (relating to road section), “turn left” (relating to turning at a crossroad) etc.The results of the AGV steering simulation are presented in the third part of the paper. An exact kinematic AGV model used for stimulating control models is also presented.     

Sensor management for tracking smart targets

We consider the problem of tracking a “smart” target. That is, a target that is aware it is being tracked and modifies its behaviour accordingly. To track such targets effectively it is necessary to modify the behaviour of the tracking sensor in response to the target. We consider that the best framework for such a problem is that of a mathematical game. In this paper, we consider an idealised version of this problem that illustrates some of the issues that can occur when attempting to track a smart target and the utility of a game theoretic framework.