Multi - objective sliding mode control of active magnetic bearing system

Active Magnetic Bearing (AMB) system is known to inherit many nonlinearity effects due to its rotor dynamic motion and the electromagnetic actuators which make the system highly nonlinear, coupled and open-loop unstable. The major nonlinearities that are associated with AMB system are gyroscopic effect, rotor mass imbalance and nonlinear electromagnetics in which the gyroscopics and imbalance are dependent to the rotational speed of the rotor. In order to provide satisfactory system performance for a wide range of system condition, active control is thus essential. The main concern of the thesis is the modeling of the nonlinear AMB system and synthesizing a robust control method based on Sliding Mode Control (SMC) technique such that the system can achieve robust performance under various system nonlinearities. The model of the AMB system is developed based on the integration of the rotor and electromagnetic dynamics which forms nonlinear time varying state equations that represent a reasonably close description of the actual system. Based on the known bound of the system parameters and state variables, the model is restructured to become a class of uncertain system by using a deterministic approach. In formulating the control algorithm to control the system, SMC theory is adapted which involves the formulation of the sliding surface and the control law such that the state trajectories are driven to the stable sliding manifold. The surface design involves the transformation of the system into a special canonical representation such that the sliding motion can be characterized by a convex representation of the desired system performances. Optimal Linear Quadratic (LQ) characteristics and regional pole-clustering of the closed-loop poles are designed to be the objectives to be fulfilled in the surface design where the formulation is represented as a set of Linear Matrix Inequality optimization problem. For the control law design, a new continuous SMC controller is proposed in which asymptotic convergence of the system’s state trajectories in finite time is guaranteed. This is achieved by adapting the equivalent control approach with the exponential decaying boundary layer technique. The newly designed sliding surface and control law form the complete Multi-objective SMC (MO-SMC) and the proposed algorithm is applied into the nonlinear AMB in which the results show that robust system performance is achieved for various system conditions. The findings also demonstrate that the MO-SMC gives better system response than the reported ideal SMC (I-SMC) and continuous SMC (C-SMC)

Capital Inflows, Inflation and Exchange Rate Volatility : An Investigation for Linear and Nonlinear Causal Linkages

Since the early 1990s, there is an upsurge in foreign capital flows to developing economies, particularly into emerging markets. One view argues that capital inflows do help to increase efficiency, a better allocation of capital and to fill up the investment-saving gap. Adherents to that view advise countries to launch capital account liberalisation. In this study, we investigate the effects of capital inflows on domestic price level, monetary expansion and exchange rate volatility. To proceed with this, linear and nonlinear cointegration and Granger causality tests are applied in a bi-variate as well as in multivariate framework. The key message of the analysis is that there is a significant inflationary impact of capital inflows, in particular during the last 7 years. The finding suggest that there is a need to manage the capital inflows in such a way that they should neither create an inflationary pressure in the economy nor fuel the exchange rate volatility.Capital Inflows, Inflationary Pressures, exchange rate volatility, Monetary Expansion, Nonlinear Dynamics

Economic Liberalization and the Causal Relations among Money, Income, and Prices: The Case of Pakistan

This study re-examines the causal relations between money and the two variables, i.e., income and prices. Using annual data from 1959/60 to 2003/04, examining the stochastic properties of the variables used in the analysis, and taking care of the shifts in the series due to the start of the economic liberalization program in the early 1990s, we investigate the causal relations between real money and real income, between nominal money and nominal income, and between nominal money and prices. The analysis indicates, in general, the long run relationship among money, income, and prices. The analysis further suggests a one way causation from income to money in the long run implying that probably real factors rather than money supply has played a major role in increasing Pakistan’s national income. The study fails to find the active role of money in changing income even after taking care of possible shifts in these variables due to the economic reforms. As Regards the causal relationship between money and prices, the analysis suggests a unidirectional causality from money to prices implying monetary expansion increases inflation in Pakistan.Money; Income; Prices; Economic Liberalization; Causal Relations; Pakistan

Economic Liberalization and the Causal Relations among Money, Income, and Prices: The Case of Pakistan

This study re-examines the causal relations between money and the two variables, i.e., income and prices. Using annual data from 1959/60 to 2003/04, examining the stochastic properties of the variables used in the analysis, and taking care of the shifts in the series due to the start of the economic liberalization program in the early 1990s, we investigate the causal relations between real money and real income, between nominal money and nominal income, and between nominal money and prices. The analysis indicates, in general, the long run relationship among money, income, and prices. The analysis further suggests a one way causation from income to money in the long run implying that probably real factors rather than money supply has played a major role in increasing Pakistan’s national income. The study fails to find the active role of money in changing income even after taking care of possible shifts in these variables due to the economic reforms. As Regards the causal relationship between money and prices, the analysis suggests a unidirectional causality from money to prices implying monetary expansion increases inflation in Pakistan.Money; Income; Prices; Economic Liberalization; Causal Relations; Pakistan

Capital Inflows, Inflation and Exchange Rate Volatility: An Investigation for Linear and Nonlinear Causal Linkages

Since the early 1990s, there is an upsurge in foreign capital flows to developing economies, particularly into emerging markets. One view argues that capital inflows do help to increase efficiency, a better allocation of capital and to fill up the investment-saving gap. Adherents to that view advise countries to launch capital account liberalisation. In this study, we investigate the effects of capital inflows on domestic price level, monetary expansion and exchange rate volatility. To proceed with this, linear and nonlinear cointegration and Granger causality tests are applied in a bi-variate as well as in multivariate framework. The key message of the analysis is that there is a significant inflationary impact of capital inflows, in particular during the last 7 years. The finding suggest that there is a need to manage the capital inflows in such a way that they should neither create an inflationary pressure in the economy nor fuel the exchange rate volatility.Capital Inflows, Inflationary Pressures, Exchange Rate Volatility, Monetary Expansion, Nonlinear Dynamics

Sliding mode control with linear quadratic hyperplane design : an application to an active magnetic bearing system

This paper deals with modeling and control of a nonlinear horizontal active magnetic bearing (AMB) system via current control scheme. The gyroscopic effect and mass imbalance inherited in the system are proportional to the rotor speed in which these nonlinearities cause high system instability as the rotational speed increases. In order to synthesize a robust controller that can stabilize the system under a wide range of rotational speed, the dynamic AMB model is transformed into a deterministic model to form a class of uncertain system. Then, based on Sliding Mode Control (SMC) theory and Lyapunov method, a new robust controller that stabilizes the system is proposed wherein the Linear Quadratic Regulator (LQR) is used to design the sliding surface. Under this control, the reaching condition is guaranteed and the closed loop system is stable. The performance of the controller applied to the AMB model is demonstrated through simulation works under various rotational speeds and system conditions

Price Hikes, Economic Reforms and Causality in Money, Income and Prices: Evidence from Pakistan

This study extends the analysis of causality by Husain and Rashid (2008) by examining the shift in the variables due to the price hikes in Pakistan in the early 1970s. We investigate the causal relations between real money and real income, between nominal money and nominal income, and between nominal money and prices using the annual data set from 1959-60 to 2003-04. Moreover, we examine the stochastic properties of the variables used in the analysis, and take care of the shifts in the series due to price hikes and liberalisation measures through dummy variables. The results indicate significant shifts in the variables during the sample period. In this context, the shift that occurred due to price hikes in the early 1970s seems to be more important to be incorporated in the analysis. The study finds the active role of money as the leading variable in changing prices without any feedback. In the earlier studies on income the feedback mechanism of money is found missing perhaps because of overlooking the shift in the macro economic variables in the early 1970s. JEL classification: E3, E4, N3 Keywords: Money, Income, Prices, Price Hikes, Causal Relations, Pakista

On the modeling of exchange rate: some evidence from Pakistan

This paper tests the interconnected form of PPP and UIP while allowing the random component of exchange rate in the specification. We find a significant long-run association among exchange rates, price and interest rate differentials. Besides the PPP and UIP conditions, the previous period exchange rate plays an important role in explaining exchange rate variability. The coefficient of error correction term reveals substantial convergence towards long-run equilibrium. These findings are interesting because they explicate the dilemma of PPP and UIP and illustrate the significance of the joint modelling of these parity conditions in explaining the convergence towards equilibrium exchange rates